A method for regulating dynamic overvoltage during blocking of multiple DC sending terminals

Abstract

The present invention discloses a method for regulating dynamic overvoltage during multi-DC sending-end locking. The method comprises the following steps: firstly, aiming at the problem of dynamic rising overvoltage during locking of multi-DC sending-end system, a key slow system model for calculating rising overvoltage is established in combination with singular perturbation theory; then, in order to quickly obtain the magnitude of system overvoltage, an analytical calculation method for overvoltage peak value without simulation integration is proposed based on the established slow system model. Finally, the smooth suppression of rising overvoltage can be achieved by adjusting relevant dynamic parameters based on monotonic order-preserving property. The present invention establishes an AC / DC slow system model of overvoltage during locking to accurately describe the rising process of locking overvoltage, and proposes a method for effectively suppressing dynamic rising overvoltage by using monotonic system theory. In addition, the dynamic maximum value of overvoltage is calculated by linearizing the slow system proposed in combination with the DC equivalent static load, which greatly improves the calculation efficiency and is expected to be used for online safety and stability analysis.

Description

Technical Field

[0001] The invention belongs to the technical field of power grid dynamic characteristic analysis, and in particular relates to a method for regulating dynamic overvoltage when multiple DC sending ends are locked. Background Art

[0002] With its advantages in large-capacity and long-distance transmission, high-voltage direct current transmission has now become an important means for my country to solve the problem of "reverse distribution of sources and loads" and cross-regional power transmission. The DC converter consumes a lot of reactive power to transmit power, accounting for about 40% to 60% of the normal active power transmitted by DC, so a large number of reactive compensation equipment is usually required in the converter station. When the DC is blocked due to a serious fault in itself or the AC system, the reactive power consumed by the blocked DC is reduced, and its reactive compensation equipment still generates a large amount of reactive power. The pole control system will cut it off after about 200ms. A large amount of surplus reactive power injected into the system will cause overvoltage in the DC converter station and its adjacent converter stations. The regional power grid adopts DC interconnection, and the number of DC transmissions at the sending end of the power grid is gradually increasing. The problem of blocking overvoltage between multiple sending end converter stations needs urgent attention.

[0003] In view of the problem of lockout overvoltage, existing literature mainly combines the relationship between power and voltage from a macroscopic perspective to derive the overvoltage formula for quantitative and qualitative analysis. The derivation of the lockout overvoltage is mainly based on the equivalent constant voltage source of the AC power grid, and the voltage dynamics of the AC power grid after the lockout are ignored. Therefore, the results derived based on the equivalent AC power grid are often more suitable for lockout instantaneous overvoltage or steady-state overvoltage. System short-circuit ratio indicators such as effective short-circuit ratio and multi-feed short-circuit ratio quantify the strength of the AC system and can be used to characterize the power grid's ability to resist DC fault disturbances. However, the short-circuit ratio indicator only reflects the anti-disturbance strength of the power grid voltage, and cannot effectively and quantitatively calculate the overvoltage level. At the same time, the indicators do not involve the dynamic process of overvoltage. In addition, under specific network structures and working conditions, the overvoltage will continue to rise after the DC lockout until the capacitor is removed. Therefore, in this case, the maximum overvoltage is higher than the voltage rise value at the lockout instant. For this type of dynamic overvoltage, the overvoltage formula derived based on the static power flow equation does not take into account the dynamic changes of the system, and cannot analyze the influence of the system dynamic parameters on the overvoltage, and the results are limited.

[0004] To analyze the dynamic process of the system during the lockout period, it is essential to understand the roles played by the DC and AC power grids during the lockout fault. The sending-end power grid composed of synchronous machines and DC control systems is a complex and high-order nonlinear differential algebraic (DAE) system. When analyzing, the AC and DC power grid models are high-order and the DC interface equations are complex, which increases the difficulty of problem analysis. Therefore, based on the difference in response speed between AC and DC systems, a new perspective on the calculation of AC and DC problems is given using singular perturbation theory. Summary of the invention

[0005] In view of this, the present invention provides a method for regulating dynamic overvoltage during multi-DC sending-end lockout, by establishing a multi-DC equivalent sending-end system model, using singular perturbation theory, the system is divided into fast and slow subsystems, which shows that the AC / DC slow system model of overvoltage during lockout can accurately describe the lockout overvoltage rising process; the slow system linearization analytical calculation of the dynamic maximum value of the overvoltage proposed in combination with the DC equivalent static load greatly improves the calculation efficiency and is expected to be used for online safety and stability analysis; in addition, a method for effectively suppressing the dynamic rising overvoltage is obtained based on the monotonic system theory.

[0006] In order to achieve the above object, the present invention adopts the following technical solution:

[0007] A method for regulating dynamic overvoltage when multiple DC sending terminals are locked comprises the following steps:

[0008] S1: Construct DC transmission system model, AC system model and AC / DC system network equation model;

[0009] S2: Combined with the dynamic dual-time-scale characteristics of overvoltage, the singular perturbation reduction-order decoupling of AC and DC systems is performed to establish an AC and DC singular perturbation model;

[0010] S3: Under the slow time scale, the voltage subsystem model that dominates the voltage rise and the equivalent static load model are established;

[0011] S4: Calculate the dynamic maximum value of the lock-up rising overvoltage according to the slow system linearization analytical method;

[0012] S5: Adjust the overvoltage that exceeds the set threshold in step S4, and judge whether the voltage subsystem satisfies the monotonic system theory through the system power angle and phase angle difference matrix. If it does, the voltage has a monotonic sequence-preserving characteristic with respect to the dynamic parameters of the synchronous machine, such as the proportional coefficient of the synchronous machine excitation system or the d-axis open-circuit time constant, so as to smoothly and monotonically suppress the overvoltage level by adjusting the dynamic parameters of the synchronous machine.

[0013] The step S1 is specifically as follows:

[0014] 1.1) Construct the DC quasi-steady-state model, DC line model and DC control system model of the traditional LCC DC transmission system: The traditional LCC DC transmission system mainly consists of two parts: one is the DC quasi-steady-state model and DC line model of the converter station under three-phase balanced conditions, and the other is the DC control system that maintains normal DC operation.

[0015] The normalized DC quasi-steady-state model is constructed, and the specific equation is as follows:

[0016]

[0017] In the formula, the subscripts "R" and "I" represent the rectifier side and the inverter side respectively, the subscript "dc" represents the direct current, and "DC" represents the alternating current; V dc 、V DC are DC voltage and AC voltage respectively, V dcR 、V DCR are the DC voltage on the rectifier side and the AC voltage on the rectifier side respectively; I dc is the DC current; X c is the equivalent reactance of the converter transformer; k is the transformation ratio of the converter transformer; α, β, They are trigger angle, leading trigger angle, rectifier side power factor angle, inverter side power factor angle; P dc and Q dc They are DC active power and DC reactive power respectively;

[0018] For DC lines, the RL model is used:

[0019]

[0020] In the formula, R d and L d are the line resistance and inductance respectively;

[0021] Assume that during the blocking period, the DC inverter voltage V DCI Constant, the leading trigger angle β is constant, the DC is constant power control, and the DC control system model is established as follows:

[0022]

[0023] Where, the subscript “mes” represents the measured quantity, x1 represents the PI control state quantity; T vp 、T Idcmes 、T IdR are the DC voltage measurement time constant, DC current measurement time constant and constant current PI control integral constant in constant power control respectively; P ref is the DC active power reference value; V dcRmes is the measured value of the DC voltage on the rectifier side, I dcmes is the DC current measurement value;

[0024] (2) Constructing AC system model

[0025] Synchronous machines are the main component of traditional AC power grids and provide voltage support for the entire power grid.

[0026] The AC system model is mainly composed of synchronous machines. The salient pole effect of synchronous machines is ignored. The synchronous machine adopts a third-order transient model including a first-order excitation system. The specific mathematical model is as follows:

[0027]

[0028] Among them, δ, ω s and ω are the synchronous machine power angle vector, nominal speed and actual speed vector respectively; T j , T′ do 、T A are the inertia time constant diagonal matrix, the generator d-axis open-circuit time constant diagonal matrix and the regulator time constant diagonal matrix respectively; E′ q is the diagonal matrix of the internal potential of the generator; i d and i q are the generator d-axis and q-axis current vectors respectively; D ω is the load-damping constant diagonal matrix; X d and X′ d are the d-axis reactance matrix and the d-axis transient reactance diagonal matrix respectively; E f is the excitation voltage vector; K A They represent the diagonal matrix of the proportional coefficient of the first-order excitation system, U ref 、V G are the voltage regulation internal reference value diagonal matrix and the generator terminal voltage respectively; the operator Represents the Hadamard product, which is the product of corresponding elements of vectors or matrices;

[0029] (3) Establishing AC / DC system network equation model

[0030] The load adopts a constant impedance model, forming the following AC / DC system network equation:

[0031]

[0032] Among them, the admittance matrix Y is composed of Y GG , Y GD , Y DG , Y DD It consists of four block sub-matrices, where subscript G corresponds to the generator nodes and subscript D corresponds to the DC nodes; They represent the complex form of synchronous machine terminal voltage and synchronous machine injection current vector respectively; denote the DC rectifier station voltage and the DC rectifier station injected current vector in complex form respectively;

[0033] The interface equations of the synchronous machine adopt the classic model: And expand the DC rectifier station injection current vector, the AC / DC system network equation is specifically transformed into:

[0034]

[0035] In the formula, Y′ GG Combined with synchronous machine transient reactance, Y′ GG =Y GG -jX′ d, j refers to the imaginary part; the DC rectifier station injects current vector Expressed as is the power injected by the rectifier station, The overline "-" indicates the conjugation of the complex vector, and the ". / " operation indicates the division of the corresponding elements of the vector; jδ It means taking the exponential value of each element of the vector δ, that is Later Same reason.

[0036] The step S2 is specifically as follows:

[0037] The DC transmission system and AC system are decomposed into fast system and slow system by using singular perturbation theory. The fast and slow state quantities are divided according to the time constant, and the following AC and DC singular perturbation model is established:

[0038]

[0039] In the formula, f slow , f fast The slow and fast state quantities are the differential equations respectively.

[0040] In the formula, T′ fast =T fast / ε, the small parameter ε is taken as ε=L d ; Fast system time constant T fast Including the excitation regulator time constant T A , DC current measurement time constant T Idcmes , constant current PI control integral constant T IdR And the line inductance L d ; Slow system time constant T slow Including the inertia time constant T j , Generator d-axis transient time constant T′ d0 and DC voltage measurement time constant T vp .

[0041] The step S3 is specifically as follows:

[0042] Since the overvoltage occurs in the slow system, a voltage subsystem model that dominates the voltage rise in the slow system and an equivalent static load model are established: the system is decomposed into a fast system and a slow system using singular perturbation theory, and the fast system will reach equilibrium in a short time after DC blocking. From then on until the capacitor is removed, the system dynamics is mainly determined by the slow system.

[0043] The algebraic relations in the degenerate system obtained by singular perturbation theory are: dc，s =I dcmes，s =P ref / V dcRmes，s, V dcR，s -V dcI，s -R d I dc，s =0, the subscript "s" represents the slow system part of the state quantity; combined with the DC quasi-steady-state equation, the DC state quantity in the slow system satisfies the following equation:

[0044]

[0045] In the above equation, the equilibrium point before and after the fault remains unchanged, so V dcRmes，s is constant, then I dc，s It is also constant in the slow system. Finally, the equivalent load power model of the DC rectifier station in the slow system during the blocking period is obtained as follows:

[0046]

[0047] In the formula, the subscript "0" represents the initial value of the system, and t represents time;

[0048] Under the slow time scale, the voltage subsystem with the dominant voltage rise based on the AC system model is:

[0049]

[0050] Where V Gq Represents the q-axis component of the synchronous machine terminal voltage.

[0051] The step S4 is specifically as follows:

[0052] 4.1) Linearize the unbalanced point of the voltage subsystem in step S3:

[0053]

[0054] In the formula, The Jacobian matrix when the DC transmission system model adopts the equivalent load power model, represents the non-equilibrium term; The matrix is ​​a Metzner matrix, which is approximately symmetric, has distinct non-zero real eigenvalues, and can be converted to a diagonal matrix by non-singular transformation; let E′ q =Tz, substituting into formula (11) we can get:

[0055]

[0056] Where: z refers to E′ q The quantity transformed by the matrix T; T = [v1, ..., v i ..., v n ],v1∈R n , where R n is an n-dimensional real vector, v i yes Right eigenvector; λ i is a matrix Eigenvalue;

[0057] Solving equation (12) gives the time domain solution:

[0058]

[0059] By transforming E′ q =Tz has:

[0060]

[0061] 3.2) Assume that during the locking period the angular acceleration a δ Constant, that is Solve at t cl When the reactive power compensation is removed, the power angle of the i-th generator is:

[0062]

[0063] Among them, ω s is the rated speed, t cl is the capacitor removal time, δ i0 is the initial value of the power angle of the i-th synchronous machine;

[0064] Substituting the internal potential obtained by equation (14) and the power angle obtained by equation (15) into the AC / DC system network equation of equation (6) in step 1), the dynamic maximum value of the overvoltage when the reactive compensation is removed can be solved.

[0065] The step S5 is specifically as follows:

[0066] When the matrix cos(Δθ δ ) is a non-negative matrix, the monotone system theory can be used to monotonically control the voltage. When the matrix is ​​not a non-negative matrix, other related control methods must be found. The premise of monotone control is that the system is a monotone system, that is, the non-diagonal elements of the Jacobian matrix of the system must be non-negative. Through the matrix cos(Δθ δ ), then we can infer whether the voltage subsystem after locking satisfies the monotonic system.

[0067] 5.1) According to the relationship between the phasor and amplitude of the complex number, the Jacobian matrix of the voltage subsystem that dominates the voltage rise in step S3 is obtained as follows:

[0068]

[0069] In the formula, the voltage at the terminal of the synchronous machine is about E′ q Sensitivity have:

[0070]

[0071] In the formula, Since the reactance of the transmission line in the actual network is often much larger than the resistance, the imaginary part of the impedance matrix is ​​usually much larger than the real part. Therefore, the line resistance can be ignored, and the admittance matrix taking into account the transient reactance of the synchronous machine in step 1) (6) is approximated as a pure imaginary matrix, that is, Y≈jB, where the matrix B is the imaginary part of Y. Combined with the definition of the M matrix, -B is a non-singular M matrix, and its inverse -B -1 is a non-negative matrix, then the impedance matrix Z = Y -1 = jX imaginary reactance X = -B -1 is a non-negative matrix, so we can get X aug is a non-negative matrix;

[0072] In the formula, K = [I ng×ng 0] is the selection matrix, I ng×ng Yes g The identity matrix of order n g is the number of generators, Ignore K CG The term is calculated by calculating the matrix cos(Δθ δ ) The positive and negative nature of the matrix Δθ δ Indicates the difference between the terminal voltage phase and the power angle of each generator: Δθ δ =diag(θ G )1 ng×ng -1 ng×ng diag(δ), 1 ng×ng Indicates n g The matrix of order matrix elements are all 1, θ G Indicates the voltage phase at the machine end;

[0073] When the locked matrix cos(Δθ δ ) is a non-negative matrix, then is a non-negative matrix; since the generator parameter X′ d <<X d , the coefficient matrix satisfies: X d / X′ d ≥K A / cos(δ-θ G )+1, based on The non-negativity of obtains the non-diagonal elements of the Jacobian matrix J(x) in equation (16) which are non-negative and is a Metzner matrix. Then the voltage subsystem is a monotonic system and can be monotonically controlled in step 5.2);

[0074] When the matrix cos(Δθ δ ) is not a non-negative matrix, other control measures are required to suppress overvoltage;

[0075] 5.2) Consider the input and output system:

[0076]

[0077] Among them, x∈X, u∈U, y∈Y, X, u, y are the state set, control set, and output set respectively; f is first-order differentiable.

[0078] Let the generator excitation parameters and open-loop time constant be the control quantity u=-[K A , T′ d0 ]; According to the relationship during the lockout period a) the slow system voltage continues to rise - (V G0 -V G )≥0 and relation b) reactive current i d The potential inside the generator continues to increase due to the reduction Get the symbolic characteristics of the input control variable u:

[0079]

[0080] About the output quantity converter station bus voltage y=V DC , from circuit theory we know that E′ q Increase the converter station voltage V DC will also rise, then non-negative;

[0081] Therefore, during the lockout period, according to formula (19) and It is non-negative, and the converter station voltage is a monotonic input-output system with respect to the control quantity u, that is, the converter station bus voltage has a monotonic sequence-preserving characteristic with respect to the input control quantity, the proportional coefficient of the synchronous machine excitation system and the d-axis open-circuit time constant. Therefore, when the dynamic overvoltage problem of multiple DC locking occurs, the dynamic rising overvoltage can be effectively suppressed by increasing the proportional coefficient of the synchronous machine excitation system or increasing the d-axis open-circuit time constant.

[0082] Beneficial effects of the present invention:

[0083] The present invention points out that the power grid has dual time scale characteristics when DC overvoltage is locked, and decomposes the AC / DC system into a fast system and a slow system by combining the singular perturbation theory, and explains that the AC / DC slow system model of overvoltage during the lockout period can accurately describe the lockout overvoltage rising process, thereby simplifying the calculation of dynamic overvoltage problems and improving calculation efficiency. The monotonic system theory is used to explain that during the lockout period, the converter station voltage has a monotonic sequence-preserving characteristic with respect to the input control quantity synchronous machine excitation system proportional coefficient and d-axis open circuit time constant, thereby proposing a method that can effectively suppress the dynamic rising overvoltage by increasing the synchronous machine excitation system proportional coefficient and d-axis open circuit time constant in the event of a fault. BRIEF DESCRIPTION OF THE DRAWINGS

[0084] Figure 1 A schematic diagram of a flow chart of an analysis and method for analyzing dynamic overvoltage when multiple DC sending ends are locked provided by the present invention;

[0085] Figure 2 An equivalent system diagram of multiple DC sending ends provided by the present invention;

[0086] Figure 3 The overvoltage and reactive power consumption diagram of the converter station provided by the present invention;

[0087] Figure 4 A graph of the potential, reactive current and reactive power changes in the generator provided by the present invention;

[0088] Figure 5 A comparison result diagram of the influence of the dynamic state of the AC side on overvoltage provided by the present invention;

[0089] Figure 6 A voltage comparison diagram of the original system and the slow system provided by the present invention;

[0090] Figure 7 Different K provided by the present invention A and T′ d0 The overvoltage dynamic response diagram under different K A Impact on system overvoltage; Figure (b) shows different T' d0 Impact on system overvoltage;

[0091] Figure 8 A comparison diagram of the dynamic voltage of converter station nodes of the slow system provided by the present invention and the original system; Figure (a) is a comparison of the dynamic voltage of nodes when the electrical distance between converter stations is far; Figure (b) is a comparison of the dynamic voltage of nodes when the electrical distance between converter stations is close;

[0092] Fig. 9 A comparison diagram of active power transmission and reactive power consumption of the converter station of the slow-load system provided by the present invention and the original system; DETAILED DESCRIPTION

[0093] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0094] The embodiment of the present invention discloses a method for regulating dynamic overvoltage when multiple DC sending ends are locked. Figure 1 As shown, the following steps are included:

[0095] S1. The dynamic characteristics and mechanism of overvoltage in three stages when multiple DC sending-end power grids are locked are analyzed, indicating that the overvoltage response process has dual time scale characteristics; a full-order AC / DC system model that dominates the system overvoltage rise dynamics is established, and the singular perturbation theory is introduced to divide the system into fast and slow subsystems as follows:

[0096]

[0097]

[0098] The former is the fast state quantity of the system, and the latter is the slow state quantity. The system is divided into fast and slow subsystems by using the boundary layer method (0th order singular perturbation) for decoupling and solution.

[0099] According to the singular perturbation theory, the AC / DC system model is written in the form of singular perturbation:

[0100]

[0101] Based on the singular perturbation theory, the fast-slow interactive dynamic process of AC and DC and the response mechanism of dynamic voltage during the blocking period are analyzed, and it is explained that the slow system voltage can accurately describe the rising process of overvoltage in the middle and later stages. For this purpose, a key voltage subsystem model for analyzing and calculating the blocking rising overvoltage is established:

[0102]

[0103] Then the equivalent static load model of the DC sending end in the slow system is:

[0104] P dcR，s (t) = V dcR，s (t)I dc，s (t) = V dcR0 I dc0 =P dcR0

[0105]

[0106] S2. Rapidly and accurately calculate the dynamic maximum value of overvoltage based on the slow system linearization analytical method to provide an estimate of the overvoltage level.

[0107] S3. Regarding the suppression of overvoltage, it is proved that the voltage subsystem that dominates the rising overvoltage after locking is a monotonic system, and the voltage is monotonically sequence-preserving with respect to the dynamic parameters of the synchronous machine. Based on this, a strategy for parameter adjustment to smoothly suppress overvoltage is proposed.

[0108] In order to further implement the above technical solution, it is necessary to explain that:

[0109] (1) Singular perturbation theory

[0110] For singular perturbation theory, consider the following two-time-scale system:

[0111]

[0112]

[0113] Where ε is a small parameter 0<ε<<1, x∈R n , z∈R m , the functions f and g on the right side have the same order and size relationship.

[0114] For this system, the variable z changes much faster than x. We call the former the fast state variable of the system and the latter the slow state variable. The boundary layer method (0th order singular perturbation) divides the system into fast and slow subsystems for decoupling and solving.

[0115] Let ε→0, the system degenerates into a slow system:

[0116]

[0117] In the formula, the subscript "s" represents the slow time scale component of the state quantity. The initial value of the slow system is xs0 = x0, where x0 is the initial value of the original system. By assuming that the response dynamics of the fast state quantity is instantaneous, the fast state quantity has responded quickly under the slow time scale to reach the equilibrium manifold of the fast system 0 = g(x s , z s ), also known as the integral manifold. From the integral manifold, we can solve the relation z s =h(x s ).

[0118] On the other hand, by transforming the time scale τ=(t-t0) / ε and setting ε→0, we can obtain the boundary layer equation of the fast system, also known as the original system:

[0119]

[0120] The initial value z f0 =z0-z s0 , z s0 =h(x s0 ).

[0121] After the above transformation, the original system is reduced to an n-order slow system and an m-order fast system. When for any xs, the integral manifold equation z s =h(x s ) is the stable, isolated equilibrium point of the fast part of the system. According to Tikhonov’s theorem, there exists a constant T>0. Within a certain time period [t0, t0+T], the original system solution can be approximated by the 0th-order singular perturbation solution:

[0122] x(t)=x s(t)+o(ε)

[0123]

[0124] where z f =0 is the stable equilibrium point of the fast system. The fast system will quickly decay to 0, after which the system dynamics will be mainly dominated by the slow system.

[0125] (2) Monotonic system theory

[0126] Consider the system The solution satisfies the order preservation property: If and only if the system is a monotone (cooperative) system, that is, the non-diagonal elements of the system Jacobian matrix are non-negative:

[0127]

[0128] Where x∈R n , f is first-order differentiable. x1≥x2 means that the components of the state vector satisfy φ(t, x) represents the solution of the system with respect to the initial value x.

[0129] (3) Monotonic control of monotonic input-output system

[0130] Consider the input and output system:

[0131]

[0132] y=h(x)

[0133] in here are the state set, control set, and output set respectively. f is first-order differentiable.

[0134] The input and output of the above system are monotonic, that is:

[0135]

[0136] And only if:

[0137]

[0138] If this holds true, then it is a monotonic control system and satisfies the order-preserving property.

[0139] In this embodiment, firstly, an equivalent sending-end system model of a multi-DC sending-end power grid is established to analyze its blocking overvoltage characteristics:

[0140] The normal operation of DC requires a large amount of reactive power. Usually, reactive power compensation devices such as reactive power compensation capacitors are configured in DC converter stations to support reactive power consumption. When DC is blocked, the DC line no longer transmits active power and no longer consumes reactive power. At this time, the reactive power compensation equipment configured in the sending-end converter station will continue to generate reactive power, causing blocking overvoltage at the sending end. When the sending-end power grid contains only a single DC line and a blocking fault occurs in the DC line, it is equivalent to the disconnection of the DC transmission line, and the sending end is declassified as a pure AC power grid without DC. At this time, the analysis of the system voltage is converted to the analysis of the traditional AC power grid. For a multi-DC sending-end power grid, if one of the DC lines is blocked due to a fault, the remaining DC lines will continue to operate. The excess reactive power generated by the blocked DC converter station is injected into the sending-end power grid, which will have an impact on the AC network and the adjacent DC. The resulting overvoltage dynamics are jointly determined by the unblocked DC and the AC power grid.

[0141] For multi-DC sending-end power grid, this paper first establishes an equivalent sending-end system model as follows Figure 2 The equivalent sending end system is mainly composed of the normally operating DC and the blocked DC and adjacent generators.

[0142] The grid voltage is mainly affected by reactive power fluctuations. Here we first consider the excess reactive power Q after blocking. C2 The second DC block is set at 0.1s. After 200ms, the pole control system removes the reactive power compensation of the blocking converter station. The converter bus voltage and the reactive power consumption of the converter station are shown in Figure 2. Figure 3 .

[0143] The voltage in the converter station changes dynamically at two speeds, fast and slow. The overvoltage has two peaks, which can be divided into three stages:

[0144] In stage 1, at the moment of blocking, the converter station stops consuming reactive power, and a large amount of reactive power generated by the capacitor is injected into the bus, causing a sudden increase in voltage, and the bus voltage experiences the first step-type overvoltage peak.

[0145] In stage 2, as the sending end voltage rises instantly, the DC current will increase rapidly, and the DC transmission power will increase. Combined with the reactive power consumption formula of the converter station:

[0146]

[0147] As the DC current increases rapidly, the reactive power consumption of the converter station at the sending end will decrease, and the reactive power surplus will decrease, resulting in a rapid drop in the voltage at the sending end. At the same time, in order to maintain the constant DC transmission power, the DC constant power control module will increase the trigger angle to reduce the DC voltage on the rectifier side, thereby reducing the DC current. As the DC current decreases, the DC power returns to normal, and the reactive power consumption of the rectifier station gradually decreases, causing the bus voltage to gradually increase. This process occurs relatively quickly within 30ms.

[0148] In stage 3, after the bus voltage experiences a short “sudden increase followed by a drop in speed” (stage 1+2), the voltage will continue to increase at a slower rate until the excess capacitors are removed, at which point the overvoltage reaches the second peak. It is worth noting that, unlike stages 1 and 2, the reactive power consumption of the rectifier station during the rising process also increases with the increase in voltage. The simultaneous increase in voltage and reactive power consumption indicates that the factor that determines the voltage of the converter station at this time is no longer the reactive power exchange between the converter station and the power grid, but is dominated by another factor that jointly determines the voltage, the AC power grid. Figure 4 The role of the generator in the voltage rise process in stage 3 is revealed. After DC blocking, excess reactive power is injected into the system to balance the system reactive power. The reactive power Q generated by the synchronous machine G decrease, corresponding to the reactive current i d According to the AC system model formula, the reduction of reactive current will raise the internal potential E′ q , which causes the voltage to continue to rise after blocking. The overvoltage will not be restored until the pole control device cuts off the reactive power compensation of the blocking converter station, at which time the overvoltage will reach the second peak.

[0149] The first peak value generated at the instant of DC blocking in stage 1 is an instantaneous change caused by reactive power impact. At this time, the system state quantity does not change. The peak value has nothing to do with the system dynamic model and is determined by the system operating conditions and network structure before and after blocking. A large number of literatures have proposed such overvoltage expressions based on the equivalent network of converter stations, among which the common formulas are:

[0150]

[0151] Where: ΔU is the transient voltage rise of the converter station bus; ΔQ is the change in reactive power exchange between the converter station and the AC system; S d is the bus short-circuit capacity of the converter station, which can be approximately expressed as U n is the rated voltage of the commutation bus, Z eq is the equivalent impedance of the AC system, which is equal to the impedance matrix Z=Y corresponding to the commutation bus node i -1 The diagonal element Z in ii . Equivalent impedance has nothing to do with system flow and is a representation of the grid structure. Combined with the analysis of the effective short-circuit ratio, it can be seen that for the first peak of overvoltage, adding generators or phase regulators will effectively reduce the equivalent impedance, that is, increase the effective short-circuit ratio, and strengthening the electrical connection of the network will also increase the effective short-circuit ratio. The larger the effective short-circuit ratio, the stronger the converter station busbar's resistance to reactive impact energy, thereby reducing the first peak at the moment of locking.

[0152] Since the converter station is under constant power control, the reactive power consumed will gradually return to normal levels, and the internal potential of the AC side generator will continue to increase due to the continuous surplus of reactive power. In the actual process, the second peak value will often be higher than the first peak value of the voltage value at the moment of blocking. When analyzing overvoltage problems, it is more necessary to pay attention to the second peak value. The second peak value is generated during the continuous rise of voltage during the blocking period, and the dynamic process of the system is jointly determined by the AC and DC system components.

[0153] The DC transmission system is composed of power electronic equipment, whose control and response speed is in microseconds, while the synchronous machine transient response process is slow, and its corresponding change is in seconds. The difference in the response speed between the two is the inherent dual time scale characteristic of the AC and DC system. By introducing the singular perturbation theory, it helps to analyze the fast and slow interactive dynamic process between AC and DC during the blocking period, and quantitatively and qualitatively analyze the dynamic voltage maximum value.

[0154] The DC blocking overvoltage scenario of the above-mentioned multi-DC sending-end power grid is verified and analyzed through a calculation example.

[0155] (1) Equivalent power grid case at the sending end

[0156] In a multi-DC power grid, after a DC line is blocked, the node voltage dynamics are affected by both the unblocked DC and AC system dynamics. In previous literature analyzing DC blocking overvoltage, the dynamics of the AC side are often ignored, and the AC grid is analyzed from the perspective of a constant voltage source after the DC node is equivalent to an impedance. The results obtained cannot fully reflect the change process of the system voltage, affecting the judgment of the overvoltage level. Figure 2 The equivalent power grid at the sending end shown in the figure is simulated by comparing whether the dynamic state of the AC side is considered. The results are as follows Figure 5 shown.

[0157] As can be seen from the figure, the dynamics of the AC side dominated by the synchronous machine are the cause of the dynamic rise of the blocking overvoltage. After ignoring the dynamics of the AC side, the voltage no longer rises in the third stage, and the overvoltage during the blocking period is lower than the true value. Therefore, the impact of the dynamics of the AC side needs to be considered when analyzing the system blocking overvoltage level.

[0158] Therefore, considering the impact of the dynamics on the AC side and based on the singular perturbation theory, the fast system will reach equilibrium in a short time after DC blocking. From then on until the capacitor is removed, the system dynamics are mainly determined by the slow system. Figure 3 The fast response of the voltage in stages 1 and 2 corresponds to the fast system response dominated by DC. At this time, the reactive power consumed by the rectifier station determines the dynamics of the voltage. After a short time, the fast system reaches the integral manifold and the system enters stage 3 dominated by the generator. At this time, the slow rise of the voltage is no longer dominated by DC but by the potential system inside the synchronous machine.

[0159] The voltage of the slow system obtained by the above division is compared with the original system. Figure 6 As shown in the figure, in the early stage of the lockout, the slow system voltage changes slowly because the fast dynamics of DC are ignored. There are no stages 1 and 2 dominated by DC, which is quite different from the original system. After a short period of time (fast system stability), the voltages of the original system and the slow system gradually overlap, which is consistent with the theory and shows the effectiveness of the proposed decomposition method. On the other hand, the slow system voltage is close to the original system voltage in the rising stage, which also shows that the voltage dynamic rise is mainly caused by the AC system dominated by the synchronous machine.

[0160] The above theoretical analysis shows that the slow system voltage can accurately approximate the dynamic rising overvoltage in the middle and late stages, so we can use the reduced-order slow system to describe the overvoltage rising process and simplify the problem.

[0161] In the overvoltage rising stage, according to the monotonic influence of dynamic parameters analyzed in the previous article, the two coefficients of the generator are adjusted, and the corresponding bus voltage change of the converter station is as follows: Figure 7 As shown. Note that the voltage subsystem is a monotonic system, so the voltages under different control variables are strictly kept in order at any time during the blocking period, and the voltage curves in the figure do not cross.

[0162] Figure 7 (a) The voltage regulation effect of the excitation system is explained. When KA increases, the overvoltage rise is suppressed. Figure 7 (b) shows that the larger the open-loop time constant, the slower the voltage rises. In physical terms, reducing the generator excitation proportional coefficient means reducing the voltage regulation capability of the generator excitation system, which cannot effectively constrain the rise of the internal potential, thus leading to higher dynamic overvoltage. d0 The generator means that the internal potential responds faster, so the increase of the internal potential is accelerated, thereby increasing the bus voltage of the converter station.

[0163] Furthermore, it is hoped that the maximum value of the overvoltage (the second peak) can be quickly estimated. According to the analytical solution method proposed in this paper, the maximum value of the overvoltage in the equivalent example is 1.081, which is only 0.5% error compared with the actual value of 1.076.

[0164] (2) Ningxia Power Grid Example

[0165] Based on the data of the multi-sending power grid structure in Ningxia, China, Matlab / Simulink is used to simulate the actual power grid lockout fault. The Ningxia power grid contains two outbound DC lines, the ±800kV Lingshao DC line transmits 8000MW of power from Ningxia to Zhejiang power grid, and the ±660kV Yindong DC line transmits 4000MW of power from Ningxia to Shandong. The Lingshao DC sending-end converter station is taken as the analysis object, and the Lingshao DC lockout fault is set. After 200ms, the Lingshao DC reactive compensation equipment is cut off. At this time, the Yindong DC line continues to operate, and the overvoltage problem at the sending end is explored.

[0166] In actual large power grids, there are many generators and the differential order of the power grid is high. Using the slow voltage system after singular perturbation reduction for fast calculation will effectively save the calculation cost and time. The complete model and the singular perturbation slow system model are used for simulation respectively, and the calculation efficiency is compared. The required time is shown in Table 1. When simulating the locked overvoltage, since the DC is equivalent to a static load in the slow system, the generator excitation system is merged into the reactive subsystem, so the system order is reduced by 181 (excitation system) + 4 (DC sending end model) = 185, and the calculation time is reduced by 6s. Furthermore, the overvoltage peak estimation method proposed based on the slow system is adopted. Since no integration is required, the time consumption is reduced by 70 times, which greatly improves the calculation efficiency and is expected to be used for online safety and stability analysis.

[0167] Table 1

[0168]

[0169] The voltage comparison between the two converter stations of the full-order system and the slow system is shown in Figure 8 (a), the dotted line represents the slow system, and the solid line represents the original system. In the early stage of blocking, the reactive power absorbed by the unlocked Yindong DC converter station experienced a brief rise and fall with the DC current, resulting in a rapid drop and recovery of the Yindong converter bus voltage, that is, the 1st and 2nd stages of overvoltage. The voltage in this stage is significantly different from the slow system voltage, which cannot be simulated by ignoring the fast dynamics after the singular perturbation reduction. This part of the difference is reflected in the boundary layer equation. Since this paper mainly analyzes the overvoltage in the rising stage, it can be ignored.

[0170] At the same time, it can be seen from the figure that the voltage of the Yindong converter bus will continue to rise after experiencing a short DC dynamic. At this time, the slow system voltage can more accurately approximate the system overvoltage rising dynamics, because at this time the DC-dominated AC / DC system fast state process has stabilized, and the system dynamics are dominated by the slow system. Therefore, according to the Tikhonov theory, the system state quantity can be approximated by the slow state quantity and the slow part of the fast state quantity. The slow system voltage can be approximated by the rising process voltage, and the second peak value can be analyzed and approximately calculated by the slow system voltage. For the Lingshao DC bus voltage, since the two converter stations have a certain electrical distance, the rapid dynamics of the reactive exchange between the Yindong DC and the sending-end power grid during the blocking period have little effect on the Lingshao DC node, and the overvoltage stages 1 and 2 are no longer obvious. During the whole process, the slow system voltage is close to the original system voltage. When the network structure is adjusted to reduce the equivalent electrical distance between the two converter stations, the reactive exchange between the Yindong converter station and the system affects the adjacent blocked Lingshao DC node. The voltage change waveforms of the two are similar, and there are two peaks, such as Figure 8 (b) As shown in the two cases, it can be seen that regardless of whether the DC converter stations are closely connected, the voltage of the slow system after the reduction can effectively approach the original system voltage.

[0171] Under the slow time scale, the sending-end DC converter station adopts the above-mentioned equivalent static load, and its equivalent error is as follows: Fig. 9 As shown in the figure, after the dynamics of the DC overvoltage shock are adjusted by the constant power controller, that is, during the voltage rise period after 0.1s, the active and reactive power consumption of the converter station is similar to the static load model. The static load model can effectively simulate the impact of DC on the AC system after the system has experienced a short period of rapid dynamics in the early stage of the fault. Since the DC blocking fault is similar to non-short-circuit faults such as other power fluctuation faults except DC commutation failure, and the system disturbance degree is similar, the proposed static load model can be extended to other similar fault applications.

[0172] At the same time from Fig. 9 It can be seen that the increase in active and reactive power consumed by the running DC during the blocking period is limited. Therefore, when proving Proposition 1, the converter station can be conservatively taken as a constant power load with an upper limit of power fluctuation. At the same time, the increase in power consumed by the Yindong converter station is much smaller than the power consumption of the blocked Lingshao converter station during normal operation. Therefore, the load level of the system after blocking is lower than the normal operating level before blocking (the converter station is regarded as the load of the sending-end power grid). Blocking the DC does not affect -B aug The Laplace self-loop property of , that is, the property that it becomes a non-singular M matrix, can further prove the non-negativity of the voltage-internal potential of the synchronous machine. G -E′ q The elements of the sensitivity matrix are all non-negative, the internal potentials of the synchronous machines are positively related to the voltage between each other, and the synchronous machines in the sending end cooperate to adjust the voltage changes. Further, the Jacobian matrix of the system, except for the negative elements in the diagonal elements, the non-diagonal elements are all non-negative. The Jacobian matrix is ​​a Metzner matrix, which is approximately symmetrical. From the monotone system theory, it is known that the post-locking slow system is a monotone system. Combined with the monotone control properties of the monotone input-output system, it can be known that the Jacobian matrix can be converted into a diagonal matrix through a non-singular transformation. According to the fast method proposed in this paper, the overvoltage is analytically solved.

[0173] According to the proposed overvoltage fast calculation method, the overvoltage values ​​under different parameters are estimated, and the results are shown in Table 2. The results obtained are conservative in terms of the estimation of the maximum overvoltage value (second peak), but the estimation error does not exceed 2% within the actual parameter range, with high accuracy, and can effectively estimate the overvoltage level. At the same time, it can be seen from the table that increasing T′ d0 , K A Both can suppress the rise of overvoltage, select a larger T' d0 Therefore, from the perspective of system dynamic characteristics, the use of a generator with strong excitation and large d-axis open-circuit time constant near the rectifier station can effectively suppress the overvoltage problem at the sending end.

[0174] Table 2

[0175]

Claims

1. A method for regulating dynamic overvoltage when multiple DC sending ends are locked, characterized in that: The following steps are involved: S1: Construct DC transmission system model, AC system model and AC / DC system network equation model; S2: Combined with the dynamic dual-time-scale characteristics of overvoltage, the singular perturbation reduction-order decoupling of AC and DC systems is performed to establish an AC and DC singular perturbation model; S3: Under the slow time scale, the voltage subsystem model that dominates the voltage rise and the equivalent static load model are established; S4: Calculate the dynamic maximum value of the lock-up rising overvoltage according to the slow system linearization analytical method; S5: adjusting the overvoltage exceeding the set threshold in step S4, judging whether the voltage subsystem satisfies the monotonic system theory through the system power angle and phase angle difference matrix. If so, the voltage has a monotonic sequence-preserving characteristic with respect to the dynamic parameters of the synchronous machine, thereby adjusting the dynamic parameters of the synchronous machine to smoothly and monotonically suppress the overvoltage level; The step S2 is specifically as follows: The DC transmission system and AC system are decomposed into fast system and slow system by using singular perturbation theory. The fast and slow state quantities are divided according to the time constant, and the following AC and DC singular perturbation model is established: In the formula, The slow and fast state quantities are the differential equations respectively. In the formula, T′ fast =T fast / ε, the small parameter ε is taken as ε=L d ; Fast system time constant T fast Including the excitation regulator time constant T A , DC current measurement time constant T Idcmes , constant current PI control integral constant T IdR And the line inductance L d ; Slow system time constant T slow Including the inertia time constant T j , Generator d-axis transient time constant T′ d0 and DC voltage measurement time constant T vp ; The step S3 is specifically as follows: Since overvoltage occurs in the slow system, a voltage subsystem model that dominates the voltage rise in the slow system and an equivalent static load model are established: The algebraic relations in the degenerate system obtained from the singular perturbation theory are: V dcR,s -V dcI,s -R d I dc,s =0, the subscript "s" represents the slow system part of the state quantity; combined with the DC quasi-steady-state equation, the DC state quantity in the slow system satisfies the following equation: From the above formula (8), the equivalent load power model of the DC rectifier station in the slow system during the blocking period can be obtained as follows: In the formula, the subscript "0" represents the initial value of the system, and t represents time; Under the slow time scale, the voltage subsystem with the dominant voltage rise based on the AC system model is: Where V Gq It represents the q-axis component of the synchronous machine terminal voltage; The step S5 is specifically as follows: 5.1) According to the relationship between the phasor and amplitude of the complex number, the Jacobian matrix of the voltage subsystem that dominates the voltage rise in step S3 is obtained as follows: In the formula, the voltage at the terminal of the synchronous machine is about E′ q Sensitivity have: In the formula, Ignore the line resistance and approximate the admittance matrix of the synchronous machine transient reactance in step 1) (6) as a pure imaginary matrix, that is, Y≈jB, where matrix B is the imaginary part of Y. Combined with the definition of M matrix, -B is a non-singular M matrix, and its inverse -B -1 is a non-negative matrix, then the impedance matrix Z = Y -1 = jX imaginary reactance X = -B -1 is a non-negative matrix, so we can get X aug is a non-negative matrix; In the formula, is the selection matrix, Yes g The identity matrix of order n g is the number of generators, Ignore K CG The term is calculated by calculating the matrix cos(Δθ δ ) The positive and negative nature of the matrix Δθ δ Indicates the difference between the terminal voltage phase and the power angle of each generator: Indicates n g The matrix of order matrix elements are all 1, θ G Indicates the voltage phase at the machine end; When the locked matrix cos(Δθ δ ) is a non-negative matrix, then is a non-negative matrix; since the generator parameter X′ d <<X d , the coefficient matrix satisfies: X d / X′ d ≥K A / cos(δ-θ G )+1, based on The non-negativity of obtains the non-diagonal elements of the Jacobian matrix J(x) in equation (16) which are non-negative and is a Metzner matrix. Then the voltage subsystem is a monotonic system and can be monotonically controlled in step 5.2); When the matrix cos(Δθ δ ) is not a non-negative matrix, other control measures are required to suppress overvoltage; 5.2) Consider the input and output system: Among them, x∈X,u∈U,y∈Y,X, are state set, control set, and output set respectively; f is first-order differentiable; Let the generator excitation parameters and open-loop time constant be the control variables According to the relationship during the lockout period a) the slow system voltage continues to rise - (V G0 -V G )≥0 and relation b) reactive current i d The potential inside the generator continues to increase due to the reduction Get the symbolic characteristics of the input control variable u: About the output quantity converter station bus voltage y=V DC , from circuit theory we know that E′ q Increase the converter station voltage V DC will also rise, then non-negative; Therefore, during the lockout period, according to formula (19) and It is non-negative, and the converter station voltage is a monotonic input-output system with respect to the control quantity u, that is, the converter station bus voltage has a monotonic sequence-preserving characteristic with respect to the input control quantity, the proportional coefficient of the synchronous machine excitation system and the d-axis open-circuit time constant. The dynamic rising overvoltage can be effectively suppressed by increasing the proportional coefficient of the synchronous machine excitation system or increasing the d-axis open-circuit time constant.

2. The method for regulating dynamic overvoltage during blocking of multiple DC sending ends according to claim 1, characterized in that: The step S1 is specifically as follows: (1) Construct the DC quasi-steady-state model, DC line model and DC control system model of the traditional LCC DC transmission system: The normalized DC quasi-steady-state model is constructed, and the specific equation is as follows: In the formula, the subscripts "R" and "I" represent the rectifier side and the inverter side respectively, the subscript "dc" represents the direct current, and "DC" represents the alternating current; V dc 、V DC are DC voltage and AC voltage respectively, V dcR 、V DCR are the DC voltage on the rectifier side and the AC voltage on the rectifier side respectively; I dc is the DC current; X c is the equivalent reactance of the converter transformer; k is the transformation ratio of the converter transformer; α, β, They are trigger angle, leading trigger angle, rectifier side power factor angle, inverter side power factor angle; P dc and Q dc They are DC active power and DC reactive power respectively; For DC lines, the RL model is used: In the formula, R d and L d are the line resistance and inductance respectively; Assume that during the blocking period, the DC inverter voltage V DCI Constant, the leading trigger angle β is constant, the DC is constant power control, and the DC control system model is established as follows: Wherein, the subscript "mes" represents the measured quantity, x1 represents the PI control state quantity; T vp 、T Idcmes 、T IdR are the DC voltage measurement time constant, DC current measurement time constant and constant current PI control integral constant in constant power control respectively; P ref is the DC active power reference value; V dcRmes is the measured value of the DC voltage on the rectifier side, I dcmes is the DC current measurement value; (2) Constructing AC system model The AC system model is mainly composed of synchronous machines. The salient pole effect of synchronous machines is ignored. The synchronous machine adopts a third-order transient model including a first-order excitation system. The specific mathematical model is as follows: Among them, δ, ω s and ω are the synchronous machine power angle vector, nominal speed and actual speed vector respectively; T j , T′ do , T A are the inertia time constant diagonal matrix, the generator d-axis open-circuit time constant diagonal matrix and the excitation regulator time constant diagonal matrix respectively; E′ q is the diagonal matrix of the internal potential of the generator; i d and i q are the generator d-axis and q-axis current vectors respectively; D ω is the damping constant diagonal matrix; X d and X′ d are the d-axis reactance matrix and the d-axis transient reactance diagonal matrix respectively; E f is the excitation voltage vector; K A They represent the diagonal matrix of the proportional coefficient of the first-order excitation system, U ref 、V G are the internal reference value of voltage regulation and the generator terminal voltage vector respectively; the operator Represents the Hadamard product, which is the product of corresponding elements of vectors or matrices; (3) Establishing AC / DC system network equation model The load adopts a constant impedance model, forming the following AC / DC system network equation: Among them, the admittance matrix Y is composed of Y GG , Y GD , Y DG , Y DD It consists of four block sub-matrices, where the subscript "G" corresponds to the generator nodes and the subscript "D" corresponds to the DC nodes; They represent the complex form of synchronous machine terminal voltage and synchronous machine injection current vector respectively; denote the DC rectifier station voltage and the DC rectifier station injected current vector in complex form respectively; The interface equations of synchronous machines use the classic model: And expand the DC rectifier station injection current vector, the AC / DC system network equation is specifically transformed into: Where, Y′ GG Combined with synchronous machine transient reactance, Y′ GG =Y GG -jX′ d , j refers to the imaginary part; the DC rectifier station injects current vector Expressed as is the power injected by the rectifier station, The overline "-" indicates the conjugation of the complex vector, and the ". / " operation indicates the division of the corresponding elements of the vector; jδ It means taking the exponential value of each element of the vector δ, that is 3. The method for regulating dynamic overvoltage during blocking of multiple DC sending ends according to claim 1, characterized in that: The step S4 is specifically as follows: 4.1) Linearize the unbalanced point of the voltage subsystem in step S3: In the formula, The Jacobian matrix when the DC transmission system model adopts the equivalent load power model, represents the non-equilibrium term; let E′ q =Tz, substituting into formula (11) we can get: Where: z refers to E′ q Quantity transformed by matrix T; T = [v1, ..., v i ...,v n ],v1∈R n , where R n is an n-dimensional real vector, v i yes Right eigenvector; λ i is a matrix Eigenvalue; Solving equation (12) gives the time domain solution: By transforming E′ q =Tz has: 3.2) Assume that during the locking period the angular acceleration a δ Constant, that is Solve at t cl When the reactive power compensation is removed, the power angle of the i-th generator is: Among them, ω s is the rated speed, t cl is the capacitor removal time, δ i0 is the initial value of the power angle of the i-th synchronous machine; Substituting the internal potential obtained by equation (14) and the power angle obtained by equation (15) into the AC / DC system network equation of equation (6) in step 1), the dynamic maximum value of the overvoltage when the reactive compensation is removed can be solved.

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