A method for calculating and suppressing transient overvoltages at the sending end of an ultra-high voltage direct current (UHVDC) transmission system, considering the influence of multiple control links.

Abstract

This invention discloses a method for calculating and suppressing transient overvoltage at the sending end of an ultra-high voltage direct current (UHVDC) transmission system, considering the influence of multiple control links. Specifically, it involves: analyzing the operating characteristics and transient voltage influencing factors of the LCC-HVDC system, revealing that DC current is the key factor affecting the transient voltage change of the bus; decomposing the entire process of transient DC current under commutation failure based on the characteristics of DC current changes in the DC control system's operating curve, and deriving an approximate analytical expression for the DC current after the fault occurs; calculating the voltage drop across the equivalent resistance and reactance on the line respectively, and then substituting it into the DC current analytical expression to derive a quantitative calculation expression for the transient overvoltage of the sending end converter bus; obtaining the minimum allowable DC current value based on the upper limit of the transient overvoltage, and proposing an improved method for suppressing transient overvoltage under commutation failure with an improved minimum current command value for the VDCOL link. This invention achieves quantitative analysis of transient voltage and effectively reduces the transient overvoltage level of the sending end converter bus.

Description

Technical Field

[0001] This invention pertains to high-voltage direct current (HVDC) transmission system technology, and particularly relates to a method for calculating and suppressing transient overvoltages at the sending end of an ultra-high-voltage direct current (UHVDC) transmission system, taking into account the influence of multiple control links. Background Technology

[0002] With the large-scale construction of new energy power generation equipment, high-voltage direct current (LCC-HVDC) transmission projects based on grid-commutated converters play an important role in long-distance power transmission due to their advantages such as large DC transmission power, strong power regulation capability, and relatively low cost, effectively solving the problem of reverse distribution of energy and load centers in my country. Commutation failure is a unique fault in LCC-HVDC transmission systems. Compared with DC blocking faults, commutation failure has a shorter duration, and equipment in the grid is not disconnected during the fault. With the increasing penetration rate of new energy, more and more power electronic equipment is connected to the sending-end grid, leading to a weakening of the sending-end grid structure and a more serious problem of transient overvoltage caused by faults. When the transient voltage exceeds a certain threshold, it can cause the sending-end new energy equipment to disconnect from the grid, and in severe cases, it can also damage equipment in the DC system. Therefore, it is urgent to analyze and study the transient voltage stability under commutation failure conditions in LCC-HVDC systems.

[0003] Currently, numerous studies have analyzed the influencing factors of transient voltage at the sending end of HVDC transmission systems under fault conditions. Some studies divide the transient voltage change process into multiple stages, revealing the effects and extent of different DC control parameters on transient voltage. Other studies analyze the impact of DC system parameters on sending-end transient voltage through simulation, but do not explain or analyze the reasons for these effects.

[0004] Qualitative analysis of transient voltage alone cannot fully reveal the transient change process of the system. A mathematical model of the transient voltage is also needed for further quantitative analysis. Numerous studies have addressed the calculation of peak transient overvoltages, with three main methods commonly used: derivation through the relationship between reactive power increment and short-circuit capacity, the short-circuit ratio index, and power flow equations. Some literature analyzes the dynamic changes in the reactive power consumption characteristics of the rectifier during commutation failure and provides a method for calculating the peak transient overvoltage. Other literature uses formulas to express the reactive power transmitted from the DC system to the AC system, further solving for the analytical expression of the peak transient overvoltage at the sending-end bus, and studying the influence of the sending-end system strength and transmission power on the peak transient overvoltage.

[0005] Research on overvoltage suppression mainly focuses on reactive power compensation devices, wind farm operation optimization, and rectifier reactive power optimization. Some literature analyzes the suppression effect of reactive power compensation devices on transient overvoltages at the sending end during commutation failure. Other literature studies the effect of improving the high-voltage ride-through capability of wind farms on suppressing transient overvoltages. Still others investigate methods to suppress overvoltages by optimizing DC control system parameters. However, most research on VDCOL control focuses on how to suppress commutation failures, lacking mechanistic analysis of the impact of VDCOL control on AC overvoltages at the sending end. Since VDCOL control provides a DC current reference value to the DC control system, affecting the reactive power characteristics of the rectifier, transient overvoltages at the sending end can also be suppressed by improving the VDCOL circuit.

[0006] In summary, in order to overcome the overvoltage problem at the sending end caused by the failure of receiving-end commutation in UHVDC, it is urgent to propose a more detailed calculation method and design a transient overvoltage suppression strategy accordingly. Summary of the Invention

[0007] To address the transient overvoltage problem at the sending end of an HVDC system due to commutation failure, this invention provides a method for calculating and suppressing transient overvoltage at the sending end of an ultra-high voltage direct current transmission system, taking into account the influence of multiple control links.

[0008] The present invention provides a method for calculating and suppressing transient overvoltages at the sending end of an ultra-high voltage direct current transmission system, considering the influence of multiple control links, comprising the following steps:

[0009] Step 1: Analysis of the operating characteristics and transient voltage influencing factors of the LCC-HVDC system reveals that DC current is the key factor affecting the change of bus transient voltage.

[0010] Step 2: Based on the characteristics of DC current change in the DC control system operating curve, decompose the entire process of transient DC current under commutation failure and derive an approximate analytical expression for DC current after the fault occurs.

[0011] Step 3: Calculate the voltage drop across the equivalent resistance and reactance on the line respectively, and then substitute it into the DC current analytical formula to derive the quantitative calculation expression for the transient overvoltage of the sending-end converter bus.

[0012] Step 4: Based on the upper limit of transient overvoltage, the minimum allowable DC current is obtained, and an improved method for suppressing transient overvoltage under commutation failure with minimum current command value of VDCOL circuit is proposed.

[0013] Furthermore, step 1 specifically involves:

[0014] S1.1: Analysis of the operating characteristics of the LCC-HVDC system.

[0015] In the equivalent circuit of the LCC-HVDC system, U sP is the equivalent power supply voltage in the sending-end AC system; s Q s These represent the active and reactive power transmitted from the sending-end power source to the converter station along the line; R s and X s These are the equivalent resistance and equivalent reactance on the sending-end system lines, respectively, and their values ​​affect the electrical strength of the sending-end system; U p Q is the voltage of the sending-end converter bus; cp The reactive power compensated by the AC filter at the sending end; U dr U is the DC voltage on the rectifier side. di I is the DC voltage on the inverter side. dc It is direct current.

[0016] In the LCC-HVDC control system, both the rectifier side and the inverter side are equipped with constant current (CC) control and low-voltage current limiting (VDCOL) control loops. The constant current control loop generates a lead trigger angle command value through a PI controller, while the low-voltage current limiting control loop generates a DC current command value by measuring the DC voltage in real time. Moreover, the DC current command value on the inverter side is lower than that on the rectifier side by a margin. In addition, the inverter side is also equipped with a current deviation (CE) controller and a constant turn-off angle (CEA) controller. The function of the current deviation control is to achieve smooth switching between the inverter side's CC and CEA.

[0017] S1.2: Analysis of factors affecting transient voltage.

[0018] During commutation failure, the rectifier's ability to consume reactive power directly affects the transient overvoltage level of the sending-end converter bus; the reactive power Q consumed by the rectifier during the transient response process... dc Represented as:

[0019]

[0020] In the formula, P r The rectifier transmits active power; the subscript r represents the rectifier side. The power factor angle; U r0 This is the DC open-circuit voltage.

[0021] The DC voltage on the rectifier side satisfies the following relationship:

[0022]

[0023] In the formula, N r The number of 6 pulsed converters per pole; T r X is the converter transformer turns ratio; α is the rectifier-side firing angle, γ is the inverter-side turn-off angle; cr This is the commutation reactance.

[0024] Combining equations (1) and (2), we get Q. dcThe expression is:

[0025]

[0026] As can be seen from equation (3), the dynamic reactive power characteristics of the rectifier are related to the firing angle α and the DC current I. dc They are closely related, and the reactive power consumed by the rectifier is positively correlated with the DC current. The magnitude of the DC current directly determines the magnitude of the reactive power consumed by the rectifier.

[0027] The relationship between the surplus reactive power of the sending-end system and the transient overvoltage of the sending-end converter bus is expressed as follows:

[0028]

[0029] The expression for ΔQ is:

[0030] ΔQ=Q dc -Q cp (5)

[0031] In the formula, ΔU is the transient voltage change of the sending-end converter bus; ΔQ is the reactive power exchange between the rectifier and the sending-end AC system; S d This refers to the short-circuit capacity at the sending-end converter bus.

[0032] As can be seen from equation (4), when the short-circuit capacity of the sending-end converter bus is constant, the transient voltage change of the converter bus directly depends on the reactive power exchange ΔQ between the rectifier and the sending-end AC system. A positive value is the reactive power absorbed from the system, and a negative value is the reactive power sent to the system. Therefore, the dynamic reactive power characteristics of the rectifier directly affect the reactive power exchange between the DC and the sending-end AC system during the transient process, which further affects the transient voltage of the sending-end converter bus.

[0033] Therefore, it can be concluded that direct current is the key factor affecting the change of bus transient voltage.

[0034] Furthermore, step 2 specifically involves:

[0035] Based on the characteristics of DC current variation in the DC control system's operating curve, the entire transient DC current process under commutation failure is decomposed into the following six processes:

[0036] (1) The process of DC current rising.

[0037] After a three-phase short circuit occurs on the receiving end AC bus, the receiving end AC voltage drops due to the system short circuit fault, causing the inverter-side converter to fail to commutate. Due to the short circuit on the inverter side, the inverter-side DC voltage drops rapidly to 0, and the DC current rises rapidly in a short time. At this time, the rectifier-side CC control has not yet responded, and the DC current is affected by the inverter-side turn-off angle control.

[0038] The shut-off angle γ and the minimum shut-off angle γ in steady state of the control system min The deviation value is processed by the proportional-integral stage G. PI (s) The inverter-side lead-fire angle β is obtained, and the lead-fire angle is further used as a control signal to adjust and control the turn-off angle.

[0039] G γ (s) is a function for calculating the inverter-side turn-off angle, obtained through the relationship between the turn-off angle and the lead-out angle in steady state, as shown in equation (6):

[0040]

[0041] In the formula, U Li The transient voltage of the receiving-end converter bus is represented by the subscript i, indicating the inverter side; T i X represents the turns ratio of the converter transformer. ci This is the commutation reactance.

[0042] G meas (s) represents the valve group signal measurement stage, indicating the delay effect during signal processing:

[0043]

[0044] In the formula, K m For measuring the gain coefficient of the circuit; T m This is the delay coefficient for the measurement process.

[0045] When the LCC-HVDC system is operating in steady state, the DC current is expressed as:

[0046]

[0047] The expression for the lead firing angle β obtained from the above calculations can be substituted into the transfer function to obtain the expression for the turn-off angle γ. Substituting γ into equation (8) yields the expression for the DC current I. dc1 As shown below:

[0048]

[0049] The expression for variable K1 is:

[0050] K1=m1cosh(a1t-b1)+n1sinh(a1t-b1) (10)

[0051] In the formula, a i b i m i n i p i q i θ i k i hi i = 1 to 6 are the calculation parameters for the intermediate process; I dN This represents the steady-state value of the DC current before the fault.

[0052] (2) The process of DC current decrease.

[0053] When the DC voltage drops to the upper limit of the VDCOL voltage threshold, VDCOL starts and adjusts the DC current command value to limit the DC current and suppress the continuous increase of the DC current.

[0054] Due to the continuous decrease in the DC voltage on the inverter side, the current command I output by VDCOL... order The DC current decreases because the actual value is still higher than the commanded value, causing the inverter-side CC control to fail to respond; the rectifier-side CC control takes effect, reducing U by increasing the firing angle α. dr This causes the DC current to decrease and gradually approach the current DC current command value; G PI (s) is the transfer function of the PI element, G α (s), G R (s) and G meas (s) are the transfer functions of the converter link, DC line link and measurement link, respectively.

[0055] The transfer functions in the control loop are as follows:

[0056]

[0057] In the formula, Kcα is the proportional gain coefficient of the converter stage; Tcα is the delay coefficient.

[0058] The relationship between the rectifier-side firing angle α and the lead firing angle β is as follows:

[0059] α=180°-β (13)

[0060] Substituting the obtained lead firing angle β into equation (13), we get the expression for the firing angle α. Substituting this into equation (8), we get the expression for the DC current I. dc2 As shown below:

[0061]

[0062] The expressions for K2 and K3 are:

[0063] K2=m2cos(a2t-b2)+n2sin(a2t-b2) (15)

[0064] K3=p2t-q2 (16)

[0065] In the formula, I dcmax This is the maximum value that the DC current can reach during its rise.

[0066] (3) DC current oscillation process.

[0067] At this point, the DC voltage on the inverter side has decreased to 0. According to the VDCOL characteristics, once the DC voltage on the inverter side falls below its lower voltage threshold, the output DC current command value I... order The current drops to the minimum command value, and then I... order If it remains unchanged, the DC current will oscillate within a small range near the minimum current command value.

[0068] The DC current expression for this process is I dc3 As shown below:

[0069]

[0070] (4) DC current fluctuation process.

[0071] During the DC system recovery phase after fault clearance, due to overshoot in the CEA control on the inverter side, the turn-off angle γ will rapidly jump to over 90°. At this time, the DC current will increase slightly. The rectifier-side CC circuit increases the firing angle command value through PI control, and simultaneously, the rectifier-side DC voltage U... dr The continued decline has led to I dc A slight decrease; the DC current expression for this process is I. dc4 As shown below:

[0072]

[0073] (5) DC current recovery process, i.e. constant current control.

[0074] Since the inverter has resumed normal commutation at this time, the AC bus voltage recovers quickly, and the DC voltage U on the inverter side increases. di As I increases rapidly, the current command value output by VDCOL gradually rises, until I... dc When the current is less than the inverter-side CC control current command value, the inverter-side DC control system will switch from CEA control to CC control. During this process, the DC short-circuit current will gradually increase and approach the current command value. The regulating effect of the rectifier-side CC control can be ignored at this time, and the inverter side will take the lead in control and regulation. The DC current expression for this process is I. dc5 As shown below:

[0075]

[0076] (6) DC current recovery process, i.e. fixed turn-off angle control.

[0077] Under the action of the CC control loop on the inverter side, I dcAs the DC current gradually approaches the current command value, when the DC current exceeds the reference value of the inverter-side CC control, the CC control effect weakens. At the same time, the set turn-off angle is still greater than the steady-state value. The inverter-side DC control system begins to enter CE control for transition, ensuring the stability of each transient control quantity during this process, so that the transition process of the control loop can proceed smoothly. Then, it switches to CEA control.

[0078] The expression for the lead-fire angle β is obtained through calculation. Substituting β into the transfer function yields the expression for the turn-off angle γ. Substituting γ into equation (8) yields the expression for the DC current I. dc6 As shown below:

[0079]

[0080] K4=m6 cos(a6t+b6)+n6 sin(a6t+b6) (21)

[0081] Furthermore, step 3 specifically involves:

[0082] From the power flow calculation relationship from the power source to the converter bus in the equivalent circuit of the LCC-HVDC sending-end system, the longitudinal and transverse components of the voltage drop on the transmission line of the sending-end system can be obtained respectively. Therefore, the voltage at the sending-end converter bus is expressed as:

[0083]

[0084] In the formula, ΔU s The longitudinal component of voltage drop in an AC line; δU s This represents the transverse component of voltage drop in an AC line.

[0085] In steady state, the active and reactive power transmitted on the transmission lines of the sending-end system is equal to the output power P of the sending-end power source. s and Q s That is, it satisfies the following relationship:

[0086]

[0087] The reactive power generated by the reactive power compensation device is expressed as follows:

[0088]

[0089] In the formula, B c The equivalent susceptance is the reactive power compensation device at the sending end.

[0090] When the converter bus voltage increases, the reactive power compensation of the AC filter increases with the voltage increase. Simultaneously, during the recovery from a commutation failure, the reactive power consumed by the converter station also changes. Therefore, the actual reactive power transmitted from the converter station to the AC system during the transient process is expressed as:

[0091]

[0092] In the formula, U p0 It is the voltage of the AC bus at the feed end before the fault, Q. cp0 This represents the reactive power output of the AC filter before the fault; neglecting the effect of commutation reactance, the active and reactive power consumed by the rectifier are expressed as follows:

[0093]

[0094] During the transient process, the active power and reactive power exchanged between the DC system and the sending-end AC system are respectively:

[0095]

[0096] By simplifying the analysis of the sending-end system, it is assumed that the voltage drop between the sending-end power supply and the sending-end converter bus exists only in the equivalent impedance of the line. The voltage drops across the equivalent resistance and equivalent reactance are calculated separately, and the expression for calculating the transient voltage of the sending-end converter bus is obtained as follows:

[0097]

[0098] In the formula, R s X is the equivalent resistance of the sending-end AC power grid. s The equivalent reactance of the sending-end AC power grid.

[0099] By combining equations (27) and (28), we can derive U. p The expression is:

[0100]

[0101] In the formula, the expression for algebraic b is:

[0102]

[0103] By substituting the analytical expression for DC current into the above formula, the quantitative calculation formula for transient voltage at the sending-end converter bus can be obtained.

[0104] Furthermore, step 4 specifically involves:

[0105] VDCOL is a crucial control element in a DC control system. It can detect the DC voltage in real time and output corresponding DC current command values ​​based on the characteristic curve to adjust the current and promote the commutation process. The VDCOL characteristic curve mainly consists of two parts: one is the VDCOL inflection point parameter, namely the low-voltage start-up threshold U. dl and high voltage start threshold U dh The lower limit of the current command value I dl and the upper limit of the current command value I dhSecondly, there is the VDCOL line type. In traditional VDCOL, the voltage and current have a linear relationship and the slope is fixed.

[0106] The DC current command value output by the VDCOL stage is expressed as:

[0107]

[0108] In the formula, U d * The voltage per unit value at the midpoint of the DC line after conversion is used as the input value of VDCOL; k and b are the coefficients of the operating characteristic curve, where k = (I dh -I dl ) / (U dh -U dl b = -U dl (I dh -I dl ) / (U dh -U dl ).

[0109] After the DC current reaches its minimum value during its fluctuation phase, it begins to recover. Solving the expression for the DC current during this phase, we obtain that the minimum DC current value is 0.23pu. When the peak value of the transient overvoltage is limited to below 1.1pu, according to equation (32), the DC current must be higher than 0.4pu.

[0110]

[0111] Because the transfer function in the DC current decrease, oscillation, and fluctuation processes all have a measurement element G. meas (s) Measurement delay T m The influence of this causes the rectifier side constant current control loop to increase the firing angle command during the DC current fluctuation phase, resulting in DC current overshoot. The DC current will drop to a smaller value below the lower limit of the current command value of 0.55pu.

[0112] In the improved VDCOL, the DC current overshoot effect caused by the rectifier side constant current control remains basically unchanged in this stage. Therefore, the lower limit of the current command value needs to be increased by the value ΔI. dl =0.4-0.23=0.17pu. By adding this value to the original control strategy, we can obtain that the lower limit of the current command value output by the VDCOL stage needs to be greater than 0.72pu.

[0113] The beneficial technical effects of this invention are as follows:

[0114] 1) This invention analyzes the impact of the DC control system on transient voltage during commutation failure, and concludes that DC current is the key influencing factor on the transient voltage at the sending end. It also derives an approximate analytical expression for DC current and further considers the voltage drop between the converter bus and the equivalent power supply at the sending end caused by power transmission. The invention derives a quantitative calculation formula for the transient voltage at the converter bus at the sending end under commutation failure, thus realizing the quantitative analysis of transient voltage.

[0115] 2) Compared with the conventional VDCOL control loop, the present invention improves the VDCOL control loop based on the transient overvoltage limit constraint. The current command value output by the improved VDCOL control loop can suppress the excessive DC current drop, effectively reduce the transient overvoltage level of the sending-end converter bus, and help the equipment in the high voltage DC sending-end system to operate safely and stably. Attached Figure Description

[0116] Figure 1 This is the equivalent circuit of the LCC-HVDC system.

[0117] Figure 2 This is a DC control system in an LCC-HVDC system.

[0118] Figure 3 The transient voltage curve of the converter bus at the sending end is shown in the figure for a failed commutation.

[0119] Figure 4 This is the DC system operation curve during fault recovery.

[0120] Figure 5 This is the transfer function for the inverter side's fixed shut-off angle control.

[0121] Figure 6 The block diagram shows the transfer function for the constant current control on the rectifier side.

[0122] Figure 7 This is the transfer function for the rectifier side constant current control after the low-voltage current limiting reaches the threshold.

[0123] Figure 8 This is the transfer function for the inverter side's fixed shut-off angle control.

[0124] Figure 9 This is the VDCOL characteristic curve.

[0125] Figure 10 The relationship between low-voltage current limiting circuit parameters and overvoltage ((a) Lower limit of VDCOL circuit current command value I) dl (b) VDCOL high-voltage start-up threshold U dh (c) VDCOL low-voltage start-up threshold U dl ).

[0126] Figure 11To improve the VDCOL curve.

[0127] Figure 12 A comparison diagram of theoretical calculations and actual simulations ((a) DC current I) dc (a) Transient response process; (b) Transient response process of rectifier side firing angle α; (c) Sending-end bus voltage U p (Transient response process).

[0128] Figure 13 Transient voltage and DC current of the sending-end converter bus under a three-phase short-circuit fault ((a) transient voltage of the sending-end converter bus; (b) DC current).

[0129] Figure 14 Transient voltage and DC current of the sending-end converter bus under a single-phase short-circuit fault ((a) transient voltage of the sending-end converter bus; (b) DC current). Detailed Implementation

[0130] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0131] The present invention provides a method for calculating and suppressing transient overvoltages at the sending end of an ultra-high voltage direct current transmission system, considering the influence of multiple control links, comprising the following steps:

[0132] Step 1: Analysis of the operating characteristics and transient voltage influencing factors of the LCC-HVDC system reveals that DC current is the key factor affecting the change of bus transient voltage.

[0133] S1.1: Analysis of the operating characteristics of the LCC-HVDC system.

[0134] The equivalent circuit of an LCC-HVDC system is as follows: Figure 1 As shown: U s P is the equivalent power supply voltage in the sending-end AC system; s Q s These represent the active and reactive power transmitted from the sending-end power source to the converter station along the line; R s and X s These are the equivalent resistance and equivalent reactance on the sending-end system lines, respectively, and their values ​​affect the electrical strength of the sending-end system; U p Q is the voltage of the sending-end converter bus; cp The reactive power compensated by the AC filter at the sending end; U dr U is the DC voltage on the rectifier side. di I is the DC voltage on the inverter side. dc It is direct current.

[0135] The control system in LCC-HVDC, such as Figure 2As shown, both the rectifier and inverter sides are equipped with constant current (CC) control and low-voltage current limiting (VDCOL) control loops. The constant current control loop generates an advance firing angle command value through a PI controller, while the low-voltage current limiting control loop generates a DC current command value by measuring the DC voltage in real time. Moreover, the DC current command value on the inverter side is lower than that on the rectifier side by a margin (0.1pu). In addition, the inverter side is also equipped with a current deviation (CE) controller and a constant turn-off angle (CEA) control. The function of the current deviation control is to achieve smooth switching between CC and CEA on the inverter side.

[0136] S1.2: Analysis of factors affecting transient voltage.

[0137] Commutation failure occurs only on the inverter side of the system and is usually caused by an AC fault on the inverter side. At the initial moment of the fault, the DC current suddenly rises, increasing the rectifier's reactive power consumption capacity. The rectifier absorbs a large amount of reactive power from the sending-end system, causing a drop in the transient voltage of the sending-end converter bus. During the recovery process after the commutation failure, the DC current is smaller, and the reactive power consumption of the sending-end converter station is smaller. However, the sending-end AC filter cannot be disconnected in time, causing a large amount of surplus reactive power to surge to the sending-end system, resulting in a transient overvoltage at the bus. The transient voltage curve is shown below. Figure 3 As shown.

[0138] During commutation failure, the rectifier's ability to consume reactive power directly affects the transient overvoltage level of the sending-end converter bus; the reactive power Q consumed by the rectifier during the transient response process... dc Represented as:

[0139]

[0140] In the formula, P r Transmit active power to the rectifier (the subscript r represents the rectifier side, the same below); The power factor angle; U r0 This is the DC open-circuit voltage.

[0141] The DC voltage on the rectifier side satisfies the following relationship:

[0142]

[0143] In the formula, N r The number of 6 pulsed converters per pole; T r X is the converter transformer turns ratio; α is the rectifier-side firing angle, γ is the inverter-side turn-off angle; cr This is the commutation reactance (which can be ignored for simplified analysis).

[0144] Combining equations (1) and (2), we get Q. dc The expression is:

[0145]

[0146] As can be seen from equation (3), the dynamic reactive power characteristics of the rectifier are related to the firing angle α and the DC current I. dc They are closely related, and the reactive power consumed by the rectifier is positively correlated with the DC current. The magnitude of the DC current directly determines the magnitude of the reactive power consumed by the rectifier.

[0147] The relationship between the surplus reactive power of the sending-end system and the transient overvoltage of the sending-end converter bus is expressed as follows:

[0148]

[0149] The expression for ΔQ is:

[0150] ΔQ=Q dc -Q cp (5)

[0151] In the formula, ΔU is the transient voltage change of the sending-end converter bus; ΔQ is the reactive power exchange between the rectifier and the sending-end AC system; S d This refers to the short-circuit capacity at the sending-end converter bus.

[0152] As can be seen from equation (4), when the short-circuit capacity of the sending-end converter bus is constant, the transient voltage change of the converter bus directly depends on the reactive power exchange ΔQ between the rectifier and the sending-end AC system. A positive value is the reactive power absorbed from the system, and a negative value is the reactive power sent to the system. Therefore, the dynamic reactive power characteristics of the rectifier directly affect the reactive power exchange between the DC and the sending-end AC system during the transient process, which further affects the transient voltage of the sending-end converter bus.

[0153] In summary, the main reason for transient overvoltage at the sending-end converter bus is that during commutation failure, the overshoot of the rectifier-side current control circuit reduces the DC current to a very small value, even close to zero. This causes a change in the firing angle command value, which in turn reduces the rectifier's ability to consume reactive power. The AC filter then injects a large amount of reactive power into the sending-end AC system, leading to overvoltage. Therefore, DC current is a key factor affecting the transient voltage change of the bus. To quantitatively analyze the transient voltage change characteristics of the sending-end converter bus under commutation failure, it is necessary to clarify the transient response process of the DC control system and the DC current.

[0154] Step 2: Based on the characteristics of DC current change in the DC control system operating curve, decompose the entire process of transient DC current under commutation failure and derive an approximate analytical expression for DC current after the fault occurs.

[0155] Detailed calculations of DC current require consideration of the switching effects of control loops and the establishment of transfer functions for these control loops. Due to the nonlinear characteristics of thyristor devices in the converter unit, the converter's response during a fault is highly complex, making it difficult to accurately describe the dynamic changes during the transient period after the fault. Furthermore, it involves complex differential calculations. Therefore, a linearization method is used to approximate the DC system over a certain period after the fault to reduce the complexity of the problem. The DC system operation curve during the fault recovery period of the LCC-HVDC system is shown below. Figure 4 As shown.

[0156] In an LCC-HVDC system, the DC control system comprises multiple control links. During a fault-induced transient process, different control links may switch or multiple control links may operate simultaneously. Therefore, based on the switching logic of the control links, the entire transient process is divided into three stages: the initial stage of the fault, the control system response stage after the fault causes commutation failure, and the fault clearing and recovery stage. Further, based on the characteristics of DC current changes in the DC control system's operating curve, the entire transient DC current process under commutation failure is decomposed into the following six processes:

[0157] (1) The process of DC current rising.

[0158] After a three-phase short circuit occurs on the receiving-end AC bus, the receiving-end AC voltage drops due to the system short-circuit fault, causing commutation failure in the inverter-side converter. Because of the inverter-side short circuit, the inverter-side DC voltage rapidly drops to 0, and the DC current rises rapidly within a short time. At this time, the rectifier-side CC control has not yet responded, and the DC current is affected by the inverter-side turn-off angle control. The transfer function block diagram of the inverter-side constant turn-off angle control is shown below. Figure 5 As shown.

[0159] The shut-off angle γ and the minimum shut-off angle γ in steady state of the control system min The deviation value is processed by the proportional-integral stage G. PI (s) The inverter-side lead-fire angle β is obtained, and the lead-fire angle is further used as a control signal to adjust and control the turn-off angle.

[0160] G γ (s) is a function for calculating the inverter-side turn-off angle, obtained through the relationship between the turn-off angle and the lead-out angle in steady state, as shown in equation (6):

[0161]

[0162] In the formula, U Li The transient voltage of the receiving-end converter bus is represented by the subscript i, indicating the inverter side; T i X represents the turns ratio of the converter transformer. ci This is the commutation reactance.

[0163] G meas (s) represents the valve group signal measurement stage, indicating the delay effect during signal processing:

[0164]

[0165] In the formula, K m For measuring the gain coefficient of the circuit; T m This is the delay coefficient for the measurement process.

[0166] When the LCC-HVDC system is operating in steady state, the DC current is expressed as:

[0167]

[0168] The expression for the lead firing angle β obtained from the above calculations can be substituted into the transfer function to obtain the expression for the turn-off angle γ. Substituting γ into equation (8) yields the expression for the DC current I. dc1 As shown below:

[0169]

[0170] The expression for variable K1 is:

[0171] K1=m1cosh(a1t-b1)+n1sinh(a1t-b1) (10)

[0172] In the formula, a i b i m i n i p i q i θ i k i h i i = 1 to 6 are the calculation parameters for intermediate processes; I dN This represents the steady-state value of the DC current before the fault.

[0173] (2) The process of DC current decrease.

[0174] When the DC voltage drops to the upper limit of the VDCOL voltage threshold, VDCOL starts and adjusts the DC current command value to limit the DC current and suppress the continuous increase of the DC current.

[0175] Due to the continuous decrease in the DC voltage on the inverter side, the current command I output by VDCOL... order The DC current decreases because the actual value is still higher than the commanded value, causing the inverter-side CC control to fail to respond; the rectifier-side CC control takes effect, reducing U by increasing the firing angle α. dr This causes the DC current to decrease and gradually approach the current commanded DC current value. The transfer function block diagram is as follows: Figure 6 As shown, G PI (s) is the transfer function of the PI element, G α (s), G R (s) and G meas (s) are the transfer functions of the converter link, DC line link and measurement link, respectively.

[0176] The transfer functions in the control loop are as follows:

[0177]

[0178] In the formula, Kcα is the proportional gain coefficient of the converter stage; Tcα is the delay coefficient.

[0179] The relationship between the rectifier-side firing angle α and the lead firing angle β is as follows:

[0180] α=180°-β (13)

[0181] Substituting the obtained lead firing angle β into equation (13), we get the expression for the firing angle α. Substituting this into equation (8), we get the expression for the DC current I. dc2 As shown below:

[0182]

[0183] The expressions for K2 and K3 are:

[0184] K2=m2cos(a2t-b2)+n2sin(a2t-b2) (15)

[0185] K3=p2t-q2 (16)

[0186] In the formula, I dcmax This is the maximum value that the DC current can reach during its rise.

[0187] (3) DC current oscillation process.

[0188] At this point, the DC voltage on the inverter side has decreased to 0. According to the VDCOL characteristics, once the DC voltage on the inverter side falls below its lower voltage threshold, the output DC current command value I... order The current drops to the minimum command value, and then I... order The DC current remains unchanged, oscillating within a small range near the minimum current command value. The transfer function block diagram is as follows: Figure 7 As shown.

[0189] The DC current expression for this process is I dc3 As shown below:

[0190]

[0191] (4) DC current fluctuation process.

[0192] During the DC system recovery phase after fault clearance, due to overshoot in the CEA control on the inverter side, the turn-off angle γ will rapidly jump to over 90°. At this time, the DC current will increase slightly. The rectifier-side CC circuit increases the firing angle command value through PI control, and simultaneously, the rectifier-side DC voltage U... dr The continued decline has led to I dc A slight decrease; the DC current expression for this process is I. dc4 As shown below:

[0193]

[0194] (5) DC current recovery process, i.e. constant current control.

[0195] Since the inverter has resumed normal commutation at this time, the AC bus voltage recovers quickly, and the DC voltage U on the inverter side increases. di As I increases rapidly, the current command value output by VDCOL gradually rises, until... dc When the current is less than the inverter-side CC control current command value, the inverter-side DC control system will switch from CEA control to CC control. During this process, the DC short-circuit current will gradually increase and approach the current command value. The regulating effect of the rectifier-side CC control can be ignored at this time, and the inverter side will take the lead in control and regulation. The DC current expression for this process is I. dc5 As shown below:

[0196]

[0197] (6) DC current recovery process, i.e. fixed turn-off angle control.

[0198] Under the action of the CC control loop on the inverter side, I dc As the DC current gradually approaches the current command value, when it exceeds the inverter-side CC control reference value, the CC control effect weakens. Simultaneously, the set-off angle remains greater than the steady-state value, and the inverter-side DC control system transitions to CE control to ensure the stability of transient control quantities during this process, allowing for a smooth transition in the control loop. Then, it switches to CEA control. The transfer function block diagram is shown below. Figure 8 As shown, the cut-off angle is used to calculate the transfer function G. r (s), PI element transfer function G PI The transfer function (s) and the measurement link are consistent with the transfer function expression in the aforementioned process.

[0199] The expression for the lead-fire angle β is obtained through calculation. Substituting β into the transfer function yields the expression for the turn-off angle γ. Substituting γ into equation (8) yields the expression for the DC current I. dc6 As shown below:

[0200]

[0201] K4=m6 cos(a6t+b6)+n6 sin(a6t+b6) (21)

[0202] Step 3: Calculate the voltage drop across the equivalent resistance and reactance on the line respectively, and then substitute it into the DC current analytical formula to derive the quantitative calculation expression for the transient overvoltage of the sending-end converter bus.

[0203] In practical DC transmission projects, the voltage drop caused by the equivalent impedance on the sending-end transmission line needs to be considered. Therefore, current research generally uses power flow equations to calculate the transient voltage at the sending-end bus. This invention simplifies the analysis by calculating the voltage drop across the equivalent resistance and reactance on the line separately, and then substituting these values ​​into the DC current analytical formula to derive a quantitative expression for the transient voltage at the converter bus.

[0204] From the power flow calculation relationship from the power source to the converter bus in the equivalent circuit of the LCC-HVDC sending-end system, the longitudinal and transverse components of the voltage drop on the transmission line of the sending-end system can be obtained respectively. Therefore, the voltage at the sending-end converter bus is expressed as:

[0205]

[0206] In the formula, ΔU s The longitudinal component of voltage drop in an AC line; δU s This represents the transverse component of voltage drop in an AC line.

[0207] In steady state, the active and reactive power transmitted on the transmission lines of the sending-end system is equal to the output power P of the sending-end power source. s and Q s That is, it satisfies the following relationship:

[0208]

[0209] The reactive power generated by the reactive power compensation device is expressed as follows:

[0210]

[0211] In the formula, B c The equivalent susceptance is the reactive power compensation device at the sending end.

[0212] When the converter bus voltage increases, the reactive power compensation of the AC filter increases with the voltage increase. Simultaneously, during the recovery from a commutation failure, the reactive power consumed by the converter station also changes. Therefore, the actual reactive power transmitted from the converter station to the AC system during the transient process is expressed as:

[0213]

[0214] In the formula, U p0 It is the voltage of the AC bus at the feed end before the fault, Q. cp0 This represents the reactive power output of the AC filter before the fault; neglecting the effect of commutation reactance, the active and reactive power consumed by the rectifier are expressed as follows:

[0215]

[0216] During the transient process, the active power and reactive power exchanged between the DC system and the sending-end AC system are respectively:

[0217]

[0218] By simplifying the analysis of the sending-end system, it is assumed that the voltage drop between the sending-end power supply and the sending-end converter bus exists only in the equivalent impedance of the line. The voltage drops across the equivalent resistance and equivalent reactance are calculated separately, and the expression for calculating the transient voltage of the sending-end converter bus is obtained as follows:

[0219]

[0220] In the formula, R s X is the equivalent resistance of the sending-end AC power grid. s The equivalent reactance of the sending-end AC power grid.

[0221] By combining equations (27) and (28), we can derive U. p The expression is:

[0222]

[0223] In the formula, the expression for algebraic b is:

[0224]

[0225] By substituting the analytical expression for DC current into the above formula, the quantitative calculation formula for transient voltage at the sending-end converter bus can be obtained. Step 4: Based on the upper limit of transient overvoltage, the minimum allowable DC current value is obtained, and an improved method for suppressing transient overvoltage under commutation failure with the minimum current command value of the VDCOL link is proposed.

[0226] VDCOL is a crucial control element in a DC control system. It can detect the DC voltage in real time and output corresponding DC current command values ​​based on its characteristic curve to adjust the current and facilitate the commutation process. The VDCOL characteristic curve is shown below. Figure 9 As shown, it mainly consists of two parts: one is the VDCOL inflection point parameter, namely the low-voltage start-up threshold U. dl and high voltage start threshold U dh The lower limit of the current command value I dl and the upper limit of the current command value Idh Secondly, there is the VDCOL line type. In traditional VDCOL, the voltage and current have a linear relationship and the slope is fixed.

[0227] The DC current command value output by the VDCOL stage is expressed as:

[0228]

[0229] In the formula, U d * The voltage per unit value at the midpoint of the DC line after conversion is used as the input value of VDCOL; k and b are the coefficients of the operating characteristic curve, where k = (I dh -I dl ) / (U dh -U dl b = -U dl (I dh -I dl ) / (U dh -U dl ).

[0230] like Figure 10 The impact of relevant parameters on the overvoltage of the AC bus at the sending end after commutation failure is presented. The high and low starting thresholds of the DC voltage in the VDCOL characteristic curve determine the dynamic performance of the low-voltage current limiting control. If the high voltage starting threshold is too large, the current command value will fluctuate drastically under small disturbances, while if it is too small, the system will not be sensitive enough to voltage fluctuations. If the low voltage starting threshold is too low, the current will recover too early. The difference between the high and low voltage starting thresholds determines the rate of change of the current command value. The larger the value, the better the effect of limiting DC current, but the current rise during the voltage recovery process after the fault will be rapid, which will have a greater impact on the system.

[0231] When the DC current follows the VDCOL circuit, the minimum current command value I is output. dl When the voltage drops and continues to drop to its minimum value due to the overshoot effect of the constant current control loop, the reactive power consumed by the rectifier also reaches its minimum. At this time, the severity of transient overvoltage is the greatest.

[0232] Since the inflection point parameters and slope of the traditional VDCOL characteristic curve are fixed, it is impossible to achieve good control performance of the system during transient changes. Therefore, this invention affects the DC current recovery characteristics by improving the lower limit of the DC current command value output by the VDCOL link. During the transient overvoltage of the sending-end converter bus, the DC current is adjusted to increase the reactive power consumption of the rectifier and reduce the reactive power imbalance between the AC and DC systems, so as to suppress the peak value of transient overvoltage.

[0233] right Figure 10 Analysis shows that the lower limit of the current command value I dlThe change has a greater impact on transient voltage than other inflection point parameters. Therefore, the suppression strategy proposed in this invention uses the transient voltage of 1.1pu at the sending end converter bus as a constraint condition. The minimum limit of DC current is obtained through the quantitative calculation expression of transient voltage. Based on this limit, the lower limit of the current command value output by VDCOL is improved. By suppressing the DC current drop too low, the minimum value of DC current during the decreasing process is increased, thereby achieving the method of suppressing transient overvoltage.

[0234] Analysis of the DC current curve shows that the DC current begins to recover after reaching its minimum value during its fluctuation phase. Solving the DC current expression for this phase yields a minimum DC current value of 0.23 pu. When the peak value of the transient overvoltage is limited to below 1.1 pu, according to equation (32), the DC current must be higher than 0.4 pu.

[0235]

[0236] Because the transfer function in the DC current decrease, oscillation, and fluctuation processes all have a measurement element G. meas (s) Measurement delay T m The influence of this causes the rectifier side constant current control loop to increase the firing angle command during the DC current fluctuation phase, resulting in DC current overshoot. The DC current will drop to a smaller value below the lower limit of the current command value of 0.55pu.

[0237] The improved VDCOL characteristic curve diagram is shown below. Figure 11 As shown, during this stage, the DC current overshoot effect caused by the rectifier side constant current control remains basically unchanged, so the lower limit of the current command value needs to be increased by the value ΔI. dl =0.4 - 0.23 = 0.17 pu. Adding this value to the existing control strategy yields a lower limit for the current command value output by the VDCOL stage, which needs to be greater than 0.72 pu. Simulation verification:

[0238] To verify the transient voltage calculation formula and transient overvoltage suppression strategy derived from the analytical expression of DC current under the condition of commutation failure caused by receiving-end fault, this invention establishes a test system based on the CIGRE DC transmission standard model in PSCAD / EMTDC, where the specific parameters of the CIGRE model are shown in Table 1.

[0239] Table 1 Actual simulation parameters of the CIGRE standard model

[0240]

[0241]

[0242] In the CIGRE model, a three-phase short-circuit fault is set at the receiving-end AC bus, causing commutation failure in the system. The short-circuit ratio of the sending-end AC system is 2.5, the rated transmission power of the DC line is 1000MW, the fault occurrence time is set to 2s, the fault duration is 0.1s, the grounding inductance is 0.01H, the grounding resistance is 0.01Ω, and the simulation duration is 2.35s. At this time, the commutation failure has been completely recovered, and the system returns to steady-state operation.

[0243] Simulation analysis of transient voltage quantitative calculation method:

[0244] Based on the preceding analysis of DC current, by substituting the derived expressions for each segment of DC current into the parameters of the CIGRE standard model, the DC current curve can be plotted.

[0245] From the onset of the fault (t=2s) to the recovery to steady state (t=2.35s), the DC current is divided into 6 stages, corresponding to... Figure 12 The stages (1) to (6) are as follows. Since both the firing angle curve and the transient voltage curve of the sending-end converter bus are calculated based on the DC current, the firing angle and the transient voltage curve are also divided into the above 6 stages.

[0246] Figure 12 The theoretical calculation curves of DC current, rectifier side firing angle and transient voltage of AC bus at the sending end under commutation failure of LCC-HVDC system are presented, and the actual simulation curves of CIGRE standard example are compared.

[0247] Theoretical calculations need to consider changes in the DC current reference value and calculate in real time based on the difference between the actual DC current value and the reference value. Therefore, the firing angle α and transient voltage U mentioned above... p The calculation is performed by further dividing the intervals (2) and (5) of the curve into subintervals.

[0248] As shown in the simulation diagram above, when a commutation failure occurs in the system, the DC current surges suddenly within a short period. After a while, the firing angle on the rectifier side begins to rise, suppressing the increase in DC current. Subsequently, the VDCOL circuit on the inverter side starts generating a DC current command value, causing the DC current to decrease. After a slight change near the minimum command value, it begins to recover and gradually rises to a steady-state value. The transient voltage exhibits a "low first, then high" trend, proving that the simulation results of the DC current and transient voltage response process are consistent with the theoretical analysis results above. However, the actual simulation results show high-frequency oscillations with small amplitudes, while the theoretical calculations are the result of linear approximation. Therefore, this calculation method can only describe the general trend of transient changes and cannot accurately describe the details of the changes in system electrical quantities during the transient response.

[0249] Simulation results show that the theoretical calculation results of the transient voltage of the sending-end converter bus are in good agreement with the actual simulation results in terms of variation trend, and the calculation error at the peak of the transient overvoltage is about 0.21%. Therefore, within the allowable error range, this calculation method can be used as a theoretical calculation method for the transient overvoltage of the sending-end converter bus, and provides a theoretical basis for the research on transient overvoltage suppression strategies in engineering design.

[0250] Analysis of the effect of improved VDCOL on transient overvoltage suppression

[0251] To verify the effectiveness of the proposed control strategy in suppressing transient overvoltages, based on the CIGRE standard example in PSCAD, three-phase short-circuit and single-phase short-circuit ground faults were respectively set at the inverter-side converter bus to simulate different operating conditions, such as... Figure 13 , 14 As shown.

[0252] Under different short-circuit fault conditions, the transient voltage and DC current variation characteristics of the sending-end converter bus are compared between the original control strategy of the CIGRE model and the system control strategy after the improvement of the VDCOL control loop proposed in this invention.

[0253] By comparing the two control strategies under different short-circuit fault conditions, it can be seen that the transient overvoltage under the proposed control strategy is below 1.1 pu, proving that the control strategy has a significant suppression effect on transient overvoltage.

Claims

1. A method for calculating and suppressing transient overvoltages at the sending end of an ultra-high voltage direct current (UHVDC) transmission system, considering the influence of multiple control links, characterized in that... Includes the following steps: Step 1: Analysis of the operating characteristics and transient voltage influencing factors of the LCC-HVDC system, revealing that DC current is the key factor affecting the change of bus transient voltage; Step 2: Based on the characteristics of DC current change in the DC control system operating curve, decompose the entire process of transient DC current under commutation failure and derive an approximate analytical expression for DC current after the fault occurs. Based on the characteristics of DC current variation in the DC control system's operating curve, the entire transient DC current process under commutation failure is decomposed into the following six processes: (1) The process of DC current rising; After a three-phase short circuit occurs on the AC bus at the receiving end, the AC voltage at the receiving end drops due to the system short circuit fault, causing the inverter-side converter to fail to commutate. Due to the short circuit on the inverter side, the DC voltage on the inverter side drops rapidly to 0, and the DC current rises rapidly in a short time. At this time, the rectifier-side CC control has not yet responded, and the DC current is affected by the inverter-side turn-off angle control. The shut-off angle γ and the minimum shut-off angle γ in steady state of the control system min The deviation value is processed by the proportional-integral stage G. PI (s) The inverter-side lead trigger angle β is obtained, and the lead trigger angle is further used as a control signal to adjust and control the turn-off angle; G γ (s) is a function for calculating the inverter-side turn-off angle, obtained through the relationship between the turn-off angle and the lead-out angle in steady state, as shown in equation (6): In the formula, U Li The transient voltage of the receiving-end converter bus is represented by the subscript i, indicating the inverter side; T i X represents the turns ratio of the converter transformer. ci For commutation reactance; G meas (s) represents the valve group signal measurement stage, indicating the delay effect during signal processing: In the formula, K m For measuring the gain coefficient of the circuit; T m The delay coefficient for the measurement process; When the LCC-HVDC system is operating in steady state, the DC current is expressed as: The expression for the lead firing angle β obtained from the above calculations can be substituted into the transfer function to obtain the expression for the turn-off angle γ. Substituting γ into equation (8) yields the expression for the DC current I. dc1 As shown below: The expression for variable K1 is: K1=m1 cosh(a1t-b1)+n1 sinh(a1t-b1) (10) In the formula, a i b i m i n i p i q i θ i k i h i i = 1 to 6 are the calculation parameters for intermediate processes; I dN This represents the steady-state value of the DC current before the fault. (2) The process of DC current decreasing; When the DC voltage drops to the upper limit of the VDCOL voltage threshold, VDCOL starts and adjusts the DC current command value to limit the DC current and suppress the continuous increase of the DC current. Due to the continuous decrease in the DC voltage on the inverter side, the current command I output by VDCOL... order The DC current decreases because the actual value is still higher than the commanded value, causing the inverter-side CC control to fail to respond; the rectifier-side CC control takes effect, reducing U by increasing the firing angle α. dr This causes the DC current to decrease and gradually approach the current DC current command value; G PI (s) is the transfer function of the PI element, G α (s), G R (s) and G meas (s) are the transfer functions of the converter link, DC line link and measurement link, respectively; The transfer functions in the control loop are as follows: In the formula, Kcα is the proportional gain coefficient of the converter stage; Tcα is the delay coefficient; The relationship between the rectifier-side firing angle α and the lead firing angle β is as follows: α＝180°-β (13) Substituting the obtained lead firing angle β into equation (13), we get the expression for the firing angle α. Substituting this into equation (8), we get the expression for the DC current I. dc2 As shown below: The expressions for K2 and K3 are: K2=m2 cos(a2t-b2)+n2 sin(a2t-b2) (15) K3=p2t-q2 (16) In the formula, I dcmax This is the maximum value that the DC current can reach during its rise. (3) DC current oscillation process; At this point, the DC voltage on the inverter side has decreased to 0. According to the VDCOL characteristics, once the DC voltage on the inverter side falls below its lower voltage threshold, the output DC current command value I... order The current drops to the minimum command value, and then I... order If it remains unchanged, the DC current will oscillate within a small range near the minimum current command value; The DC current expression for this process is I dc3 As shown below: (4) DC current fluctuation process; During the DC system recovery phase after fault clearance, due to overshoot in the CEA control on the inverter side, the turn-off angle γ will rapidly jump to over 90°. At this time, the DC current will increase slightly. The rectifier-side CC circuit increases the firing angle command value through PI control, and simultaneously, the rectifier-side DC voltage U... dr The continued decline has led to I dc A slight decrease; the DC current expression for this process is I. dc4 As shown below: (5) DC current recovery process, i.e. constant current control; Since the inverter has resumed normal commutation at this time, the AC bus voltage recovers quickly, and the DC voltage U on the inverter side increases. di As I increases rapidly, the current command value output by VDCOL gradually rises, until I... dc When the current is less than the inverter-side CC control current command value, the inverter-side DC control system will switch from CEA control to CC control. During this process, the DC short-circuit current will gradually increase and approach the current command value. The regulating effect of the rectifier-side CC control can be ignored at this time, and the inverter side will take the lead in control and regulation. The DC current expression for this process is I. dc5 As shown below: (6) DC current recovery process, i.e., constant turn-off angle control; Under the action of the CC control loop on the inverter side, I dc As the DC current gradually approaches the current command value, when the DC current exceeds the reference value of the inverter-side CC control, the CC control effect weakens. At the same time, the turn-off angle is still greater than the steady-state value. The inverter-side DC control system begins to enter CE control for transition, ensuring the stability of each transient control quantity during this process, so that the transition process of the control loop can proceed smoothly. Then, it switches to CEA control. The expression for the lead-fire angle β is obtained through calculation. Substituting β into the transfer function yields the expression for the turn-off angle γ. Substituting γ into equation (8) yields the expression for the DC current I. dc6 As shown below: K4=m6 cos(a6t+b6)+n6 sin(a6t+b6) (21) Step 3: Calculate the voltage drop across the equivalent resistance and reactance on the line respectively, and then substitute it into the DC current analytical formula to derive the quantitative calculation expression for the transient overvoltage of the sending end converter bus; From the power flow calculation relationship from the power source to the converter bus in the equivalent circuit of the LCC-HVDC sending-end system, the longitudinal and transverse components of the voltage drop on the transmission line of the sending-end system can be obtained respectively. Therefore, the voltage at the sending-end converter bus is expressed as: In the formula, ΔU s The longitudinal component of voltage drop in an AC line; δU s The transverse component of voltage drop in an AC line; In steady state, the active and reactive power transmitted on the transmission lines of the sending-end system is equal to the output power P of the sending-end power source. s and Q s That is, it satisfies the following relationship: The reactive power generated by the reactive power compensation device is expressed as follows: In the formula, B c The equivalent susceptance of the reactive power compensation device at the sending end; When the converter bus voltage increases, the reactive power compensation of the AC filter increases with the voltage increase. Simultaneously, during the recovery from a commutation failure, the reactive power consumed by the converter station also changes. Therefore, the actual reactive power transmitted from the converter station to the AC system during the transient process is expressed as: In the formula, U p0 It is the voltage of the AC bus at the feed end before the fault, Q. cp0 It is the reactive power output of the AC filter device before the fault; Ignoring the effects of commutation reactance, the active and reactive power consumed by the rectifier are expressed as follows: During the transient process, the active power and reactive power exchanged between the DC system and the sending-end AC system are respectively: By simplifying the analysis of the sending-end system, it is assumed that the voltage drop between the sending-end power supply and the sending-end converter bus exists only in the equivalent impedance of the line. The voltage drops across the equivalent resistance and equivalent reactance are calculated separately, and the expression for calculating the transient voltage of the sending-end converter bus is obtained as follows: In the formula, R s X is the equivalent resistance of the sending-end AC power grid. s Equivalent reactance of the sending-end AC power grid; By combining equations (27) and (28), we can derive U. p The expression is: In the formula, the expression for algebraic b is: By substituting the analytical expression of DC current into the above formula, the quantitative calculation formula for transient voltage at the sending-end converter bus can be obtained. Step 4: Based on the upper limit of transient overvoltage, the minimum allowable DC current is obtained, and an improved method for suppressing transient overvoltage under commutation failure with minimum current command value of VDCOL circuit is proposed. VDCOL is a crucial control element in a DC control system. It can detect the DC voltage in real time and output corresponding DC current command values ​​based on the characteristic curve to adjust the current and promote the commutation process. The VDCOL characteristic curve mainly consists of two parts: one is the VDCOL inflection point parameter, namely the low-voltage start-up threshold U. dl and high voltage start threshold U dh The lower limit of the current command value I dl and the upper limit of the current command value I dh Secondly, the VDCOL line type: in traditional VDCOL, the voltage and current have a linear relationship with a fixed slope. The DC current command value output by the VDCOL stage is expressed as: In the formula, U d * The voltage per unit value at the midpoint of the DC line after conversion is used as the input value of VDCOL; k and b are the coefficients of the operating characteristic curve, where k = (I dh -I dl ) / (U dh -U dl b = -U dl (I dh -I dl ) / (U dh -U dl ); After the DC current reaches its minimum value during its fluctuation phase, it begins to recover. Solving the expression for the DC current during this phase, we obtain that the minimum DC current value is 0.23 pu. When the peak value of the transient overvoltage is limited to below 1.1 pu, according to equation (32), the DC current must be higher than 0.4 pu. Because the transfer function in the DC current decrease, oscillation, and fluctuation processes all have a measurement element G. meas (s) Measurement delay T m The influence of this causes the rectifier side constant current control loop to increase the firing angle command during the DC current fluctuation phase, resulting in DC current overshoot. The DC current will drop to a smaller value below the lower limit of the current command value of 0.55pu. In the improved VDCOL, the DC current overshoot effect caused by the rectifier side constant current control remains basically unchanged in this stage. Therefore, the lower limit of the current command value needs to be increased by the value ΔI. dl =0.4-0.23=0.17pu. By adding this value to the original control strategy, we can obtain that the lower limit of the current command value output by the VDCOL stage needs to be greater than 0.72pu.

2. The method for calculating and suppressing transient overvoltage at the sending end of an ultra-high voltage direct current transmission system considering the influence of multiple control links, as described in claim 1, is characterized in that... Step 1 specifically involves: S1.1: Analysis of the operating characteristics of the LCC-HVDC system; In the equivalent circuit of the LCC-HVDC system, U s P is the equivalent power supply voltage in the sending-end AC system; s Q s These represent the active and reactive power transmitted from the sending-end power source to the converter station along the line; R s and X s These are the equivalent resistance and equivalent reactance on the sending-end system lines, respectively, and their values ​​affect the electrical strength of the sending-end system; U p Q is the voltage of the sending-end converter bus; cp The reactive power compensated by the AC filter at the sending end; U dr U is the DC voltage on the rectifier side. di I is the DC voltage on the inverter side. dc It is direct current; In the LCC-HVDC control system, both the rectifier and inverter sides are equipped with constant current (CC) control and low-voltage current limiting (VDCOL) control loops. The constant current control loop generates a lead trigger angle command value through a PI controller, while the low-voltage current limiting control loop generates a DC current command value by measuring the DC voltage in real time. Moreover, the DC current command value on the inverter side is lower than that on the rectifier side by one margin. In addition, the inverter side is also equipped with a current deviation (CE) controller and a constant turn-off angle (CEA) controller. The function of the current deviation control is to achieve smooth switching between the inverter side's CC and CEA. S1.2: Analysis of factors affecting transient voltage; During commutation failure, the rectifier's ability to consume reactive power directly affects the transient overvoltage level of the sending-end converter bus; the reactive power Q consumed by the rectifier during the transient response process... dc Represented as: In the formula, P r The rectifier transmits active power; the subscript r represents the rectifier side. The power factor angle; U r0 This is the DC open-circuit voltage; The DC voltage on the rectifier side satisfies the following relationship: In the formula, N r The number of 6 pulsed converters per pole; T r X is the converter transformer turns ratio; α is the rectifier-side firing angle, γ is the inverter-side turn-off angle; cr For commutation reactance; Combining equations (1) and (2), we get Q. dc The expression is: As can be seen from equation (3), the dynamic reactive power characteristics of the rectifier are related to the firing angle α and the DC current I. dc Closely related, and the reactive power consumed by the rectifier is positively correlated with the DC current. The magnitude of the DC current directly determines the magnitude of the reactive power consumed by the rectifier. The relationship between the surplus reactive power of the sending-end system and the transient overvoltage of the sending-end converter bus is expressed as follows: The expression for ΔQ is: ΔQ=Q dc -Q cp (5) In the formula, ΔU is the transient voltage change of the sending-end converter bus; ΔQ is the reactive power exchange between the rectifier and the sending-end AC system; S d This refers to the short-circuit capacity at the sending-end converter bus. As can be seen from equation (4), when the short-circuit capacity of the sending-end converter bus is constant, the transient voltage change of the converter bus directly depends on the reactive power exchange ΔQ between the rectifier and the sending-end AC system. A positive value is the reactive power absorbed from the system, and a negative value is the reactive power sent to the system. Therefore, the dynamic reactive power characteristics of the rectifier during the transient process directly affect the reactive power exchange between the DC and the sending-end AC system, and further affect the transient voltage of the sending-end converter bus. Therefore, it can be concluded that direct current is the key factor affecting the change of bus transient voltage.

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