Method for establishing a fail-safe domain of a hybrid cascaded system

Abstract

The application relates to a method for establishing a fault safety domain of a hybrid interconnected system, belonging to the technical field of high-voltage direct-current power transmission. The application aims to face the hybrid interconnected system, fully consider the dynamic reactive power support of an inverter-side controller and an MMC, and propose a hybrid interconnected system fault safety domain. The method for establishing the hybrid interconnected system fault safety domain is of great significance and value for guaranteeing the stability of system operation. The application analyzes the inverter-side controller action and the dynamic reactive power support of a modular multilevel converter (MMC) on an LCC, and clearly defines the inverter-side multi-electricity coupling characteristics of the hybrid interconnected system. The internal relationship between the active power sent by the LCC and the reactive power absorbed by the LCC about the turn-off angle during the recovery after the first commutation failure is derived, the feasible interval of the DC current and the turn-off angle for guaranteeing the safe operation of the system is determined, and a method for establishing a fault safety domain during system recovery is proposed. The fault safety domain established by the application determines the feasible power domain in which no subsequent commutation failure occurs during the fault recovery of the hybrid interconnected system, and is of great significance and value for guaranteeing the stable operation of the system.

Description

Technical Field

[0001] This invention belongs to the field of high voltage direct current transmission technology. Background Technology

[0002] Line commutated converter-based high-voltage direct current (LCC-HVDC) transmission holds a prominent position in my country's power transmission development strategy due to its advantages such as large capacity, low cost, and high reliability. However, LCC converters are highly dependent on the AC grid for commutation voltage, and commutation failure may occur when an AC fault occurs on the inverter side, seriously jeopardizing the safe and stable operation of the power system. Modular multilevel converter-based high-voltage direct current (MMC-HVDC) transmission, based on fully controlled power electronic devices, has the ability to quickly control active and reactive power. Even under controller limiting conditions, it can provide DC and AC voltage support equivalent to its own capacity and does not have the problem of commutation failure. However, MMC-HVDC suffers from high cost and high losses, making it unsuitable for large-scale deployment.

[0003] Hybrid cascaded DC transmission inherits the advantages of both LCC-HVDC and MMC-HVDC DC transmission and represents one of the future development trends of high-voltage DC transmission. The inverter side of the hybrid cascaded system adopts a structure of cascaded LCC and MMC. When a fault occurs, the MMC can generate additional reactive power to stabilize the AC bus voltage at the receiving end, reducing the probability of commutation failure of the LCC. Currently, the State Grid Corporation of China's Baihetan UHVDC hybrid cascaded DC transmission project is the first in the world to adopt a hybrid cascaded structure to achieve… This study is based on the background of a transmission capacity of 800kV / 8000MW.

[0004] In summary, although significant progress has been made in the research on the feasible power domain of LCC-HVDC, research on hybrid cascaded systems is still in its early stages, and existing literature lacks in-depth research on the safe operating range of the system and this key issue. Summary of the Invention

[0005] The purpose of this invention is to address hybrid cascaded systems, fully considering the dynamic reactive power support role of the inverter-side controller and MMC, and propose a method for establishing a fault-safe domain for hybrid cascaded systems. This method is of great significance and value in ensuring the stability of system operation.

[0006] The steps of this invention are: S1. Hybrid Cascade System Topology and Mathematical Model: ①Topology The rectifier side consists of two sets of 6-pulse LCC converters connected in series, and the inverter side consists of one set of 6-pulse LCC converters and two sets of parallel half-bridge submodules connected in series with MMC; where U G1 Z1 and Z2 are the equivalent electromotive force and equivalent impedance of the sending-end AC system, respectively; U s1 U is the AC bus voltage on the rectifier side; G2 Z1 and Z2 are the equivalent electromotive force and equivalent impedance of the receiving-end AC system, respectively; U s The inverter-side AC bus voltage; T n For converter transformers (n=1,2,……,5); B c1 B c2 These represent the equivalent capacity of the AC filters on the rectifier and inverter sides, respectively; R and L represent the line resistance and reactance of the DC transmission system, respectively. ② Mathematical model of the inverter side The mathematical model for the inverter side of the hybrid cascade system is as follows: (1) (2) (3) (4) (5) (6) (7) (8) (9) In the formula I d U is the DC current on the inverter side. dLCC0 U is the LCC no-load DC voltage; dLCC U dMMC These are the DC voltages for LCC and MMC, respectively; P LCC Q LCC These represent the active power generated and the reactive power absorbed by the LCC, respectively; P MMC1 / 2 Q MMC1 / 2 MMC 1 / 2 Power output: active and reactive power; Q c To generate reactive power for the reactive power compensation device; P ac Q ac These are respectively the exchange of active and reactive power between the inverter side and the AC system; μ and β are divided into LCC turn-off angle, commutation overlap angle and leading trigger angle; The power factor angle is denoted by k; the transformer turns ratio between the LCC and the AC system is denoted by X. r For the leakage reactance of the LCC transformer; S2. Control strategy for inverter-side converter in hybrid cascaded systems: ①LCC control strategy The rectifier-side LCC is equipped with constant DC current control and minimum firing angle control; the inverter-side LCC is equipped with constant DC current control and constant turn-off angle control, and the switching between the two is achieved through a current deviation controller; where U d_inv This is the measured DC voltage value on the inverter side; I d_order Main control stage current command value; I d_rec I d_inv These are the measured DC current values ​​on the rectifier side and inverter side, respectively; β CC and β CEA These are the CC and CEA control output lead angle command values, respectively; γ min γ CEC These are the measured values ​​of the inverter-side turn-off angle and the CEC output command value, respectively; α r β inv These are the rectifier-side output trigger angle command value and the inverter-side output lead trigger angle command value, respectively. ②MMC control strategy The hybrid cascaded MMC converter employs direct current vector control based on dq-axis decoupling, comprising outer-loop voltage control and inner-loop current control. The outer-loop control can be divided into active and reactive power outer-loop control, while the inner-loop current control is based on the deviation U of the outer-loop output DC voltage. ref -U m and reactive power deviation Q ref -Q m1 / 2 The dq-axis current reference value i is obtained after the PI circuit. dref and i qref By adjusting the actual current value of the dq axis, the reference value of the three-phase AC voltage u at the MMC outlet is finally obtained. ref ; S3, Hybrid Cascaded System Fault Recovery Characteristics: ① The impact of multi-controller interaction on system recovery The controller interaction and the changing trends of various electrical quantities are divided into four stages, t1-t5: 1) Stage 1, i.e., time t1 to -t2: At time t0, an AC fault occurs in the receiving-end system; at time t1, the LCC experiences its first commutation failure, and the turn-off angle γ drops to 0. d The increase is rapid, and the system is under CEA control. 2) Stage 2, from t2 to -t3: Under the combined action of rectifier-side CC control and VDCOL, I dr_order With effective constraints, I at time t2d A rapid decline occurs; once overshoot is detected, CEC is activated, and β... CC The system begins to increase, but due to the late start of CC control, the system in stage 2 is still under CEA control. 3) Stage 3, from t3 to -t4: The system enters the recovery process, with U di Gradually recovering, under the action of VDCOL, at time t3, I d Gradually increase; simultaneously, under continuous CEA control, γ recovers to its steady-state value, β CEA The sudden drop system switches to CC control; 4) Phase 4, from t4 to -t5: The system enters the final stage of the recovery phase, I d Gradually towards the reference value I dref Approaching but still below I dr_order ; ②LCC reactive power demand The reactive power consumed by the inverter-side LCC is: (11) Q LCC to I d The partial derivatives of γ and γ are: (12) in: ; (13) in: ; In the formula, k and X r Both N and N are constants; S4. Method for establishing fault-safe domains in hybrid cascaded systems: ①Multi-electrical quantity coupling characteristics AC bus voltage change ΔU s The transient reactive power ΔQ exchanged between the inverter side and the AC system is as follows: (14) Where SCR is the short-circuit ratio of the receiving-end AC system; ΔQ greater than zero indicates that the inverter side generates reactive power to the receiving-end AC system. AC bus voltage U considering the reactive power support effect of MMC s With the initial AC bus voltage U of the system s0 and MMC reactive power increase ΔQ MMC The relationship between them is: (15) P LCC and Q LCCRepresented as: (16) in: ; From the above formula, we get P LCC Q LCC respectively with U s I d The coupling characteristics of γ; ② Fault-safe domain modeling and analysis CEA control command values ​​are represented as follows: (17) In the formula K p K i These represent the proportional gain and integral gain of the PI control element in the CEA control, respectively. When a fault occurs, the CEA control dynamically adjusts β to increase the γ margin. Differentiating the above equation yields: (18) The equivalent transformation of dβ / dt is: (19) During system recovery, the change in the shut-off angle over time, dγ / dt, can be approximated as K. γ ,have to: (20) Integrating the above equation yields the expression for β in terms of γ: (twenty one) U after considering the control effect of CEA dLCC Represented as: (twenty two) When the system enters the recovery phase and the LCC resumes normal commutation, I is obtained. d Regarding P LCC Two solutions: (twenty three) Will I d1 When we insert it into the above formula, we get: (twenty four) in: , ; Solve P separately LCC to I d The partial derivatives of γ and γ are: (25) In the formula, k and Xr Since both N and P are constants, substituting them into the system control parameters yields: P LCC with I d It is directly proportional to γ ​​and inversely proportional to γ; γ should satisfy the following constraints: (26) In the formula, γ0 is the critical turn-off angle at which the system does not experience subsequent commutation failure, γ ref This is the reference value for the shut-off angle when the system is in steady state; Maximum DC current limit I to avoid subsequent commutation failure in LCC dmax for: (27) In the formula α ref This is the rated firing angle. I d The following constraints must be met: (28) In the above I d P under γ constraint LCC and Q LCC Meets the following range: (29) Where P max P min and Q max Q min Each is in a certain U s and I d The maximum and minimum values ​​of active power output and reactive power absorption by the LCC under the constraints of γ and γ; The above extreme values ​​are expressed as: (30) (31) Finally, substituting the solved extreme power operating point into the two boundary fault safety lines yields the safe operating region where the LCC does not experience subsequent commutation failures during the recovery period of the hybrid cascaded system under safety electrical quantity constraints.

[0007] The analysis process of the four-stage controller interaction and the changing trends of various electrical quantities in the hybrid cascade system of this invention yields the following results: 1) I starting from phase 3 d The recovery process causes µ to increase rapidly, which in turn leads to a continuous decrease in γ. (34) 2) In stage 3, as I d Gradually recovering, γ CECThe longer the system remains under CC control, the lower β becomes when the controller switches. inv The smaller; 3) After the first commutation failure, P ac Recovery begins, P ac Increasing the size of U will lead to s Phase shifting directly compresses the turn-off angle margin, leading to subsequent commutation failure in the system. (32) In the formula, δ is U s Relative to U G2 Phase offset; X G δ is the equivalent reactance of the receiving-end tie line; P is the total active power flowing into the AC grid; ΔP is the active power increment during system recovery; δ 1 / 2 Represents different times U s with U G2 Phase angle difference; 4) CEA control on I d The response is achieved by reducing the CEC output, thereby lowering β. CEA Achieved, inverter side to I d The response speed lags significantly behind the rectifier side, resulting in U... during system recovery. di Unable to track U in a timely manner dr This causes the pressure difference between the sending and receiving ends to increase, I d Exceeding the baseline value, Q LCC Gradually increase (33) In the formula: U dr L is the DC voltage on the rectifier side. r and L i These represent the inductances of the smoothing reactors on the rectifier and inverter sides, respectively.

[0008] The fault-safe domain established in this invention defines a feasible power domain in which subsequent commutation failures do not occur during fault recovery in a hybrid cascaded system, which is of great significance and value for ensuring stable system operation. Finally, a corresponding simulation model was built in PSCAD / EMTDC to verify the accuracy of the theoretical analysis and the established fault-safe domain. Attached Figure Description

[0009] Figure 1 This is a topology diagram of a hybrid cascaded DC transmission system; Figure 2 This is a topology diagram of the inverter side of a hybrid cascaded system; Figure 3 This is a block diagram of the LCC control strategy; Figure 4 This is a block diagram of the MMC control strategy; Figure 5 This is a diagram of the inverter-side control system response process; Figure 6 This is a waveform diagram of the AC bus voltage on the inverter side; Figure 7a This is a diagram showing the active power coupling characteristics of electrical quantities on the inverter side; Figure 7b This is a diagram showing the reactive power coupling characteristics of electrical quantities on the inverter side; Figure 8 This is the fault safety domain diagram of the inverter side. Detailed Implementation

[0010] This invention discloses a method for establishing a fault-safe domain for a hybrid cascaded system. Based on the application background of the Baihetan-Jiangsu ±800kV UHVDC transmission project, a safe operating range is established for the inverter-side grid commutator (LCC) to prevent subsequent commutation failures. First, the role of the inverter-side controller and the dynamic reactive power support role of the modular multilevel converter (MMC) on the LCC are analyzed, clarifying the coupling characteristics of multiple electrical quantities on the inverter side of the hybrid cascaded system. Second, the intrinsic relationship between the active power generated and the reactive power absorbed by the LCC during the recovery period after the first commutation failure is derived with respect to the turn-off angle, and the feasible range of DC current and turn-off angle to ensure the safe operation of the system is determined. A method for establishing a fault-safe domain during system recovery is proposed.

[0011] The hybrid cascaded system topology studied is as follows: Figure 1 As shown. The rectifier side consists of two sets of 6-pulse LCC converters connected in series, while the inverter side consists of one set of 6-pulse LCC converters and two sets of parallel half-bridge submodules connected in series. U in the figure... G1 Z1 and Z2 are the equivalent electromotive force and equivalent impedance of the sending-end AC system, respectively; U s1 U is the AC bus voltage on the rectifier side; G2 Z1 and Z2 are the equivalent electromotive force and equivalent impedance of the receiving-end AC system, respectively; U s The inverter-side AC bus voltage; T n For converter transformers (n=1,2,……,5); B c1 B c2 The equivalent capacity of the AC filters on the rectifier side and inverter side are respectively; R and L are the line resistance and reactance of the DC transmission system, respectively.

[0012] ② Mathematical model of the inverter side Inverter-side topology of a hybrid cascaded system, such as Figure 2 As shown. By Figure 2 The mathematical model of the inverter side of the hybrid cascade system can be obtained as follows: (1) (2) (3) (4) (5) (6) (7) (8) (9) In the formula I d U is the DC current on the inverter side. dLCC0 U is the LCC no-load DC voltage; dLCC U dMMC These are the DC voltages for LCC and MMC, respectively; P LCC Q LCC These represent the active power generated and the reactive power absorbed by the LCC, respectively; P MMC1 / 2 Q MMC1 / 2 MMC 1 / 2 Power output: active and reactive power; Q c To generate reactive power for the reactive power compensation device; P ac Q ac These are respectively the exchange of active and reactive power between the inverter side and the AC system; μ and β are divided into LCC turn-off angle, commutation overlap angle and leading trigger angle; The power factor angle is denoted by k; the transformer turns ratio between the LCC and the AC system is denoted by X. r This refers to the leakage reactance of the LCC transformer.

[0013] The inverter-side converter control strategy of the hybrid cascaded system of the present invention: ①LCC control strategy Hybrid cascaded system LCC converter control strategy, such as Figure 3 As shown. The rectifier-side LCC is equipped with constant current (CC) control and a minimum firing angle (min-α) controller; the inverter-side LCC is equipped with constant current control and constant extinction angle (CEA) control, and the switching between the two is achieved through a current error controller (CEC). In addition, the inverter-side LCC is also equipped with a voltage-dependent current order limiter (VDCOL). When an AC fault occurs in the receiving-end system, causing the inverter-side DC voltage U to decrease... diDuring a sudden drop, VDCOL promotes LCC commutation and accelerates the system recovery process by limiting the DC current command value.

[0014] U in the figure d_inv This is the measured DC voltage value on the inverter side; I d_order Main control stage current command value; I d_rec I d_inv These are the measured DC current values ​​on the rectifier side and inverter side, respectively; β CC and β CEA These are the CC and CEA control output lead angle command values, respectively; γ min γ CEC These are the measured values ​​of the inverter-side turn-off angle and the CEC output command value, respectively; α r β inv These are the rectifier-side output trigger angle command value and the inverter-side output leading trigger angle command value, respectively.

[0015] ②MMC control strategy The hybrid cascaded MMC converter employs direct current vector control based on dq-axis decoupling, comprising outer-loop voltage control and inner-loop current control. Its control strategy is as follows: Figure 4 As shown. The outer loop control can be divided into active power outer loop control and reactive power outer loop control. To maintain the stability of Udi, at least one MMC needs to be in constant DC voltage control. Therefore, in this paper, constant DC voltage control (MMC1) and constant active power control (MMC2) are used as active power control methods for the two MMCs, respectively. Considering the voltage level and strength of the AC grid at the receiving end, both MMCs use constant reactive power control as reactive power control. The inner loop current control is based on the deviation of the outer loop output DC voltage U. ref -U m (Active power deviation P) ref -P m1 / 2 and reactive power deviation Q ref -Q m1 / 2 The dq-axis current reference value i is obtained after the PI circuit. dref and i qref By adjusting the actual current value of the dq axis, the reference value of the three-phase AC voltage u at the MMC outlet is finally obtained. ref .

[0016] The hybrid cascaded system fault recovery characteristics of this invention: ① The impact of multi-controller interaction on system recovery From the occurrence of an AC fault in the system to the stabilization of various electrical quantities, this section divides the process into four stages, t1-t5, based on the controller interaction and the trends of changes in various electrical quantities. Figure 5 As shown.

[0017] 1) Stage 1 (times t1 to -t2): At time t0, an AC fault occurs in the receiving-end system; at time t1, the LCC experiences its first commutation failure, and the turn-off angle γ drops to 0. d The voltage increases sharply, and the system is under CEA control. In stage 1, compared to LCC-HVDC, the hybrid cascaded system effectively suppresses U voltage through MMC reactive power support and voltage stabilization. s Fall and I d The sudden increase, in turn, reduced P to some extent. LCC The magnitude of the drop.

[0018] 2) Stage 2 (times t2 to -t3): Under the combined action of rectifier-side CC control and VDCOL, I dr_order With effective constraints, I at time t2 d A rapid decline occurs; once overshoot is detected, CEC is activated, and β... CC It begins to increase. However, due to the late start of CC control, the system in stage 2 is still under CEA control. In stage 2, with the development of stage I... d P continues to decrease LCC It is at a low level.

[0019] 3) Stage 3 (times t3 to -t4): The system enters the recovery process, with U di Gradually recovering, under the action of VDCOL, at time t3, I d Gradually increase; simultaneously, under continuous CEA control, γ recovers to its steady-state value, β CEA The system switches to CC control during the sudden drop. In Phase 3, the hybrid cascaded system, due to its stronger fault immunity, will enter the fault recovery phase faster than the LCC-HVDC.

[0020] 4) Stage 4 (times t4 to -t5): The system enters the final stage of recovery, I d Gradually towards the reference value I dref Approaching but still below I dr_order Therefore, before the CEC output drops to 0, β CEA Maintaining a slow increasing trend and β CC As the temperature continues to decrease, the system switches to CEA control at time t4. In stage 4, as I... d Restore to I dref Q LCC and P LCC It enters the recovery process and gradually approaches the steady-state value.

[0021] Based on the above analysis of the four-stage controller interaction and the changing trends of various electrical quantities in the hybrid cascade system, the following conclusions can be drawn: 1) I starting from phase 3 dThe recovery process causes a rapid increase in µ, which in turn leads to a continuous decrease in γ, increasing the risk of subsequent commutation failure in the system. (34).

[0022] 2) In stage 3, as I d Gradually recovering, γ CEC The longer the system remains under CC control, the lower β becomes when the controller switches. inv The smaller. Furthermore, when the system switches to CEA control, due to I... d Controlled only by the rectifier side, it will rapidly increase to I dr-order At the same time, CEC output drops to 0, which will cause β inv Further reduction. Therefore, regardless of the control method used during the system recovery phase, β inv Both are at low levels and have a downward trend, which will also cause γ to fall.

[0023] 3) After the first commutation failure, P ac Recovery begins, but as can be obtained from equation (32), P ac Increasing the size of U will lead to s Phase shifting directly compresses the turn-off angle margin, potentially leading to subsequent commutation failures in the system. (32) In the formula, δ is U s Relative to U G2 Phase offset; X G Here, P represents the equivalent reactance of the receiving-end tie line; P is the total active power flowing into the AC grid; and ΔP is the increase in active power during system recovery. The inverter-side AC voltage waveform during system recovery is shown below. Figure 6 As shown. Where δ 1 / 2 Represents different times U s with U G2 Phase angle difference.

[0024] 4) CEA control on I d The response is achieved by reducing the CEC output, thereby lowering β. CEA It was achieved. Therefore, in stage 4, the inverter side... d The response speed of the rectifier lags significantly behind that of the rectifier side. As mentioned above, this will cause U to lag during system recovery. di Unable to track U in a timely manner dr This causes the pressure difference between the sending and receiving ends to increase, I d Exceeding the baseline value, Q LCC Gradually increase (33) In the formula: U dr L is the DC voltage on the rectifier side.r and L i These represent the inductances of the smoothing reactors on the rectifier and inverter sides, respectively.

[0025] ②LCC reactive power demand The above analysis shows that significant fluctuations in electrical quantities during controller interaction will lead to a large reactive power demand in the LCC. When Q LCC When the system recovery process is mismatched, it will worsen the transient stability of the receiving-end power grid, causing the overall reactive power loss on the inverter side to continuously increase, resulting in a persistent "reactive load" characteristic. To meet the reactive power deficit on the inverter side, the LCC will continuously absorb a large amount of reactive power from the AC system, which may lead to subsequent commutation failures at the end of the recovery phase.

[0026] To further study the reactive power characteristics of the LCC, substituting equation (7) into the equation and solving, we can obtain the reactive power consumed by the LCC on the inverter side as follows: (11).

[0027] The above equation characterizes Q in the DC quasi-steady-state model of the inverter side of the hybrid cascaded system. LCC with U s I d The intrinsic connection between Q and γ. To further explore Q LCC Follow me d The changing trends of γ are used to solve for Q. LCC to I d The partial derivatives of γ and γ are: (12) in: ; (13) in: ; In the formula, k and X r Since N and N are both constants, substituting them into the control parameters of the CIGRE standard model, and considering the per-unit normalization of AC / DC system parameters, we can obtain A. γ >0、A I >0, therefore Q LCC to I d The partial derivatives of both γ and γ are greater than 0, and as the system recovers, I... d As γ gradually increases to recover to the baseline value, Q LCC As the inverter continues to increase, it continuously absorbs a large amount of reactive power from the receiving-end AC system, which will cause U s A second drop could lead to subsequent commutation failure in the system.

[0028] The method for establishing a fault-safe domain in a hybrid cascaded system according to the present invention: ①Multi-electrical quantity coupling characteristics The hybrid cascaded system topology is relatively complex, with the inverter-side LCC and MMC mutually coupled, increasing the difficulty of suppressing subsequent commutation failures. When an AC fault occurs in the system, the AC bus voltage change ΔU s It is related to the transient reactive power ΔQ exchanged between the inverter side and the AC system, and the specific relationship is as follows: (14) Where SCR is the short-circuit ratio of the receiving-end AC system; ΔQ greater than zero indicates that the inverter side generates reactive power to the receiving-end AC system.

[0029] From the above equation, it can be seen that the hybrid cascaded system can fully utilize the dynamic reactive power support and voltage stabilization functions of the MMC, continuously meeting the reactive power demand of the LCC by rapidly increasing reactive power generation during faults. The AC bus voltage U considering the reactive power support function of the MMC is... s With the initial AC bus voltage U of the system s0 and MMC reactive power increase ΔQ MMC The relationship between them is: (15)

[0030] From equation (15), we can obtain that P can be... LCC and Q LCC Represented as: (16) in:

[0031] From equation (16), we can obtain P LCC Q LCC respectively with U s I d The coupling characteristics of I and γ are shown in Figure 7. Reducing I d It will lower Q LCC It is beneficial to U s Recovery, but not conducive to P LCC Transmission; Increase I d It is beneficial to P LCC Quick recovery, but will cause Q LCC Increasing the size of U is not conducive to U s Recovery. Therefore, it is necessary to determine the feasible power domain of the system under multiple electrical quantity constraints and to accelerate the system recovery process by setting appropriate control strategies.

[0032] ② Fault-safe domain modeling and analysis As analyzed above, subsequent commutation failures are prone to occur when the system is in the late recovery phase with CEA control. Therefore, considering the controller's role, establishing the inverter-side LCC fault-safe domain with the late recovery phase as the analysis period can determine the safe operating range of the hybrid cascaded system. The CEA control command value can be expressed as: (17) In the formula K p K i These represent the proportional gain and integral gain of the PI control element in the CEA control, respectively.

[0033] When a fault occurs, the CEA control dynamically adjusts β to increase the γ margin. Differentiating equation (17) yields: (18) Where dβ / dt can be equivalently transformed as: (19)

[0034] During system recovery, the change in the shut-off angle over time, dγ / dt, can be approximated as K. γ Substituting equation (18) into equation (19), we get: (20)

[0035] Integrating the above equation yields the expression for β in terms of γ: (twenty one)

[0036] Therefore, considering the control effect of CEA, U dLCC It can be represented as: (twenty two)

[0037] When the system enters the recovery phase and the LCC resumes normal commutation, the quasi-steady-state equation of the system holds. Therefore, equation (5) is applicable to the recovery process after the system's first commutation failure. Substituting equation (22) into equation (5) yields I. d Regarding P LCC Two solutions: (twenty three)

[0038] Because of I d2 A value that is always less than 0 does not meet the actual operating conditions of the system and should be discarded. Therefore, I d1 This is a feasible solution for DC current. Let I... d1 Once inserted into equation (11), we can obtain: (twenty four) in: ,

[0039] In order to determine the boundary line of the fault-safe domain and the extreme power operating point, P is solved separately. LCC to I d The partial derivatives of γ and γ are: (25) In the formula, k and X r Since both N and P are constants, substituting them into the system control parameters yields: P LCC with I d It is directly proportional to γ ​​and inversely proportional to γ. P LCC Follow me d The value of γ increases with the increase of γ, but a larger active power transmission corresponds to a smaller γ. Therefore, it is also necessary to determine the I value to ensure the safe operation of the system. d And the range of values ​​for γ.

[0040] First, γ should satisfy the following constraints: (26) In the formula, γ0 is the critical turn-off angle at which the system will not experience subsequent commutation failure, typically 7°. 。 ;γ ref This is a reference value for the turn-off angle when the system is in steady state, typically 15°. 。 ~18 。 . γ0 and γ ref Substituting these values ​​into equation (24) yields two boundary fault safety lines.

[0041] Secondly, regarding I d In order to maintain the minimum power transmission of the system, I d It should be greater than the minimum limit value I dmin In addition, I d There is also an upper limit to ensure the safe operation of the converter valve. Based on the commutation voltage-time area theory, the maximum DC current limit I to avoid subsequent commutation failure in the LCC can be obtained. dmax for: (27) In the formula α ref This is the rated firing angle.

[0042] Therefore I d The following constraints must be met: (28)

[0043] In the above I d P under γ constraint LCC and Q LCC Meets the following range: (29) Where P max Pmin and Q max Q min Each is in a certain U s and I d The maximum and minimum values ​​of active power output and reactive power absorption by the LCC under the constraints of γ and γ.

[0044] Based on the partial derivative relationship above, the above extreme values ​​can be expressed as: (30) (31)

[0045] Finally, substituting the solved extreme power operating point into the two boundary fault safety lines yields the safe operating region where, under safety electrical quantity constraints, the LCC will not experience subsequent commutation failures during the recovery period of the hybrid cascaded system. Figure 8 As shown.

[0046] In region Ф1, the solid lines AB and CD represent U respectively. s Falling to U s1 Below γ=γ0 and γ=γ ref The corresponding boundary fault-safe line; the upper and lower dashed lines in region Ф2 represent U respectively. s Falling to U s2 Below γ=γ0 and γ=γ ref The corresponding boundary fault safety line; where U s1 >U s2 The dashed line indicates a more severe voltage drop on the AC bus, resulting in an overall downward shift in the fault-safe domain; regions Ф1 and Ф2 represent the hybrid cascaded system at U... s1 and U s2 The feasible power domain in which the LCC on the inverter side does not experience subsequent commutation failure; points B and C are the maximum and minimum operating points of active power output by the LCC, respectively; points A and D are the maximum and minimum operating points of reactive power absorption by the LCC, respectively.

Claims

1. A method for establishing a fault-safe domain in a hybrid cascaded system, characterized in that: The steps are as follows: S1. Hybrid Cascaded System Topology and Mathematical Model: ①Topology The rectifier side consists of two sets of 6-pulse LCC converters connected in series, and the inverter side consists of one set of 6-pulse LCC converters and two sets of parallel half-bridge submodules connected in series with MMC; where U G1 Z1 and Z2 are the equivalent electromotive force and equivalent impedance of the sending-end AC system, respectively; U s1 U is the AC bus voltage on the rectifier side. G2 Z1 and Z2 are the equivalent electromotive force and equivalent impedance of the receiving-end AC system, respectively; U s The inverter-side AC bus voltage; T n For converter transformers (n=1,2,……,5); B c1 B c2 These represent the equivalent capacity of the AC filters on the rectifier and inverter sides, respectively; R and L represent the line resistance and reactance of the DC transmission system, respectively. ② Mathematical model of the inverter side The mathematical model for the inverter side of the hybrid cascade system is as follows: (1) (2) (3) (4) (5) (6) (7) (8) (9) In the formula I d U is the DC current on the inverter side. dLCC0 U is the LCC no-load DC voltage; dLCC U dMMC These are the DC voltages for LCC and MMC, respectively; P LCC Q LCC These represent the active power generated and the reactive power absorbed by the LCC, respectively; P MMC1 / 2 Q MMC1 / 2 MMC 1 / 2 Power output: active and reactive power; Q c To generate reactive power for the reactive power compensation device; P ac Q ac These are respectively the exchange of active and reactive power between the inverter side and the AC system; , These are the LCC shutdown angle and the leading trigger angle, respectively. The power factor angle is denoted by k; the transformer turns ratio between the LCC and the AC system is denoted by X. r For the leakage reactance of the LCC transformer; S2. Control strategy for inverter-side converter in hybrid cascaded systems: ①LCC control strategy The rectifier-side LCC is equipped with constant DC current control and minimum firing angle control; the inverter-side LCC is equipped with constant DC current control and constant turn-off angle control, and the switching between the two is achieved through a current deviation controller; where β CC and β CEA These are the CC and CEA control output lead angle command values, respectively; γ min γ CEC These are the measured values ​​of the inverter-side turn-off angle and the CEC output command value, respectively; β inv The inverter side outputs the leading trigger angle command value; ②MMC control strategy The hybrid cascaded MMC converter employs direct current vector control based on dq-axis decoupling, comprising outer-loop voltage control and inner-loop current control. The outer-loop control can be divided into active and reactive power outer-loop control, while the inner-loop current control is based on the deviation U of the outer-loop output DC voltage. ref -U m and reactive power deviation Q ref -Q m1 / 2 The dq-axis current reference value i is obtained after the PI circuit. dref and i qref By adjusting the actual current value of the dq axis, the reference value of the three-phase AC voltage u at the MMC outlet is finally obtained. ref ; S3, Hybrid Cascade System Fault Recovery Characteristics: ① The impact of multi-controller interaction on system recovery The controller interaction and the changing trends of various electrical quantities are divided into four stages, t1-t5: 1) Stage 1, i.e., time t1 to -t2: At time t0, an AC fault occurs in the receiving-end system; at time t1, the LCC experiences its first commutation failure, and the turn-off angle γ drops to 0. d The increase is rapid, and the system is under CEA control. 2) Stage 2, from t2 to -t3: Under the combined action of rectifier-side CC control and VDCOL, I dr_order With effective constraints, I at time t2 d A rapid decline occurs; once overshoot is detected, CEC is activated, and β... CC The system begins to increase, but due to the late start of CC control, the system in stage 2 is still under CEA control. 3) Stage 3, from t3 to -t4: The system enters the recovery process, with U di Gradually recovering, under the action of VDCOL, at time t3, I d Gradually increase; simultaneously, under continuous CEA control, γ recovers to its steady-state value, β CEA The sudden drop system switches to CC control; 4) Phase 4, from t4 to -t5: The system enters the final stage of the recovery phase, I d Gradually towards the reference value I dref Approaching but still below I dr_order ; ②LCC reactive power demand The reactive power consumed by the inverter-side LCC is: （10） Q LCC to I d The partial derivatives of γ and γ are: （11） in: ； （12） in: ； In the formula, k and X r Both N and N are constants; S4. Method for establishing fault-safe domains in hybrid cascaded systems: ①Multi-electrical quantity coupling characteristics AC bus voltage change ΔU s The transient reactive power ΔQ exchanged between the inverter side and the AC system is as follows: （13） Where SCR is the short-circuit ratio of the receiving-end AC system; ΔQ greater than zero indicates that the inverter side generates reactive power to the receiving-end AC system. AC bus voltage U considering the reactive power support effect of MMC s With the initial AC bus voltage U of the system s0 and MMC reactive power increase ΔQ MMC The relationship between them is: （14） P LCC and Q LCC Represented as: （15） in: ； From the above formula, we get P LCC Q LCC respectively with U s I d The coupling characteristics of γ; ② Fault-safe domain modeling and analysis CEA control command values ​​are represented as follows: （16） In the formula K p K i These represent the proportional gain and integral gain of the PI control element in the CEA control, respectively. When a fault occurs, the CEA control dynamically adjusts β to increase the γ margin. Differentiating the above equation yields: （17） The equivalent transformation of dβ / dt is: （18） During system recovery, the change in the shut-off angle over time, dγ / dt, can be approximated as K. γ ,have to: （19） Integrating the above equation yields the expression for β in terms of γ: （20） U after considering the control effect of CEA dLCC Represented as: （21） When the system enters the recovery phase and the LCC resumes normal commutation, I is obtained. d Regarding P LCC Two solutions: （22） Will I d1 When we insert it into the above formula, we get: （23） in: ， ； Solve P separately LCC to I d The partial derivatives of γ and γ are: （24） In the formula, k and X r Since both N and P are constants, substituting them into the system control parameters yields: P LCC with I d It is directly proportional to γ ​​and inversely proportional to γ; γ should satisfy the following constraints: （25） In the formula, γ0 is the critical turn-off angle at which the system does not experience subsequent commutation failure, γ ref This is the reference value for the shut-off angle when the system is in steady state; Maximum DC current limit I to avoid subsequent commutation failure in LCC dmax for: （26） In the formula α ref This is the rated firing angle. I d The following constraints must be met: （27） In the above I d P under γ constraint LCC and Q LCC Meets the following range: （28） Where P max P min and Q max Q min Each is in a certain U s and I d The maximum and minimum values ​​of active power output and reactive power absorption by the LCC under the constraints of γ and γ; The above extreme values ​​are expressed as: （29） （30） Finally, substituting the solved extreme power operating point into the two boundary fault safety lines yields the safe operating region where the LCC does not experience subsequent commutation failures during the recovery period of the hybrid cascaded system under safety electrical quantity constraints.

2. The method for establishing a fault-safe domain in a hybrid cascaded system according to claim 1, characterized in that: The analysis process of the controller interaction and the changing trends of various electrical quantities in the four stages of the hybrid cascaded system yielded the following results: 1) I starting from phase 3 d The recovery process causes µ to increase rapidly, which in turn leads to a continuous decrease in γ. （31） 2) In stage 3, as I d Gradually recovering, γ CEC The longer the system remains under CC control, the lower β becomes when the controller switches. inv The smaller; 3) After the first commutation failure, P ac Recovery begins, P ac Increasing the size of U will lead to s Phase shifting directly compresses the turn-off angle margin, leading to subsequent commutation failure in the system. （32） In the formula, δ is U s Relative to U G2 Phase offset; X G P is the equivalent reactance of the receiving-end tie line; P is the total active power flowing into the AC grid; ΔP is the active power increment during system recovery. 4) CEA control on I d The response is achieved by reducing the CEC output, thereby lowering β. CEA Achieved, inverter side to I d The response speed lags significantly behind the rectifier side, resulting in U... during system recovery. di Unable to track U in a timely manner dr This causes the pressure difference between the sending and receiving ends to increase, I d Exceeding the baseline value, Q LCC Gradually increase （33） In the formula: U dr L is the DC voltage on the rectifier side. r and L i These represent the inductances of the smoothing reactors on the rectifier and inverter sides, respectively.

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