A method and system for suppressing transient overvoltage

Abstract

The application discloses a transient overvoltage suppression method and system, relates to the field of overvoltage protection of a power system, and comprises the following steps: constructing a state space expression of a high-voltage direct-current power transmission system; inputting a direct-current current and a receiving-end direct-current voltage into the state space expression to determine an equivalent control quantity; determining a tracking error determined according to the direct-current current and a reference current as a sliding mode quantity; determining a switching control quantity based on a second-order sliding mode super-helix algorithm; determining a super-helix sliding mode constant current control rate according to the equivalent control quantity and the switching control quantity; the super-helix sliding mode constant current control rate meets a constraint condition of Lyapunov stability; substituting the sliding mode quantity into the super-helix sliding mode constant current control rate to determine a rectifier side trigger angle signal; and the rectifier side trigger angle signal is used for inputting a rectifier station to suppress transient overvoltage of a sending-end alternating-current system. The application is easy to implement suppression of the sending-end transient overvoltage, is convenient and simple, and can improve dynamic performance and steady-state performance of the high-voltage direct-current power transmission system.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of power system overvoltage protection, in particular to a transient overvoltage suppression method and system. BACKGROUND

[0002] At present, the construction of the Shachanggong new energy base is steadily advancing. The new energy base is usually far away from the load center, and the high-voltage direct current transmission technology is the key technology for realizing long-distance power transmission at present. The rectifier station of the high-voltage direct current transmission system needs to consume a large amount of reactive power during normal operation, and this part of reactive power is usually compensated locally by the filter put into the rectifier station. When the receiving end AC system fails, the receiving end rectifier station may fail to commutate. During the recovery process after the commutation failure and fault clearing, the reactive power balance in the sending end rectifier station is broken, causing the sending end transient overvoltage. With the continuous improvement of new energy penetration, the strength of the sending end AC system gradually decreases, and the sending end transient overvoltage caused by commutation failure will be further aggravated, and the new energy units may be at risk of large-scale disconnection, which is not conducive to the stable operation of the power system. Therefore, how to suppress the sending end transient overvoltage after commutation failure is a problem that needs to be solved at present.

[0003] The mechanism analysis of the sending end transient overvoltage after commutation failure has been relatively mature, and it has basically reached a consensus that the reactive power consumed by the rectifier station during commutation failure first increases and then decreases, causing the voltage of the sending end AC system to present a "first low and then high" trend. On this basis, the current research on the suppression strategy of transient overvoltage after commutation failure mainly includes two aspects of adding reactive devices and optimizing control links.

[0004] For adding reactive devices, mainly through adding reactive compensation to dissipate surplus reactive power and through adding arresters and energy dissipation devices to discharge excess energy during faults. Existing research by scholars shows that the configuration of static synchronous compensator (STATCOM) can improve the strength of the power grid during faults, accelerate system recovery and stability, and reduce transient overvoltage, but STATCOM has a "reverse adjustment" problem in suppressing overvoltage, which may worsen the transient overvoltage. For control link optimization, existing research has analyzed the suppression effect of transient overvoltage under different control parameters and the influence on the dynamic and steady-state performance of the system. At present, scholars have predicted the change of direct current, changed the trigger angle signal in advance, and suppressed the commutation failure, but this method has high requirements for the accuracy of the measurement link and is not convenient to implement. SUMMARY

[0005] The purpose of the present application is to provide a transient overvoltage suppression method and system, which is easy to implement the suppression of the sending end transient overvoltage, convenient and simple, and can improve the dynamic performance and steady-state performance of the high-voltage direct current transmission system.

[0006] To achieve the above object, the application provides the following scheme.

[0007] In a first aspect, the application provides a transient overvoltage suppression method, which is used in a high-voltage direct current transmission system, and an equivalent circuit of the high-voltage direct current transmission system comprises a sending-end alternating current system, a rectifier station, a direct current transmission line, an inverter station and a receiving-end alternating current system connected in sequence.

[0008] The transient overvoltage suppression method comprises the following steps.

[0009] Obtaining a direct current in the direct current transmission line and a receiving-end direct current voltage in the receiving-end alternating current system;

[0010] Constructing a state space expression of the high-voltage direct current transmission system;

[0011] Inputting the direct current and the receiving-end direct current voltage into the state space expression to determine an equivalent control quantity;

[0012] Determining a tracking error according to the direct current and a reference current, and determining the tracking error as a sliding mode quantity; the sliding mode quantity meets the requirement of relative order 1 in a super-hyper surface sliding mode control;

[0013] Determining a switching control quantity based on a second-order sliding mode super-hyper surface algorithm;

[0014] Determining a super-hyper surface sliding mode constant current control rate according to the equivalent control quantity and the switching control quantity; the super-hyper surface sliding mode constant current control rate meets a constraint condition of Lyapunov stability;

[0015] Substituting the sliding mode quantity into the super-hyper surface sliding mode constant current control rate to determine a rectifier-side trigger angle signal; the rectifier-side trigger angle signal is used to input the rectifier station to suppress the transient overvoltage of the sending-end alternating current system.

[0016] In a second aspect, the application provides a transient overvoltage suppression system, which is used to suppress a transient overvoltage in a high-voltage direct current transmission system, and an equivalent circuit of the high-voltage direct current transmission system comprises a sending-end alternating current system, a rectifier station, a direct current transmission line, an inverter station and a receiving-end alternating current system connected in sequence.

[0017] The transient overvoltage suppression system comprises a super-hyper surface sliding mode constant current control link, which is connected with the rectifier station and the direct current transmission line respectively.

[0018] The super-hyper surface sliding mode constant current control link comprises the following steps.

[0019] a data sampling module configured to acquire a direct current in a direct current transmission line and a receiving-end direct current voltage in a receiving-end alternating current system;

[0020] a state space expression construction module configured to construct a state space expression of the high-voltage direct current transmission system;

[0021] an equivalent control quantity determination module configured to input the direct current and the receiving-end direct current voltage into the state space expression to determine an equivalent control quantity;

[0022] a sliding mode quantity determination module configured to determine a tracking error according to the direct current and a reference current, and determine the tracking error as a sliding mode quantity; the sliding mode quantity meets a requirement of a relative order of 1 in a super-hyperbolic sliding mode control;

[0023] a switching control quantity determination module configured to determine a switching control quantity based on a second-order sliding mode super-hyperbolic algorithm;

[0024] a super-hyperbolic sliding mode constant current control rate determination module configured to determine a super-hyperbolic sliding mode constant current control rate according to the equivalent control quantity and the switching control quantity; the super-hyperbolic sliding mode constant current control rate meets a constraint condition of Lyapunov stability;

[0025] a transient overvoltage suppression module configured to substitute the sliding mode quantity into the super-hyperbolic sliding mode constant current control rate to determine a rectifier-side trigger angle signal; the rectifier-side trigger angle signal is used to input a rectifier station to suppress a transient overvoltage of a sending-end alternating current system.

[0026] According to the specific embodiments provided in the application, the following technical effects are disclosed:

[0027] The application provides a transient overvoltage suppression method and system. The tracking error determined according to the direct current and the reference current is determined as the sliding mode quantity, the switching control quantity is determined based on the second-order sliding mode super-hyperbolic algorithm, the super-hyperbolic sliding mode constant current control rate is determined according to the equivalent control quantity and the switching control quantity, the sliding mode quantity is substituted into the super-hyperbolic sliding mode constant current control rate to determine the rectifier-side trigger angle signal, so as to suppress the transient overvoltage of the sending-end alternating current system. The application realizes the suppression of the transient overvoltage based on the sliding mode super-hyperbolic algorithm. Since the sliding mode super-hyperbolic algorithm can avoid the chattering problem caused by the switching control, and has the advantages of simple design and easy implementation, the application is easy to implement the suppression of the sending-end transient overvoltage, is convenient and simple, and can improve the dynamic performance and the steady-state performance of the high-voltage direct current transmission system. BRIEF DESCRIPTION OF DRAWINGS

[0028] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed in the embodiments. Obviously, the drawings in the following description only constitute some embodiments of the present application, and for those skilled in the art, other drawings can also be obtained based on these drawings without creative labor.

[0029] Figure 1 A flowchart of a transient overvoltage suppression method provided by an embodiment of the present application is shown in the figure.

[0030] Figure 2 A circuit schematic diagram of an equivalent circuit of a high-voltage direct-current transmission system provided by an embodiment of the present application is shown in the figure.

[0031] Figure 3 A second-order sliding mode trajectory provided by an embodiment of the present application is shown in the figure.

[0032] Figure 4 A rectifier-side overall control block diagram provided by an embodiment of the present application is shown in the figure.

[0033] Figure 5 A super-spiral sliding mode constant current control design flowchart provided by an embodiment of the present application is shown in the figure.

[0034] Figure 6 A super-spiral sliding mode constant current control design flowchart provided by another embodiment of the present application is shown in the figure.

[0035] Figure 7 A rectifier-side DC current response curve diagram under small disturbance provided by another embodiment of the present application is shown in the figure.

[0036] Figure 8 A rectifier-side DC voltage response curve diagram under small disturbance provided by another embodiment of the present application is shown in the figure.

[0037] Figure 9 A sending-end AC system voltage curve diagram under slight fault provided by another embodiment of the present application is shown in the figure.

[0038] Figure 10 A DC current response curve diagram under slight fault provided by another embodiment of the present application is shown in the figure.

[0039] Figure 11 A DC transmission active power curve diagram under slight fault provided by another embodiment of the present application is shown in the figure.

[0040] Figure 12 A DC voltage curve diagram under slight fault provided by another embodiment of the present application is shown in the figure.

[0041] Figure 13 A rectifier-side filter reactive power curve diagram under slight fault provided by another embodiment of the present application is shown in the figure.

[0042] Figure 14 A graph of rectifier side firing angle variation under minor fault is provided for another embodiment of the present application;

[0043] Figure 15 A graph of sending end AC system voltage under severe fault is provided for another embodiment of the present application;

[0044] Figure 16 A graph of DC current response under severe fault is provided for another embodiment of the present application;

[0045] Figure 17 A graph of DC transmission active power under severe fault is provided for another embodiment of the present application;

[0046] Figure 18 A graph of DC voltage under severe fault is provided for another embodiment of the present application;

[0047] Figure 19 A graph of rectifier side filter reactive power under severe fault is provided for another embodiment of the present application;

[0048] Figure 20 A graph of rectifier side firing angle variation under severe fault is provided for another embodiment of the present application.

[0049] Reference: sending end AC system-1, rectifier station-2, DC transmission line-3, inverter station-4, receiving end AC system-5. DETAILED DESCRIPTION

[0050] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without any creative work fall within the scope of protection of the present application.

[0051] The sliding mode control is a nonlinear control method, which is used for linear or nonlinear objects with inaccurate modeling. By designing a sliding mode surface and a discontinuous control rate, the system state variable moves along the designed sliding mode surface, which is independent of the disturbance and has strong robustness. At present, the sliding mode control has been widely used in spacecraft attitude tracking control, permanent magnet synchronous motor control, and flexible DC transmission control, etc.

[0052] The traditional sliding mode control structure is relatively complex and has the problem of chattering, which may cause serious failure in actual engineering. Super-twisting sliding mode is a second-order sliding mode, which avoids the chattering problem caused by switching control by putting the discontinuous term in the sliding mode control into the high-order derivative of the sliding mode surface. At the same time, the super-twisting algorithm has the advantages of simple design and easy implementation, and has been applied in energy storage converter and DC-DC converter control.

[0053] However, there is currently a lack of relevant literature discussing the application of sliding mode control in line commutated converter based high voltage direct current (LCC-HVDC) systems. How to realize the modeling of LCC-HVDC system suitable for sliding mode control design, and the performance of applying sliding mode control to the constant current control link for transient overvoltage suppression remain to be studied. Therefore, the present application takes advantage of the super-twisting sliding mode control, and proposes a transient overvoltage suppression method and system, which is based on the LCC-HVDC system transient overvoltage suppression strategy of super-twisting sliding mode constant current control, and can suppress the sending end transient overvoltage while improving the dynamic performance and steady-state performance of the high voltage direct current transmission system.

[0054] In order to make the above-mentioned purposes, features and advantages of the present application more obvious and easy to understand, the present application will be further described in detail below in combination with the drawings and specific embodiments.

[0055] In one exemplary embodiment, as shown in Figure 1 , a transient overvoltage suppression method for a high voltage direct current transmission system is provided.

[0056] Referring to Figure 2 , the equivalent circuit of the high voltage direct current transmission system includes a sending end alternating current system 1, a rectifier station 2, a direct current transmission line 3, an inverter station 4 and a receiving end alternating current system 5 connected in sequence. Figure 2 In the equivalent circuit, S1 is the equivalent source of the sending end alternating current system, u s1 is the equivalent source voltage of the sending end alternating current system, R s1 and L s1 are the equivalent resistance and inductance of the sending end alternating current system, i s1 and u r are the current and voltage at the junction of the sending end alternating current system 1 and the sending end alternating current bus, AC filter1 is the sending end filter and reactive power compensation device, U1 is the sending end alternating current bus voltage in the sending end alternating current system 1, PCC represents the interface point between the power grid and the independent power source, k r is the sending end converter transformer ratio, U d1 is the sending end direct current voltage (i.e. the sending end converter station direct current voltage) in the sending end alternating current system 1, Rd and L d are the equivalent resistance and inductance of the DC transmission line, respectively, I d is the DC current, U d2 is the rectifier DC voltage (i.e. the DC voltage at the rectifier station), k i is the rectifier transformer ratio, U2is the AC bus voltage, i s2 and u i are the current and voltage at the junction of the AC system 5 and the AC bus, R s2 and L s2 are the equivalent resistance and inductance of the AC system, respectively, S2is the equivalent source of the AC system, u s2 is the equivalent source voltage of the AC system, and AC filter2is the rectifier filter and reactive power compensation equipment.

[0057] The mechanism of the commutation failure of the rectifier station leading to the transient overvoltage at the sending end will first be analyzed.

[0058] As shown in Fig. Figure 2 , when the AC system 5 at the receiving end fails, the commutation failure of the rectifier at the receiving end can be induced, and during the commutation failure, the upper and lower valve groups of a phase of the rectifier at the receiving end will be simultaneously turned on, causing the DC voltage between the poles of the rectifier at the receiving end to rapidly drop to zero. The fault can be divided into the following stages:

[0059] 1) DC current rising stage.

[0060] The valves of the upper and lower bridge arms of the inverter are simultaneously turned on, which is equivalent to a short circuit on the DC side and an open circuit on the AC side of the valve, and the DC current I d is in the rising stage. In addition, the extinction angle will be instantaneously reduced to 0 after the commutation valve is turned on, and the commutation failure prediction function (CFPED) link will respond to increase the extinction angle, thereby improving the commutation margin and preventing continuous commutation failure.

[0061] At the same time, the AC voltage at the receiving end rapidly drops at the moment of the disturbance, and according to equation (1), the DC voltage U d2 at the receiving end will drop.

[0062] U d2 = 1.35U2cosβ + (3 / π)X C2 I d (1)

[0063] In the equation: β is the leading trigger angle at the inverter side; I d is the DC current; X C2 is the commutation reactance at the inverter station 4; U2is the AC voltage at the receiving end; and U d2 is the DC voltage at the receiving end.

[0064] Since the DC current I d has reached a high level, and the sending-end DC voltage U d1 has not yet been affected by the fault, the reactive power Q d consumed by the rectifier station 2 can be obtained from equation (2). The main source of the required reactive power of the rectifier station 2 in steady state is the AC filter banks and shunt capacitor banks, which cannot provide sufficient reactive power instantaneously due to their slow response. Therefore, the sending-end AC system 1 has to supply the required reactive power to the rectifier station 2, resulting in a decrease in the sending-end commutation bus voltage U1 and the occurrence of transient low voltage.

[0065]

[0066] wherein: is the sending-end power factor angle; Q d is the reactive power consumed by the rectifier station 2.

[0067] Therefore, the sending-end DC voltage U d1 decreases accordingly.

[0068] U d1 = 1.35U1 cos α - (3 / π)X C1 I d (3)

[0069] wherein: α is the rectifier-side firing angle; X C1 is the commutation reactance of the rectifier station 2; U1 is the sending-end AC voltage; and U d1 is the sending-end DC voltage.

[0070] 2) DC current reduction phase.

[0071] To suppress the increase in the first phase, the rectifier-side constant current control loop (CCA) is started to increase the sending-end firing angle α to reduce the DC current I d . In addition, due to the decrease in the DC voltage value in the first phase and the increase in the value, the low-voltage current-limiting loop (VDCOL) also responds to reduce the command value. The reduction of the command value increases the input of the CCA loop during the fault, causing excessive overshoot of the current, so that the DC current I d may also be too small after being reduced. In this process, there is an unavoidable time delay in the control loop, and when the firing angle starts to rise, the DC current I d is still increasing. At the end of the action time delay, I d reaches a peak value and then starts to decrease, and the fault enters the DC current reduction phase.

[0072] I d is reduced, the sending-end DC voltage U d1 has not yet changed, and the reactive power requirement Q dThe DC current has been greatly reduced. The security control device has limited response ability due to time delay, and the fixed reactive power compensation device at the sending end cannot be withdrawn in time, and still continuously sends a large amount of reactive power of 40% to 60% of the DC active power, so that the sending end converter station has excess reactive power, and a large amount of reactive power even flows back into the AC system, causing the sending end converter bus to have a transient overvoltage.

[0073] 3) DC recovery phase.

[0074] The voltage, current and other indicators gradually recover to the stable operation level, the reactive power demand of the rectifier station 2 rises, and a new balance is reached with the AC system, and the transient voltage recovers to the steady-state value before the fault. Therefore, the transient overvoltage phenomenon caused by commutation failure has the typical characteristics of "first decreasing and then increasing".

[0075] From the above analysis, it can be seen that the change of the system state after commutation failure is closely related to the DC current I d The low current formed by the overshoot of the constant current control link to the DC current is the key factor leading to the transient overvoltage at the sending end. Optimizing the constant current control and improving the response characteristics of the DC current is a solution to suppress the transient overvoltage at the sending end after commutation failure.

[0076] Next, the principle of super-spiral sliding mode control is analyzed.

[0077] Sliding mode variable structure control can switch control functions according to the real-time state of the system, so that the system state point always remains on the sliding surface. The sliding surface is artificially designed according to the control target, and is less affected by external disturbances and less sensitive to parameter changes, so it has strong robustness.

[0078] Consider the following form of nonlinear system

[0079]

[0080] In the formula, x is the state variable of the system; u is the control signal as the control input; f(x), g(x) are smooth unknown functions; s(x) is the sliding mode of input x.

[0081] s(x) = 0 is defined as a sliding surface, and the control target is to make the state of the system reach the sliding surface s(x) = 0 in a limited time, and has a second-order sliding mode, that is, to make the state of the system reach the following sliding manifold in a limited time:

[0082]

[0083] Assume that the relative order of the sliding mode s(x) with respect to the control input u is 1, that is, At this time, we have:

[0084]

[0085] The derivative of the control input u As a new control variable, by designing discontinuous control Make the sliding mode s(x) tend to zero and maintain the second-order sliding mode, that is, The control input u is obtained by The second-order sliding mode motion trajectory is obtained by integrating , so it is continuous, thus suppressing the system's chattering. Figure 3 shown.

[0086] In order to ensure the strictness of the second-order sliding mode, the smooth unknown functions f(x) and g(x) are globally bounded:

[0087]

[0088] Where: C, K m and K M All are normal numbers.

[0089] The super spiral algorithm means that the state trajectory converges to the origin in a spiral around the origin within a finite time. This algorithm is the only one among the existing second-order sliding mode algorithms that does not require the derivative information of the sliding mode quantity. The algorithm can be directly applied when the relative order of the sliding mode s with respect to the control input u is 1 without introducing a new control variable. Can simplify the design of control systems.

[0090] The switching control rate based on the second-order sliding mode super-helical algorithm, that is, the expression of the switching control amount is as follows:

[0091]

[0092] Where: u sw represents the switching control amount; u1 represents the first control amount; u2 represents the second control amount; represents the first-order derivative of u2; s represents the sliding mode; λ1 and λ2 are both constants; sign represents the sign function.

[0093] At this time, the discontinuous high-frequency switching quantity λ2sign(s) no longer directly affects the control law u sw , but appears in the switching control law in the form of time integral, thereby obtaining a continuous control signal, thus eliminating the chattering defect in traditional sliding mode control.

[0094] The above analysis of the robustness of super-helical sliding mode control and the design of the control ratio effectively suppresses the chattering problem common in traditional sliding mode control. Based on the control ratio design principles presented in Step 2 and the second-order sliding mode super-helical algorithm, we will now apply them to the design of constant current control for HVDC transmission systems. By designing a super-helical sliding mode constant current control law, we will implement a transient overvoltage suppression method.

[0095] Still referring to Figure 1 , the transient overvoltage suppression method comprises:

[0096] Step 101: obtaining a direct current in a direct current transmission line and a receiving end direct current voltage in a receiving end alternating current system.

[0097] Step 102: constructing a state space expression of the high voltage direct current transmission system.

[0098] Step 103: inputting the direct current and the receiving end direct current voltage into the state space expression to determine an equivalent control quantity.

[0099] Step 104: determining a tracking error according to the direct current and a reference current, and determining the tracking error as a sliding mode quantity; the sliding mode quantity meets a requirement of relative order 1 in a super-helix sliding mode control.

[0100] Step 105: determining a switching control quantity based on a second order sliding mode super-helix algorithm.

[0101] Step 106: determining a super-helix sliding mode constant current control rate according to the equivalent control quantity and the switching control quantity; the super-helix sliding mode constant current control rate meets a constraint condition of Lyapunov stability.

[0102] Step 107: substituting the sliding mode quantity into the super-helix sliding mode constant current control rate to determine a rectifier side trigger angle signal; the rectifier side trigger angle signal is used for inputting a rectifier station to suppress transient overvoltage of a sending end alternating current system.

[0103] In another exemplary embodiment of the present application, step 102 specifically comprises:

[0104] 1) establishing an equivalent mathematical model of the high voltage direct current transmission system.

[0105] Specifically, according to Figure 2 , a dynamic equation of the high voltage direct current transmission system can be written, and the dynamic equation is taken as the equivalent mathematical model, and an expression of the equivalent mathematical model is:

[0106]

[0107] wherein, I d represents the direct current; d represents a first order derivative of I d ; L d1 represents an equivalent inductance of the direct current transmission line; U d represents a sending end direct current voltage in the sending end alternating current system 1; R d2 represents an equivalent resistance of the direct current transmission line; and U d represents the receiving end direct current voltage in the receiving end alternating current system 5.

[0108] 2) Based on the equivalent mathematical model, taking the direct current as the state variable and the trigger angle signal of the rectifier side of the input rectifier station 2 as the control signal, a state space expression of the high-voltage direct current power transmission system is constructed.

[0109] Specifically, formula (3) is brought into formula (9), and the following formula can be obtained:

[0110]

[0111] Since the trigger angle α of the constant current control signal is contained in the nonlinear term, it does not meet the general form of the controller design. Therefore, the first-order Taylor expansion linearization is performed at the stable operating point α0 of the system, and the processed system dynamic equation is as follows:

[0112]

[0113] Further, the state space expression can be written as:

[0114]

[0115] Wherein, x represents a state variable; represents the first derivative of x; u represents a control signal; I d represents a direct current; α represents a trigger angle signal of the rectifier side; a(x) represents a state intermediate variable; b represents a control coefficient; L d represents an equivalent inductance of the direct current transmission line; U1 represents a sending end alternating current bus voltage in the sending end alternating current system 1; α0 represents a trigger angle signal corresponding to a stable operating point of the high-voltage direct current power transmission system; X c1 represents a commutation reactance of the rectifier station 2; R d represents an equivalent resistance of the direct current transmission line; U d2 represents a receiving end direct current voltage in the receiving end alternating current system 5.

[0116] In another exemplary embodiment of the application, the determination process of the sliding mode in step 104 is as follows:

[0117] The design goal of the constant current control is that, when the system control rule mutation and various external disturbances occur, the direct current I d can strictly track its reference signal I dref . According to the design goal, the tracking error is selected as follows:

[0118] e=x * -x=I dref -I d (13)

[0119] The tracking error is used to define the sliding mode as follows:

[0120] s=e (14)

[0121] wherein s represents a sliding mode; e represents a tracking error; I dref represents a reference current; I d represents a direct current.

[0122] The derivative of the sliding mode is:

[0123]

[0124] Since the selected sliding mode s satisfies the relative order of 1 with respect to the control input u, a super-spiral sliding mode control can be used.

[0125] In another exemplary embodiment of the present application, the control method used in the present embodiment is essentially equivalent to a variable structure control, and the control signal u is composed of an equivalent control quantity u eq and a switching control quantity u sw , which are respectively responsible for bringing the state variable x into the sliding surface and ensuring that the state variable x does not leave the sliding surface. The expression of the control signal u is:

[0126] u = u eq + u sw (16)

[0127] By substituting u and u = u eq into equation (15), the specific expression of the equivalent control quantity u eq of the system can be obtained as:

[0128]

[0129] wherein u eq represents the equivalent control quantity; a(x) represents a state intermediate variable; b represents a control coefficient.

[0130] Therefore, step 103 specifically comprises: 1) inputting the direct current and the receiving-end direct voltage into the state space expression to calculate the state intermediate variable a(x) and the control coefficient b; and 2) determining the equivalent control quantity according to the state intermediate variable and the control coefficient.

[0131] wherein the switching control quantity u sw uses a super-spiral sliding mode control, and the expression of the switching control quantity is shown in equation (8), which will not be described here.

[0132] By substituting equation (8) and equation (17) into equation (16), the expression of the super-spiral sliding mode constant current control rate can be obtained as:

[0133]

[0134] where u represents the control signal; a(x) represents the state intermediate variable; b represents the control coefficient; s represents the sliding mode; λ1 and λ2 are both constants.

[0135] In another exemplary embodiment of the present application, a check is required, and the process is as follows:

[0136] The first derivative expression of the sliding mode s is obtained by bringing formula (28) into formula (15)

[0137]

[0138] In order to verify the stability of the designed super-spiral sliding mode constant current control, the Lyapunov function is used to prove the stability of formula (19). For ease of analysis, the above formula is changed to the following form:

[0139]

[0140] In the formula, m=-λ1b, n=-λ2b.

[0141] A new state variable is introduced:

[0142]

[0143] The derivative of the above formula is:

[0144]

[0145] The derivative of Z is:

[0146]

[0147] Define the Lyapunov function as:

[0148] V(Z)=Z T PZ (24)

[0149] Where P is a symmetric positive definite matrix, and λ1 and λ2 are constants.

[0150]

[0151] The Lyapunov function V(Z)≥0 can be obtained.

[0152] The derivative of V(Z) is obtained as:

[0153]

[0154] Where the matrix Q is:

[0155]

[0156] Therefore, when the matrix Q is a positive definite matrix, the function V(Z) is less than 0. According to Lyapunov's second law, equation (19) is stable.

[0157] set up

[0158]

[0159] The matrix Q can be simplified as:

[0160]

[0161] Its characteristic values ​​are:

[0162]

[0163] To make the matrix Q a positive definite matrix, only p1>0 is needed, then:

[0164]

[0165] Substituting m and n, we can obtain the constraint condition that the matrix Q is a positive definite matrix:

[0166]

[0167] When the above formula (12) is satisfied, it can be guaranteed that Therefore, as long as the control parameters satisfy the constraint condition that the matrix Q is a positive definite matrix, the control system is Lyapunov stable, that is, the constraint condition of the positive definite matrix mentioned above is used as the constraint condition of Lyapunov stability.

[0168] The following combination Figure 4 and Figure 5 The overall process of the above transient overvoltage suppression method is described.

[0169] The control process of the rectifier side of the HVDC system under super-helical sliding mode constant current control is as follows: Figure 4 As shown, Figure 4 In the figure, ST-SMC is the proposed super-helical sliding mode constant current control link, I dref is the DC current reference value, K mr / 1+sT mr is the transfer function of the DC current measurement link, where K mr is the proportional coefficient of the measurement link, T mr The transfer function is used to measure the time constant of the DC current I d After filtering, the DC current I d With reference current I dref The difference is input into ST-SMC as the sliding modulus s.

[0170] Specifically, first, the DC current I dand receiving end DC voltage U d2 Sampling is performed and a(x) and b in equation (12) are calculated. DC current I d The difference between the reference current and the current after the measurement link is used as the sliding mode input. Substituting it into formula (18) can obtain the rectifier side trigger angle signal α output by the super spiral sliding mode constant current control. The trigger angle signal α will be transmitted to the rectifier side converter as a control signal, changing the output DC voltage of the rectifier side, and the DC current will also change accordingly until it reaches the DC current reference value. By outputting the trigger angle signal α, the DC current is controlled to have better dynamic response characteristics during the fault period. By improving the low current level of the DC current during the fault period, the reactive power consumption of the converter station is increased, thereby suppressing transient overvoltage.

[0171] In summary, the design process of super spiral sliding mode constant current control is as follows: Figure 5 First, establish the equivalent mathematical model of the high-voltage direct current transmission system, as shown in formula (9). Based on the mathematical model, the DC current I d The state variable and the trigger angle signal α on the rectifier side are the control signals. The state space expression of the DC system is obtained as shown in Equation (12), and the general form of controller design is written as

[0172] Taking advantage of the fact that the sliding mode in the sliding mode control is insensitive to disturbances, according to the design goal of the constant current controller, the DC current deviation is defined as the sliding mode quantity s, and it is judged whether the sliding mode quantity s meets the requirement of the relative order of 1 in the super-helical sliding mode control. If not, the sliding mode quantity s needs to be redefined. The equivalent variable structure control design idea is adopted, and the control input u is composed of the equivalent control quantity u eq and switching control quantity u sw Finally, a stability check is performed based on the Lyapunov function, and the conditions that the control parameters need to meet in order to stabilize the controller are given.

[0173] The following provides an experimental process to verify the effectiveness of the above transient overvoltage suppression method.

[0174] In order to verify the effectiveness of super-spiral sliding mode constant current control in suppressing transient overvoltage at the sending end after commutation failure, based on the PSCAD / EMTDC simulation platform and the conventional DC standard model of the International Conference on Large Electric Systems (CIGRE), the rectifier-side PI constant current control is replaced by the super-spiral sliding mode constant current control mentioned above. Figure 6 As shown, Figure 6 Medium L dc Represents the equivalent inductance of the DC transmission line, R dc Indicates the equivalent resistance of the DC transmission line, U dc Indicates the DC voltage at the midpoint of the transmission line, I dcrIin represents the sending end DC current dic Cout represents the receiving end DC current dc C represents the DC transmission line-to-ground capacitance. The system related parameters are shown in Table 1.

[0175] Table 1 CIGRE HVDC standard model system parameters

[0176]

[0177]

[0178] Example 1: Small disturbance simulation comparison.

[0179] In order to evaluate the super-spiral sliding mode constant current control performance, small disturbance simulation test is carried out based on PSCAD / EMTDC. At the same time, since the super-spiral sliding mode control formula (8) contains a nonlinear function sign, it is difficult to solve the eigenvalue, so only time domain simulation is used to evaluate the performance.

[0180] After the DC system runs stably for a period of time, the reference voltage of the inverter side drops at 3s. Figure 7 and Figure 8 are the response curves of the rectifier side DC current and DC voltage under small disturbance respectively.

[0181] From Figure 7 and Figure 8 It can be seen that the PI control has a large fluctuation amplitude of DC current under small disturbance, while the super-spiral sliding mode constant current control designed in this paper reduces the fluctuation amplitude of DC current and has a faster recovery speed, and its control performance is better than that of PI control. The super-spiral sliding mode constant current control designed in this paper has a slightly better effect on the change amplitude and recovery speed of DC voltage, but it is significantly faster than PI control in recovery speed.

[0182] Example 2: Simulation comparison of slight fault.

[0183] In this section, a single-phase ground fault occurring in the AC transmission line is simulated by connecting a ground inductance to the receiving end AC bus. The single-phase ground fault occurs at the receiving end AC bus at 1s, and the fault duration is 0.1s.

[0184] The system response curves of different control strategies under slight fault are shown in Figures 9-14 . Figure 9 The voltage curve of the sending end AC system 1 under slight fault is shown in Figure 10 , which shows that the transient overvoltage of the super-spiral sliding mode constant current control is significantly reduced compared with the traditional PI constant current control after the fault occurs; Figure 11 The DC current response curve under slight fault is shown in Figure 12 , which shows that the overcurrent and low current level during the fault are significantly improved under the action of the super-spiral sliding mode constant current control.The curves of DC transmission active power under slight fault and DC voltage under slight fault are shown respectively, and the recovery speed is obviously accelerated under the effect of super-spiral sliding mode constant current control; Figure 13 The curve of reactive power of rectifier side filter under slight fault is shown, and the reactive power redundancy is reduced during the fault; Figure 14 The curve of rectifier side trigger angle change under slight fault is shown, and it can be seen that the change speed of trigger angle under super-spiral sliding mode constant current control is significantly improved compared with traditional PI constant current control. After single-phase fault of the receiving end AC bus, the system occurs commutation failure, and the overall trend of the sending end AC system 1 is low first and then high. Since super-spiral sliding mode constant current control can respond to current change more quickly than PI constant current control, it can increase or decrease the rectifier side trigger angle more quickly, thereby reducing the overcurrent level and improving the low current level caused by overshoot. The decrease of overcurrent level leads to the decrease of reactive power absorbed by the rectifier from the sending end AC system 1, and the transient low voltage is improved; the increase of low current level leads to the increase of reactive power consumed by the rectifier, and the reactive power surplus of the rectifier side is reduced, so the transient overvoltage can be improved more significantly. The transient overvoltage at 1.07s is reduced from 1.155p.u. to 1.101p.u. While improving the transient overvoltage, the recovery rate of DC voltage and active power is accelerated, and the dynamic and steady-state performance of the DC system is also enhanced to some extent.

[0185] Example 3: Comparison of severe fault simulation.

[0186] In this example, a three-phase ground fault occurring in the AC transmission line is simulated by connecting a grounding inductor to the receiving end AC bus. At 1s, a three-phase ground fault occurs on the receiving end AC bus, and the fault duration is 0.1s.

[0187] The system response curves of different control strategies under severe fault are shown in Figures 15-20 Figure 15 The voltage curve of the sending end AC system 1 under severe fault is shown. After the fault occurs, the system experiences two periods of commutation failure, and the transient overvoltage under super-spiral sliding mode constant current control is significantly reduced compared with traditional PI constant current control after the second commutation failure; Figure 16 The DC current response curve under severe fault is shown. Under the effect of super-spiral sliding mode constant current control, the overcurrent and low current levels during the fault are obviously improved; Figure 17 and Figure 18 The curves of DC transmission active power under severe fault and DC voltage under severe fault are shown respectively, and the recovery speed is obviously accelerated under the effect of super-spiral sliding mode constant current control; Figure 19 The curve of reactive power of rectifier side filter under severe fault is shown, and the reactive power redundancy is reduced during the fault; Figure 20 ​The trigger angle change curve under serious fault is shown, and it can be seen that the trigger angle change speed of the super-spiral sliding mode constant current control is significantly improved compared with the conventional PI constant current control. After the three-phase fault of the receiving end AC bus, the system experiences two periods of commutation failure, and the RMS value of the overvoltage of the sending end AC bus has two peaks. During the first commutation failure period, the overvoltage of the sending end AC bus has the first peak value of 1.175 p.u. at 1.15 s, because the low current level is approximately the same under the two control strategies. After the second commutation failure during the system recovery process, the DC current under the PI constant current control rapidly decreases from the maximum value at the time of commutation failure, and even decreases to 0, so that the sending end AC bus has the second overvoltage peak value of 1.245 p.u. The super-spiral sliding mode constant current control rapidly increases or decreases the trigger angle of the rectifier side, thereby reducing the overcurrent level after the second commutation failure and improving the low current level caused by the overshoot, significantly improving the transient low voltage and reducing the transient overvoltage of the sending end AC bus, and the second peak value is only 1.121 p.u. While improving the transient overvoltage, the recovery rate of the DC voltage and the active power is accelerated, the trigger angle of the rectifier side does not reach the limit, and the dynamic and steady-state performance of the DC system is also enhanced to some extent.

[0188] Based on the same inventive concept, the embodiments of the present application also provide a transient overvoltage suppression system for implementing the transient overvoltage suppression method described above. The implementation scheme for solving the problem provided by the system is similar to the implementation scheme described in the above method, so the specific limitations in one or more transient overvoltage suppression system embodiments provided below can be referred to the limitations of the transient overvoltage suppression method described above, which will not be repeated here.

[0189] In one exemplary embodiment, a transient overvoltage suppression system is provided for suppressing transient overvoltage in a high-voltage direct-current power transmission system, and an equivalent circuit of the high-voltage direct-current power transmission system includes: a sending end AC system 1, a rectifier station 2, a DC transmission line 3, an inverter station 4, and a receiving end AC system 5 connected in sequence.

[0190] The transient overvoltage suppression system includes a super-spiral sliding mode constant current control link, and the super-spiral sliding mode constant current control link is connected with the rectifier station 2 and the DC transmission line 3, respectively.

[0191] The super-spiral sliding mode constant current control link includes:

[0192] The data sampling module is configured to acquire a DC current in the DC transmission line 3 and a receiving end DC voltage in the receiving end AC system 5.

[0193] A state space expression construction module is configured to construct a state space expression of the HVDC power transmission system.

[0194] An equivalent control quantity determination module is configured to input the DC current and the receiving-end DC voltage into the state space expression to determine an equivalent control quantity.

[0195] A sliding mode quantity determination module is configured to determine a tracking error according to the DC current and a reference current, and determine the tracking error as a sliding mode quantity; the sliding mode quantity meets a requirement of a relative order of 1 in a hyper-spiral sliding mode control.

[0196] A switching control quantity determination module is configured to determine a switching control quantity based on a second-order sliding mode hyper-spiral algorithm.

[0197] A hyper-spiral sliding mode constant current control rate determination module is configured to determine a hyper-spiral sliding mode constant current control rate according to the equivalent control quantity and the switching control quantity; the hyper-spiral sliding mode constant current control rate meets a constraint condition of Lyapunov stability.

[0198] A transient overvoltage suppression module is configured to substitute the sliding mode quantity into the hyper-spiral sliding mode constant current control rate to determine a rectifier-side trigger angle signal; the rectifier-side trigger angle signal is configured to be input into a rectifier station 2 to suppress a transient overvoltage of a sending-end AC system 1.

[0199] The technical features of the above embodiments can be combined in any manner. To make the description concise, all possible combinations of the technical features in the above embodiments are not described, but as long as the combinations of the technical features do not contradict, they should be considered as the scope of the present application.

[0200] The principles and implementation manners of the present application are described by using specific examples in the present application. The above embodiments are only used to help understand the method and its core idea of the present application; meanwhile, for those skilled in the art, the specific implementation manners and application ranges can be changed according to the idea of the present application. In conclusion, the content of the present application should not be understood as a limitation.

Claims

1. A transient overvoltage suppression method, characterized in that: The transient overvoltage suppression method is used in a high-voltage direct current (HVDC) power transmission system, wherein the equivalent circuit of the high-voltage direct current (HVDC) power transmission system comprises: a sending-end AC system, a rectifier station, a DC transmission line, an inverter station, and a receiving-end AC system connected in sequence; The transient overvoltage suppression method comprises: Obtaining the DC current in the DC transmission line and the receiving-end DC voltage in the receiving-end AC system; Constructing the state space representation of the HVDC system; Inputting the DC current and the receiving-end DC voltage into the state-space expression to determine an equivalent control variable; Determining a tracking error based on the DC current and the reference current, and determining the tracking error as a sliding mode amount; wherein the sliding mode amount satisfies a requirement that the relative order in super-helical sliding mode control is 1; Determine the switching control quantity based on the second-order sliding mode super-helical algorithm; Determining a super-helical sliding mode constant current control rate according to the equivalent control amount and the switching control amount; wherein the super-helical sliding mode constant current control rate satisfies a constraint condition of Lyapunov stability; The sliding mode quantity is substituted into the super-helical sliding mode constant current control rate to determine the rectifier side trigger angle signal; the rectifier side trigger angle signal is used to input the rectifier station to suppress transient overvoltage of the sending end AC system.

2. The transient overvoltage suppression method according to claim 1, characterized in that: Construct the state space expression of the HVDC transmission system, including: Establish an equivalent mathematical model of the HVDC transmission system; Based on the equivalent mathematical model, a state space expression of a high-voltage direct current transmission system is constructed with direct current as a state variable and a rectifier-side trigger angle signal input to a rectifier station as a control signal.

3. The transient overvoltage suppression method according to claim 1, characterized in that: The state space expression is: Among them, x represents the state variable; represents the first-order derivative of x; u represents the control signal; I d represents the DC current; α represents the trigger angle signal on the rectifier side; a(x) represents the state intermediate variable; b represents the control coefficient; L d represents the equivalent inductance of the DC transmission line; U1 represents the sending-end AC bus voltage in the sending-end AC system; α0 represents the trigger angle signal corresponding to the stable operating point in the HVDC transmission system; X c1 Represents the commutation reactance of the rectifier station; R d Indicates the equivalent resistance of the DC transmission line; U d2 Indicates the receiving-end DC voltage in the receiving-end AC system.

4. The transient overvoltage suppression method according to claim 1, characterized in that: Inputting the DC current and the receiving-end DC voltage into the state-space expression to determine the equivalent control quantity specifically includes: Inputting the DC current and the receiving-end DC voltage into the state space expression to calculate the state intermediate variable and the control coefficient; The equivalent control amount is determined according to the state intermediate variable and the control coefficient; the expression for determining the equivalent control amount is: Among them, u eq represents the equivalent control quantity; a(x) represents the state intermediate variable; x represents the state variable; b represents the control coefficient.

5. The transient overvoltage suppression method according to claim 1, characterized in that: The expression of the sliding modulus is: s=e; e=I dref -I d ; Where s represents the sliding mode; e represents the tracking error; I dref Indicates the reference current; I d Indicates direct current.

6. The transient overvoltage suppression method according to claim 1, characterized in that: The expression of the switching control amount is: Among them, u sw represents the switching control variable; u1 represents the first control variable; u2 represents the second control variable; u·2 represents the first-order derivative of u2; s represents the sliding mode; λ1 and λ2 are both constants; sign represents the sign function.

7. The transient overvoltage suppression method according to claim 1, characterized in that: The expression of the super-helical sliding mode constant current control rate is: Where u represents the control signal; a(x) represents the state intermediate variable; x represents the state variable; b represents the control coefficient; s represents the sliding mode; λ1 and λ2 are both constants; and sign represents the sign function.

8. The transient overvoltage suppression method according to claim 7, characterized in that: The constraints for Lyapunov stability are:

9. The transient overvoltage suppression method according to claim 2, characterized in that: The expression of the equivalent mathematical model is: Among them, I d Indicates direct current; Indicates I d The first derivative of L d U represents the equivalent inductance of the DC transmission line; d1 Represents the sending-end DC voltage in the sending-end AC system; R d Indicates the equivalent resistance of the DC transmission line; U d2 Indicates the receiving-end DC voltage in the receiving-end AC system.

10. A transient overvoltage suppression system, characterized in that: The transient overvoltage suppression system is used to suppress transient overvoltages in a high-voltage direct current (HVDC) transmission system. The equivalent circuit of the high-voltage direct current (HVDC) transmission system comprises: a sending-end AC system, a rectifier station, a DC transmission line, an inverter station, and a receiving-end AC system connected in sequence. The transient overvoltage suppression system includes: a super-spiral sliding mode constant current control link; the super-spiral sliding mode constant current control link is connected to the rectifier station and the DC transmission line respectively; The super spiral sliding mode constant current control link includes: A data sampling module is used to obtain the DC current in the DC transmission line and the receiving-end DC voltage in the receiving-end AC system; State space expression building module, used to build the state space expression of the HVDC transmission system; an equivalent control quantity determination module, configured to input the DC current and the receiving-end DC voltage into the state space expression to determine an equivalent control quantity; a sliding mode determination module, configured to determine a tracking error based on the DC current and a reference current, and determine the tracking error as a sliding mode amount; wherein the sliding mode amount satisfies the requirement that the relative order in super-helical sliding mode control is 1; A switching control amount determination module, used for determining the switching control amount based on a second-order sliding mode super-helical algorithm; a super-helical sliding mode constant current control rate determination module, configured to determine a super-helical sliding mode constant current control rate according to the equivalent control amount and the switching control amount; wherein the super-helical sliding mode constant current control rate satisfies a Lyapunov stability constraint condition; The transient overvoltage suppression module is used to substitute the sliding mode quantity into the super-helical sliding mode constant current control rate to determine the rectifier side trigger angle signal; the rectifier side trigger angle signal is used to input the rectifier station to suppress the transient overvoltage of the sending end AC system.

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