An efficient electromagnetic transient modeling method for hybrid HVDC systems with IGCTs

Abstract

The present invention relates to an efficient electromagnetic transient modeling method for a hybrid high-voltage direct current transmission system containing IGCT, and belongs to the field of electrical digital data processing. The IGCT high-voltage direct current transmission system includes a grid commutation converter at the sending end, an IGCT converter at the receiving end, and a DC transmission line therebetween. The efficient electromagnetic transient modeling method includes the following steps: at the grid commutation converter at the sending end, an averaging modeling method is used to simplify the switching operation of the thyristor into a port voltage and current average value model, thereby improving the simulation efficiency of the sending end converter; at the IGCT converter at the receiving end, a Thevenin equivalent method is used to simplify the IGCT switching dynamics into a Norton equivalent circuit model of current source and impedance, thereby improving the simulation efficiency of the receiving end converter; for the DC transmission line between the sending and receiving end converter stations, a Berelon model is used to decouple the two ends of the entire line, so that the electrical responses at the two ends can be processed independently, reducing the complexity of the mutual coupling between the two ends of the line and simplifying the calculation process.

Description

Technical Field

[0001] The present invention belongs to the technical field of electromagnetic transient simulation, and in particular relates to an efficient electromagnetic transient modeling method for a hybrid high-voltage direct current (HVDC) power transmission system containing an IGCT. Background Art

[0002] High-voltage direct current (HVDC) transmission technology has become a key technology in modern power grid construction due to its significant advantages in long-distance, large-capacity power transmission. HVDC systems primarily consist of rectifier stations, inverter stations, and DC transmission lines. In practical applications, the dynamic response and fault recovery capabilities of HVDC systems are crucial for their safe and stable operation. Therefore, electromagnetic transient simulation, as a core method for evaluating system dynamic behavior, plays a vital role in power system design and operation.

[0003] As the proportion of power electronic switchgear in power grids continues to increase, their high-frequency switching operations, complex control strategies, and diverse topologies pose significant challenges to improving the efficiency of electromagnetic transient simulation. Improving simulation efficiency while maintaining accuracy has become a pressing technical challenge.

[0004] In the existing technology, a variety of modeling methods have been proposed for different parts of the HVDC system, but the IGCT high-voltage direct current transmission system has not been considered, and most of these methods only consider the rectification, transmission, and inversion links. For example:

[0005] Transmitting-end line-commutated converters (LCCs): LCCs are based on thyristor components (SCRs) and rely on the grid for natural commutation. Their commutation process is relatively fixed, typically operating at a lower frequency and generating fewer harmonics. Several approaches are available for fast LCC modeling, including detailed switch modeling, dynamic phasor modeling, and averaged modeling. Detailed switch modeling accurately captures the switching behavior of the thyristors, but suffers from lower simulation efficiency. Dynamic phasor modeling tracks the system's dynamic response at varying frequencies. However, this approach overemphasizes unnecessary high-frequency responses, increasing simulation complexity and computational time. Therefore, while accurate, dynamic phasor methods are unsuitable for scenarios requiring efficient computation and simplified modeling. In contrast, averaged modeling significantly improves simulation speed by equating the converter's switching operation to a continuous signal of averaged voltage or current, rather than precisely tracking the switching transient behavior of each thyristor. In large-scale AC / DC grid simulations, the details of the converter's internal power electronic switching behavior are often ignored to improve simulation speed, focusing instead on the converter's external characteristics. Considering that in a system like LCC where low-frequency dynamics dominate, using a dynamic phasor model will increase the simulation burden without significantly improving accuracy, an averaging model is chosen that offers a good balance between accuracy and efficiency.

[0006] IGCT converter at the receiving end: Some researchers have proposed that fully controlled devices, integrated gate-commutated thyristors (IGCTs), can be used to replace the thyristors in the LCC bridge arms. This IGCT-based LCC-HVDC configuration can effectively reduce the probability of commutation failure, significantly improve the control flexibility and response speed of the system, and the transformation process is relatively simple, with significant advantages in terms of cost-effectiveness and efficiency. However, the switching dynamics of IGCT are complex. In the existing technology, precise switching modeling is often used for modeling IGCT. Although the accuracy is high, the computational complexity is extremely high, which limits the efficiency improvement of the simulation. So far, no relevant research has proposed a fast modeling method for IGCT-based converters. Therefore, the present invention innovatively proposes to use the Thevenin equivalent method to quickly model the IGCT converter. By simplifying the complex IGCT switching operation into a combination of an equivalent current source and an impedance, the simulation speed is improved while ensuring the simulation accuracy.

[0007] DC transmission lines: Modeling methods for long-distance DC transmission lines include the π-type equivalent circuit model and the Berelon model. The π-type equivalent circuit model is suitable for steady-state analysis, but it struggles to accurately describe electromagnetic wave propagation within the line. The Berelon model, based on traveling wave theory, effectively describes the propagation of voltage and current waves and is suitable for transient analysis. The Berelon model leverages the transmission characteristics of electromagnetic waves to decouple the transient behavior of the two ends of the line, effectively reducing the complexity of the coupling between the two ends, simplifying the calculation process, and improving simulation efficiency.

[0008] Although existing technologies have provided different efficient modeling options for various links of HVDC systems, there is no efficient modeling method for IGCT high-voltage direct current transmission systems that comprehensively considers the entire system.

[0009] Therefore, at this stage, it is necessary to design efficient electromagnetic transient modeling methods, systems and storage media for hybrid HVDC transmission systems containing IGCTs to solve the above problems. Summary of the Invention

[0010] The present invention aims to provide an efficient electromagnetic transient modeling method, system, and storage medium for a hybrid HVDC transmission system containing IGCTs. By comprehensively considering all components of the HVDC transmission system and rationally selecting and integrating modeling methods for the sending-end converter, DC transmission line, and receiving-end converter, the present invention improves the simulation efficiency and accuracy of the entire system, providing valuable reference for engineering applications.

[0011] To achieve the above object, the technical solution of the present invention is:

[0012] An efficient electromagnetic transient modeling method for a hybrid HVDC transmission system including an IGCT, wherein the IGCT HVDC transmission system includes a grid-commutated converter at a sending end, an IGCT converter at a receiving end, and a DC transmission line therebetween. The efficient electromagnetic transient modeling method comprises the following steps:

[0013] S1. At the sending-end grid-commutated converter, an average modeling approach is used to simplify the thyristor switching operation into a model of the average value of the port voltage and current, thereby improving the simulation efficiency of the sending-end converter.

[0014] S2. At the receiving-end IGCT converter, the Thevenin equivalent method is used to simplify the IGCT switching dynamics into a Norton equivalent circuit model of current source and impedance, thereby improving the simulation efficiency of the receiving-end converter;

[0015] S3. For the DC transmission line between the sending and receiving converter stations, the Berelon model is used to decouple the two ends of the entire line so that the electrical responses at both ends can be processed independently, reducing the complexity of the mutual coupling between the two ends of the line and simplifying the calculation process.

[0016] Furthermore, in step S1,

[0017] For a periodic fluctuating signal f(t), its instantaneous value always fluctuates around the DC component of the signal. By averaging the instantaneous values ​​of the signal within a period, the DC component of the signal can be obtained. This process is called "averaging." Specifically, for a variable or function f(t), its average value is:

[0018]

[0019] Where: t represents time; T s Represents the averaging period, and the variable values ​​after averaging are uniformly marked with an overline;

[0020] Averaging modeling uses a controlled source circuit to equate the converter and describe the relationship between AC and DC currents and voltages under the current operating conditions. On the AC and DC sides, there are a set of variables obtained through measurement and a set of variables output by the controlled source. During the simulation process, the averaging model calculates the controlled source output on the other side using the measured values ​​on one side. Specifically, it is determined that the rectifier converter is equivalent to a controlled AC voltage source on the AC side and a controlled DC current source on the DC side. The measured quantities include AC current and DC voltage. It is necessary to establish the relationship between the various components of the AC voltage and the DC voltage, as well as the averaging equations between the various components of the AC current and the DC current.

[0021] When an asymmetric fault occurs in the AC system, harmonic components will appear in the current and voltage on both sides of the AC and DC. Each harmonic component can be decomposed into positive and negative sequence symmetrical components. The voltage and current of the AC bus of the converter can be decomposed into the components shown in formula (2);

[0022]

[0023] Where: and Represent the DC components of the j-phase voltage and current respectively; and They represent the positive sequence components of the j-phase n-order voltage and current respectively; and They represent the negative sequence components of the voltage and current of the j-phase nth order; j represents the a, b or c phase;

[0024] Assume ω e is the angular velocity of the fundamental synchronous rotating coordinate system, then the instantaneous value expressions of each voltage and current component are:

[0025]

[0026] Where: k represents voltage v or current i; and Represent the amplitudes of the positive and negative sequence components of the nth harmonic respectively; and Represent the phase angles of the positive and negative sequence components of the nth harmonic respectively;

[0027] Converting the original three-phase AC signal components into steady-state components of the dq axis in the synchronous coordinate system, the relationship between the AC voltage subcomponents and the DC voltage, as well as the relationship between the AC current subcomponents and the DC current of the controlled AC voltage source can be expressed as follows:

[0028] 1) Relationship between controlled AC voltage source and DC voltage

[0029] The parameter averaging equation between the positive sequence component of the AC voltage nth harmonic and the DC voltage is:

[0030]

[0031] Where: and They represent the d-axis and q-axis components of each positive sequence component of the AC voltage obtained by the corresponding synchronous coordinate system transformation; Represents the DC voltage on the rectifier side; for The angle with the d-axis;

[0032] Similarly, the parameter averaging equation corresponding to the negative sequence component of the AC voltage is as follows:

[0033]

[0034] The parameter averaging equation corresponding to the DC bias component is as follows:

[0035]

[0036] Where: Represents the DC voltage on the rectifier side; and They represent the d-axis and q-axis components of the rectifier AC voltage negative sequence components obtained by corresponding synchronous coordinate system transformation;

[0037]

[0038] for The angle with the d-axis; and They represent the magnitude of the resultant vector of the DC component of the rectifier three-phase voltage after transformation through the stationary dq coordinate system and its angle with the d-axis;

[0039] Where, An unknown algebraic function used to describe the average behavior of the rectifier switching unit to characterize its dynamic characteristics and electrical relationships under different operating conditions;

[0040] 2) Relationship between controlled DC current source and AC current

[0041] The parameter averaging equations between the positive sequence and negative sequence components of the AC current and the DC current are as follows:

[0042]

[0043] Where: Represents the DC current on the rectifier side; in and They represent the d-axis and q-axis components of the positive sequence components of the rectifier AC current respectively, which are transformed into the corresponding synchronous coordinate system; and They represent the d-axis and q-axis components of the rectifier AC current negative sequence components obtained by corresponding synchronous coordinate system transformation;

[0044] Where, is a parameter that changes with the converter firing angle and load conditions;

[0045] Equivalent modeling of the converter using averaging equations achieves electrical decoupling of the AC and DC sides, allowing controlled sources to transmit only secondary information, such as voltage and current values. The relationship between the current and voltage at the converter's AC and DC ports is transformed from the original switching function representation into a set of parameterized algebraic equations.

[0046] The parameters in these equations are usually described by unknown algebraic functions, which depend on the operating state of the system, including the trigger angle of the converter and the load condition. To accurately identify these algebraic functions, the present invention uses a multi-gate hybrid model of experts (MMOE) to handle the nonlinear relationship in complex systems. MMOE is used to fit the voltage and current relationship under complex system conditions through multiple expert models, and the most appropriate expert is dynamically selected to handle the current state through the gate control network, so that the unknown algebraic function can be accurately obtained.

[0047] Furthermore, in step S2,

[0048] In the receiving-end IGCT converter structure, the bridge arm is composed of multiple IGCT devices connected in series and protected by a snubber circuit. A single IGCT and its snubber circuit are considered as a submodule.

[0049] In electromagnetic transient simulation, the IGCT gate trigger is processed into a control signal. The switch conduction condition is that the switch forward voltage is greater than or equal to 0, and the switch off condition is that the switch forward current is less than or equal to 0. The IGCT is equivalent to the variable resistor R0, and the switch element is equivalent.

[0050] The dynamic element capacitance is discretized using the trapezoidal method as follows:

[0051] The differential dynamic equation of capacitance can be expressed as:

[0052]

[0053] Where C0 is the submodule capacitance, v C0 (t) is the voltage across the capacitor, i C0 (t) is the current flowing through the capacitor; the capacitor C0 is discretized, and a single IGC is equivalent. The trapezoidal method is used to sort out equation (15) to obtain:

[0054] v C0 (t) = R ceq0 i C0 (t)+v ceq0 (t-Δt) (16)

[0055] Where Δt is the simulation step length, R ceq0 is the equivalent resistance of the discretized capacitor C0, vceq0 (t-Δt) is the equivalent historical voltage source after the discretization of capacitor C0, That is, the capacitor can be equivalent to a resistor series voltage source after being discretized; R smeq is the Thevenin equivalent resistance of the submodule, v smeq (t) is the Thevenin equivalent voltage source of the submodule, v SM (t) represents the voltage of each submodule port at the current moment, i SM (t) represents the current flowing through the submodule at the current moment;

[0056] The six-pulse bridge of the converter has six bridge arms, each of which is obtained by connecting n submodules in series. The equivalent model of the bridge arm can be obtained by algebraic summation.

[0057] is the Thevenin equivalent resistance of the bridge arm, is the Thevenin equivalent voltage source of the bridge arm;

[0058] Convert Norton format, is the equivalent conductance of the bridge arm, is the Norton equivalent historical current source, v arm (t) represents the terminal voltage of the bridge arm at the current moment, i arm (t) represents the current flowing through the bridge arm at the current moment;

[0059] Thus, the original multi-node network of the bridge arm is transformed into a two-node branch with a resistor and a historical current source connected in parallel.

[0060] Furthermore, in step S3,

[0061] The line parameters of the Berelon model are calculated based on a 50Hz power frequency. For a single-phase lossless line, assume the inductance L1 and capacitance C1 per unit length. The voltage and current at point f on the transmission line, a distance x from terminal m, are functions of both distance and time. The voltage at time t is u(x, t) and the current is i(x, t). When ignoring the frequency-dependent variations in line parameters and the conductance per unit length, the following wave equation can be established:

[0062]

[0063] Rewritten as a second-order wave equation:

[0064]

[0065] The d'Alembert solution is:

[0066]

[0067] Where u f(tx / v) is the forward voltage wave propagating in the positive direction, u b (t+x / v) is the reverse voltage wave propagating in the reverse direction, i f (tx / v) is the forward current wave propagating in the positive direction, i b (t+x / v) is the reverse current wave propagating in the reverse direction; is the propagation speed of the traveling wave along the line, and the wave impedance is

[0068] Combining (19) and (20) and transforming them, we get (21)

[0069]

[0070] At the m and n ends of the line, x = 0 and x = 1 respectively, and let Substituting it into formula (21), we can get the relationship between the voltage and current at both ends of the line;

[0071] u m (t-τ)+Z c i m (t-τ)=u n (t)-Z c i n (t) (22)

[0072] By rearranging formula (22), we can obtain the port current expressed by wave impedance and equivalent current source:

[0073]

[0074] Among them, the corresponding equivalent current sources are:

[0075]

[0076] That is, the wave process in the distributed line parameter model can be represented by a lumped parameter model of wave impedance and equivalent current sources, thereby constructing a two-port model of the transmission line. In this model, there is no direct physical connection between the two ports; instead, the connection is determined by the voltage and current at a previous moment through the action of a current source. This approach achieves natural decoupling of the line.

[0077] For actual transmission lines, the line resistance can be treated as a concentrated resistance and introduced in series in sections. A line of length l is divided into two sections, each of length l / 2. A concentrated resistance R / 4 is connected in series at both ends, and a concentrated resistance R / 2 is connected in series in the middle section, where R is the resistance of the entire line. This results in an equivalent two-port network that takes into account resistance loss. Separating along the dotted line yields two half-split line models.

[0078] Port current:

[0079]

[0080] The corresponding equivalent current sources are:

[0081]

[0082] The two half-split lines are cascaded and simplified to obtain the Berelon transmission line model considering resistance loss.

[0083] The corresponding equivalent current sources are:

[0084]

[0085] An efficient electromagnetic transient modeling system for a hybrid HVDC transmission system including IGCTs is disclosed. The efficient electromagnetic transient modeling system applies the efficient electromagnetic transient modeling method for a hybrid HVDC transmission system including IGCTs as described above to perform efficient electromagnetic transient modeling.

[0086] A storage medium stores a computer program, which, when executed, executes the above-mentioned efficient electromagnetic transient modeling method for a hybrid high-voltage direct current transmission system containing IGCTs.

[0087] Compared with the prior art, the present invention has the following beneficial effects:

[0088] This invention simplifies complex switching operations by selecting modeling methods for various system components, particularly the innovative use of a Thevenin equivalent model for the receiving-end IGCT-based converter. Compared to traditional, precise switch modeling methods, this invention significantly improves simulation speed while maintaining a certain level of simulation accuracy.

[0089] While this paper focuses on improving simulation efficiency, the modeling methods for each component maintain high accuracy. By averaging the modeling of the sending-end LCC converter, the low-frequency dynamic characteristics of the system are effectively captured, the high-frequency switching behavior is simplified, and simulation accuracy is ensured.

[0090] Although existing technologies have proposed replacing thyristors with IGCTs in grid-commutated converters, an efficient modeling solution for this purpose has yet to be proposed. This invention addresses this issue by using Thevenin equivalent modeling to accelerate the modeling of IGCT converters.

[0091] This invention comprehensively considers the collaborative modeling of the sending-end converter, DC transmission line, and receiving-end converter. By organically integrating these various system components, a systematic electromagnetic transient simulation method is formed, significantly improving the overall simulation efficiency of HVDC systems and meeting the real-time simulation requirements of large-scale power systems under complex operating conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0092] Figure 1 Schematic diagram of the process of LCC averaging modeling of the present invention.

[0093] Figure 2 Schematic diagram of the framework of the MMOE of the present invention.

[0094] Figure 3 It is a schematic diagram of the IGCT converter structure of the present invention.

[0095] Figure 4 Schematic diagram of the equivalent switch tube of the present invention.

[0096] Figure 5 Schematic diagram of a single IGCT equivalent model of the present invention.

[0097] Figure 6 Schematic diagram of the bridge arm equivalent model of the present invention.

[0098] Figure 7 Schematic diagram of the Berelon equivalent model of the single-phase lossless line of the present invention.

[0099] Figure 8 Schematic diagram of an equivalent two-port network considering resistance loss of the present invention.

[0100] Figure 9 Schematic diagram of the half-split circuit model of the present invention.

[0101] Figure 10 Schematic diagram of the Berylon transmission line model considering resistance loss of the present invention.

[0102] Figure 11 The figure is a flow chart of a method for efficiently modeling electromagnetic transients of an IGCT high-voltage direct current transmission system according to the present invention. DETAILED DESCRIPTION

[0103] like Figure 11 As shown, an efficient electromagnetic transient modeling method for an IGCT high-voltage direct current transmission system is provided. The IGCT high-voltage direct current transmission system includes a grid-commutated converter at the sending end, an IGCT converter at the receiving end, and a DC transmission line therebetween. The efficient electromagnetic transient modeling method is implemented by the following steps:

[0104] (1) At the grid-commutated converter on the sending end, an average modeling method is used to simplify the switching operation of the thyristor into a model of the average value of the port voltage and current, thereby improving the simulation efficiency of the sending-end converter;

[0105] (2) At the receiving-end IGCT converter, the Thevenin equivalent method is used to simplify the complex IGCT switching dynamics into a Norton equivalent circuit model of current source and impedance, thereby improving the simulation efficiency of the receiving-end converter;

[0106] (3) For the DC transmission line between the sending and receiving converter stations, the Berelon model is used to decouple the two ends of the entire line so that the electrical responses at both ends can be processed independently, reducing the complexity of the mutual coupling between the two ends of the line, simplifying the calculation process, and improving the simulation efficiency.

[0107] The averaged modeling of the sending-end grid-commutated converter simplifies the high-frequency switching behavior in the sending-end converter into continuous voltage and current signals by integrating and averaging the switching cycles of the thyristors, thereby reducing the computational complexity and ensuring simulation accuracy.

[0108] The Thevenin equivalent modeling of the receiving-end IGCT converter simplifies the switching behavior of multiple IGCT devices into an equivalent circuit composed of current sources and impedances, making it possible to accurately simulate the system voltage and current waveforms in fast simulation.

[0109] The Berelon model is used to model DC transmission lines. It can improve the computational efficiency of system-level simulation by decoupling the transient behavior of the converter stations at both ends.

[0110] By combining multiple efficient modeling methods, including averaging modeling of the sending-end grid commutation converter, Thevenin equivalent modeling of the receiving-end IGCT converter, and DC transmission line decoupling based on the Berelon model, the computational efficiency of large-scale electromagnetic transient simulation can be significantly improved. This approach is particularly suitable for real-time simulation and dynamic response analysis of complex HVDC transmission systems.

[0111] 1. Average modeling of the sending-end converter station

[0112] To improve simulation speed, in large-scale AC / DC power grid simulations, the specific details of the power electronic switching operations inside the converter are usually omitted, and the focus is placed on the external characteristics of the converter.

[0113] The core method of averaging modeling is to ignore the transient details within each switching cycle and simplify the output description of the system by taking the average value of rapidly changing variables (such as voltage and current) within one cycle.

[0114] For a periodic fluctuating signal f(t), its instantaneous value always fluctuates around the DC component of the signal. By averaging the instantaneous values ​​of the signal within a period, the DC component of the signal can be obtained. This process is called "averaging." Specifically, for a variable or function f(t), its average value is:

[0115]

[0116] Where: t represents time; T s Represents the averaging period, and the variable values ​​after averaging are uniformly marked with an overline;

[0117] The process of LCC averaging modeling is as follows Figure 1 As shown:

[0118] Averaging modeling uses a controlled source circuit to represent the converter, describing the relationship between AC and DC currents and voltages under current operating conditions. On the AC and DC sides, there are two sets of variables obtained through measurements, one set output by the controlled source. During simulation, the averaging model uses the measured values ​​on one side to calculate the controlled source output on the other side. Specifically, the rectifier converter is determined to be equivalent to a controlled AC voltage source on the AC side and a controlled DC current source on the DC side. The measured quantities include AC current and DC voltage. It is necessary to establish the relationship between the AC voltage subcomponents and the DC voltage, as well as the averaging equations between the AC current subcomponents and the DC current.

[0119] Harmonics will affect the triggering signals of the thyristors of the phase-commutating converters in the power grid. Therefore, the effects of the main harmonic components must be fully considered when constructing their models.

[0120] When an asymmetric fault occurs in the AC system, harmonic components will appear in the current and voltage on both sides of the AC and DC. Each harmonic component can be decomposed into positive and negative sequence symmetrical components. The voltage and current of the AC bus of the converter can be decomposed into the components shown in formula (2);

[0121]

[0122] Where: and Represent the DC components of the j-phase voltage and current respectively; and They represent the positive sequence components of the j-phase n-order voltage and current respectively; and They represent the negative sequence components of the voltage and current of the j-phase nth order; j represents the a, b or c phase;

[0123] Assume ω e is the angular velocity of the fundamental synchronous rotating coordinate system, then the instantaneous value expressions of each voltage and current component are:

[0124]

[0125] Where: k represents voltage v or current i; and Represent the amplitudes of the positive and negative sequence components of the nth harmonic respectively; and Represent the phase angles of the positive and negative sequence components of the nth harmonic respectively;

[0126] Converting the original three-phase AC signal components into steady-state components of the dq axis in the synchronous coordinate system, the relationship between the AC voltage subcomponents and the DC voltage, as well as the relationship between the AC current subcomponents and the DC current of the controlled AC voltage source can be expressed as follows:

[0127] 1) Relationship between controlled AC voltage source and DC voltage

[0128] The parameter averaging equation between the positive sequence component of the AC voltage nth harmonic and the DC voltage is:

[0129]

[0130] Where: and They represent the d-axis and q-axis components of each positive sequence component of the AC voltage obtained by the corresponding synchronous coordinate system transformation; Represents the DC voltage on the rectifier side; for The angle with the d-axis;

[0131] Similarly, the parameter averaging equation corresponding to the negative sequence component of the AC voltage is as follows:

[0132]

[0133] The parameter averaging equation corresponding to the DC bias component is as follows:

[0134]

[0135] Where: Represents the DC voltage on the rectifier side; and They represent the d-axis and q-axis components of the rectifier AC voltage negative sequence components obtained by corresponding synchronous coordinate system transformation;

[0136]

[0137] for The angle with the d-axis; and They represent the magnitude of the resultant vector of the DC component of the rectifier three-phase voltage after transformation through the stationary dq coordinate system and its angle with the d-axis;

[0138] Where, An unknown algebraic function used to describe the average behavior of the rectifier switching unit to characterize its dynamic characteristics and electrical relationships under different operating conditions;

[0139] 2) Relationship between controlled DC current source and AC current

[0140] The parameter averaging equations between the positive sequence and negative sequence components of the AC current and the DC current are as follows:

[0141]

[0142] Where: Represents the DC current on the rectifier side; in and They represent the d-axis and q-axis components of the positive sequence components of the rectifier AC current respectively, which are transformed into the corresponding synchronous coordinate system; and They represent the d-axis and q-axis components of the rectifier AC current negative sequence components obtained by corresponding synchronous coordinate system transformation;

[0143] Where, is a parameter that changes with the converter firing angle and load conditions;

[0144] Equivalent modeling of the converter using averaging equations achieves electrical decoupling of the AC and DC sides, allowing controlled sources to transmit only secondary information, such as voltage and current values. The relationship between the current and voltage at the converter's AC and DC ports is transformed from the original switching function representation into a set of parameterized algebraic equations.

[0145] The parameters in these equations are usually described by unknown algebraic functions, which depend on the operating state of the system, including the trigger angle of the converter and the load condition. To accurately identify these algebraic functions, the present invention uses a multi-gate hybrid model of experts (MMOE) to handle the nonlinear relationship in complex systems. MMOE is used to fit the voltage and current relationship under complex system conditions through multiple expert models, and the most appropriate expert is dynamically selected to handle the current state through the gate control network, so that the unknown algebraic function can be accurately obtained.

[0146] The basic principles are as follows:

[0147] The framework of MMOE is as follows Figure 2 Multi-task learning enables a single model to process both current and voltage simultaneously, eliminating the need to design independent architectures for each subtask and avoiding the need to repeatedly construct the same type of neuron configurations, while ensuring the flexibility and adaptability of the model.

[0148] The problem of identifying unknown algebraic functions is divided into multiple tasks. In this study, Task 1 is to fit the relationship between AC voltage and DC voltage, and Task 2 is to fit the relationship between AC current and DC current.

[0149] To accurately describe the system's behavior under different load conditions and firing angles, multiple expert models are trained to handle different state spaces. Each expert model excels at handling nonlinear relationships under specific conditions, such as low load, high load, or a specific firing angle range.

[0150] The gating network is used to dynamically assign weights to each expert model based on the current system state (such as firing angle, load conditions, etc.). The output of the gating network is the combined weight of each expert model, allowing the model to adaptively select the optimal expert under different operating conditions.

[0151] The weights of the gating network are used to combine the outputs of the various expert models to produce a final algebraic function. These functions accurately predict the relationship between AC and DC voltages and currents based on measured values ​​under different operating conditions. The expert models and gating network are trained using a large amount of measured data, and the model's accuracy and adaptability are verified through simulation. The resulting model can quickly calculate the output of the other side using measured values ​​in real-time, achieving accurate modeling of the converter system.

[0152] 2. Thevenin equivalent modeling of the receiving converter station

[0153] The structure of the receiving end IGCT converter is as follows Figure 3 As shown in the left figure, the bridge arm is composed of multiple IGCT devices connected in series and protected by a snubber circuit. A single IGCT and its snubber circuit are considered as a submodule. Figure 3 As shown in the picture on the right.

[0154] IGCT can combine the advantages of IGBT and GTO, with the conduction characteristics of GTO and the switching characteristics of IGBT. It has strong current carrying capacity and low on-state voltage. In electromagnetic transient simulation, the IGCT gate trigger is processed into a control signal. It is assumed that the IGCT is replaced by a smaller resistor in the on state and a larger resistor in the off state. The switch conduction condition is that the forward voltage of the switch is greater than or equal to 0, and the off condition is that the forward current of the switch is less than or equal to 0. The IGCT is equivalent to the variable resistor R0. After the switch element is equivalent, the equivalent model of a single IGCT and its buffer circuit switch is as follows: Figure 4 shown.

[0155] The dynamic element capacitance is discretized using the trapezoidal method as follows:

[0156] The differential dynamic equation of capacitance can be expressed as:

[0157]

[0158] Where C0 is the submodule capacitance, v C0 (t) is the voltage across the capacitor, i C0(t) is the current flowing through the capacitor. Discretizing the capacitor C0 and performing the equivalent calculation on a single IGC yields Figure 5 , using the trapezoidal method to sort out equation (15) we can get:

[0159] v C0 (t) = R ceq0 i C0 (t)+v ceq0 (t-Δt) (16)

[0160] Where Δt is the simulation step length, R ceq0 is the equivalent resistance of the discretized capacitor C0, v ceq0 (t-Δt) is the equivalent historical voltage source after the discretization of capacitor C0, That is, after the capacitor is discretized, it can be equivalent to a resistor in series with a voltage source. smeq is the Thevenin equivalent resistance of the submodule, v smeq (t) is the Thevenin equivalent voltage source of the submodule, v SM (t) represents the voltage of each submodule port at the current moment, i SM (t) represents the current flowing through the submodule at the current moment.

[0161] The six-pulse bridge of the converter has six bridge arms, each of which is obtained by connecting n submodules (including IGCT and snubber circuit) in series. The equivalent model of the bridge arm can be obtained by algebraic summation, as follows: Figure 6 shown.

[0162] In the left picture, is the Thevenin equivalent resistance of the bridge arm, is the Thevenin equivalent voltage source of the bridge arm. The right figure is the transformed Norton form. is the equivalent conductance of the bridge arm, is the Norton equivalent historical current source, v arm (t) represents the terminal voltage of the bridge arm at the current moment, i arm (t) represents the current flowing through the bridge arm at the current moment.

[0163] Thus, the original multi-node network of the bridge arm is converted into a two-node branch consisting of a resistor and a historical current source in parallel, which improves the calculation efficiency.

[0164] 3. Decoupling model of DC transmission lines

[0165] The line parameters of the Berelon model are calculated based on a 50Hz power frequency. For a single-phase lossless line, assume the inductance L1 and capacitance C1 per unit length. The voltage and current at point f on the transmission line, a distance x from terminal m, are functions of both distance and time. The voltage at time t is u(x, t) and the current is i(x, t). When ignoring the frequency-dependent variations in line parameters and the conductance per unit length, the following wave equation can be established:

[0166]

[0167] Further rewritten as a second-order wave equation:

[0168]

[0169] The d'Alembert solution is:

[0170]

[0171] Where u f (tx / v) is the forward voltage wave propagating in the positive direction, u b (t+x / v) is the reverse voltage wave propagating in the reverse direction, i f (tx / v) is the forward current wave propagating in the positive direction, i b (t+x / v) is the reverse current wave propagating in the reverse direction. is the propagation speed of the traveling wave along the line, and the wave impedance is

[0172] Combining (19) and (20) and transforming them, we get (21)

[0173]

[0174] At the m and n ends of the line, x = 0 and x = 1 respectively, and let Substituting it into formula (21) we can get the relationship between the voltage and current at both ends of the line.

[0175] u m (t-τ)+Z c i m (t-τ)=u n (t)-Z c i n (t) (22)

[0176] By rearranging formula (22), we can obtain the port current expressed by wave impedance and equivalent current source:

[0177]

[0178] Among them, the corresponding equivalent current sources are:

[0179]

[0180] That is, the distributed line parameter model containing the wave process can be expressed as a lumped parameter model of wave impedance and equivalent current source, and the obtained transmission line two-port model is as follows: Figure 7 In this model, there is no direct physical connection between the two ports. Instead, the connection is established through a current source, determined by the voltage and current at a previous moment. This approach achieves natural decoupling of the circuits.

[0181] For actual transmission lines, the line resistance can be treated as a concentrated resistance and introduced in series in sections. A line with a length of l is divided into two sections, each section is l / 2 long, and a concentrated resistance R / 4 is connected in series at both ends, and a concentrated resistance R / 2 is connected in series in the middle section, where R is the resistance of the entire line. Figure 7 You can draw as Figure 8 The equivalent two-port network considering resistance loss is shown in Figure 2. Separating along the dotted line, we get two half-circuit models as shown in Figure 2. Figure 9 shown.

[0182] Port current:

[0183]

[0184] The corresponding equivalent current sources are:

[0185]

[0186] Cascade the two half-split circuits and simplify to get Figure 10 The Berelon transmission line model considering resistive losses is shown.

[0187] contrast, Figure 9 Because the calculation conditions at both ends of the line including the time (t-τ / 2) are taken into account, only the current source term representing the history term changes.

[0188]

[0189] Actual transmission lines are typically three-phase systems. To more effectively apply the Berelon model to practical situations, the derivation of the Berelon model for single-phase transmission lines can be extended to the Berelon model for three-phase transmission lines. Unlike the single-phase model, in the three-phase model, voltages and currents are represented using vectors, while capacitances and inductances are described using matrices containing off-diagonal elements. Because the Berelon model only holds true for modal components, a matrix transformation is required to fully diagonalize the parameter matrix to eliminate interphase coupling. Specifically, the matrix transformation converts the coupled equations in the phase domain into a decoupled equation in the modal domain, allowing each modal component to be calculated independently. After this transformation, each modal circuit can be independently calculated using the Berelon model, enabling efficient analysis and simulation of three-phase systems.

Claims

1. An efficient electromagnetic transient modeling method for a hybrid HVDC transmission system containing IGCTs, wherein the IGCT HVDC transmission system comprises a grid-commutated converter at the sending end, an IGCT converter at the receiving end, and a DC transmission line therebetween, characterized in that: The efficient electromagnetic transient modeling method comprises the following steps: S1. At the sending-end grid-commutated converter, an average modeling approach is used to simplify the thyristor switching operation into a model of the average value of the port voltage and current, thereby improving the simulation efficiency of the sending-end converter. S2. At the receiving end of the IGCT converter, the Thevenin equivalent method is used to simplify the IGCT switching dynamics into a Norton equivalent circuit model of current source and impedance; S3. For the DC transmission line between the sending and receiving converter stations, the Berelon model is used to decouple the two ends of the entire line, allowing the electrical responses at both ends to be processed independently, reducing the complexity of the mutual coupling between the two ends of the line and simplifying the calculation process; In step S1, For a periodic fluctuating signal f(t), its instantaneous value always fluctuates around the DC component of the signal. The DC component of the signal can be obtained by averaging the instantaneous values ​​of the signal within a period. This process is called "averaging". Specifically, for a variable or function f(t), its average value is: Where: t represents time; T s Represents the averaging period, and the variable values ​​after averaging are uniformly marked with an overline; Averaging modeling uses a controlled source circuit to equate the converter, describing the relationship between AC and DC currents and voltages under current operating conditions. On the AC and DC sides, there are a set of variables obtained through measurement and a set of variables output by the controlled source. During the simulation process, the averaging model calculates the controlled source output on the other side using the measured values ​​on one side. Specifically, the rectifier converter is determined to be equivalent to a controlled AC voltage source on the AC side and a controlled DC current source on the DC side. Measurements include AC current and DC voltage. It is necessary to establish the relationship between the various subcomponents of the AC voltage and the DC voltage, as well as the averaging equations between the various subcomponents of the AC current and the DC current. When an asymmetric fault occurs in the AC system, harmonic components will appear in the current and voltage on both sides of the AC and DC. Each harmonic component can be decomposed into positive and negative sequence symmetrical components. The voltage and current of the AC bus of the converter can be decomposed into the components shown in formula (2); Where: and Represent the DC components of the j-phase voltage and current respectively; and They represent the positive sequence components of the j-phase n-order voltage and current respectively; and They represent the negative sequence components of the voltage and current of the j-phase nth order; j represents the a, b or c phase; Assume ω e is the angular velocity of the fundamental synchronous rotating coordinate system, then the instantaneous value expressions of each voltage and current component are: Where: k represents voltage v or current i; and Represent the amplitudes of the positive and negative sequence components of the nth harmonic respectively; and Represent the phase angles of the positive and negative sequence components of the nth harmonic respectively; Converting the original three-phase AC signal components into steady-state components of the dq axis in the synchronous coordinate system, the relationship between the AC voltage subcomponents and the DC voltage, as well as the relationship between the AC current subcomponents and the DC current of the controlled AC voltage source can be expressed as follows: 1) Relationship between controlled AC voltage source and DC voltage The parameter averaging equation between the positive sequence component of the AC voltage nth harmonic and the DC voltage is: Where: and They represent the d-axis and q-axis components of each positive sequence component of the AC voltage obtained by the corresponding synchronous coordinate system transformation; Represents the DC voltage on the rectifier side; for The angle with the d-axis; Similarly, the parameter averaging equation corresponding to the negative sequence component of the AC voltage is as follows: The parameter averaging equation corresponding to the DC bias component is as follows: Where: Represents the DC voltage on the rectifier side; and They represent the d-axis and q-axis components of the rectifier AC voltage negative sequence components obtained by corresponding synchronous coordinate system transformation; for The angle with the d-axis; and They represent the magnitude of the resultant vector of the DC component of the rectifier three-phase voltage after transformation through the stationary dq coordinate system and its angle with the d-axis; Where, An unknown algebraic function used to describe the average behavior of the rectifier switching unit to characterize its dynamic characteristics and electrical relationships under different operating conditions; 2) Relationship between controlled DC current source and AC current The parameter averaging equations between the positive sequence and negative sequence components of the AC current and the DC current are as follows: Where: Represents the DC current on the rectifier side; in and They represent the d-axis and q-axis components of the positive sequence components of the rectifier AC current respectively, which are transformed into the corresponding synchronous coordinate system; and They represent the d-axis and q-axis components of the rectifier AC current negative sequence components obtained by corresponding synchronous coordinate system transformation; Where, is a parameter that changes with the converter firing angle and load conditions; Equivalent modeling of the converter using averaging equations achieves electrical decoupling of the AC and DC sides, allowing controlled sources to transmit only secondary information, such as voltage and current values. The relationship between the current and voltage at the converter's AC and DC ports is transformed from the original switching function representation into a set of parameterized algebraic equations. The parameters in the equation are described by unknown algebraic functions, which depend on the operating state of the system, including the trigger angle of the converter and the load condition. To accurately identify the algebraic function, a multi-gate hybrid expert model (MMOE) is used to handle the nonlinear relationship in the system. MMOE is used to fit the voltage and current relationship under complex system conditions through multiple expert models, and the most appropriate expert is dynamically selected to handle the current state through the gate control network, so that the unknown algebraic function can be obtained. In step S2, In the receiving-end IGCT converter structure, the bridge arm is composed of multiple IGCT devices connected in series and protected by a snubber circuit. A single IGCT and its snubber circuit are regarded as a submodule. In electromagnetic transient simulation, the IGCT gate trigger is processed into a control signal. The switch conduction condition is that the switch forward voltage is greater than or equal to 0, and the switch off condition is that the switch forward current is less than or equal to 0. The IGCT is equivalent to the variable resistor R0, and the switch element is equivalent. The dynamic element capacitance is discretized using the trapezoidal method as follows: The differential dynamic equation of capacitance can be expressed as: Where C0 is the submodule capacitance, v C0 (t) is the voltage across the capacitor, i C0 (t) is the current flowing through the capacitor; the capacitor C0 is discretized, and a single IGC is equivalent. The trapezoidal method is used to sort out equation (15) to obtain: v C0 (t)=R ceq0 i C0 (t)+v ceq0 (t-Δt) (16) Where Δt is the simulation step length, R ceq0 is the equivalent resistance of the discretized capacitor C0, v ceq0 (t-Δt) is the equivalent historical voltage source after the discretization of capacitor C0, That is, the capacitor can be equivalent to a resistor series voltage source after being discretized; R smeq is the Thevenin equivalent resistance of the submodule, v smeq (t) is the Thevenin equivalent voltage source of the submodule, v SM (t) represents the voltage of each submodule port at the current moment, i SM (t) represents the current flowing through the submodule at the current moment; The six-pulse bridge of the converter has six bridge arms, each of which is obtained by connecting n submodules in series. The equivalent model of the bridge arm can be obtained by algebraic summation. is the Thevenin equivalent resistance of the bridge arm, is the Thevenin equivalent voltage source of the bridge arm; Convert Norton format, is the equivalent conductance of the bridge arm, is the Norton equivalent historical current source, v arm (t) represents the terminal voltage of the bridge arm at the current moment, i arm (t) represents the current flowing through the bridge arm at the current moment; Thus, the original multi-node network of the bridge arm is transformed into a two-node branch with a resistor and a historical current source in parallel; In step S3, The line parameters of the Berelon model are calculated based on a 50Hz power frequency. For a single-phase lossless line, assume the inductance L1 and capacitance C1 per unit length. The voltage and current at point f on the transmission line, a distance x from terminal m, are functions of both distance and time. The voltage at time t is u(x, t) and the current is i(x, t). When ignoring the frequency-dependent variations in line parameters and the conductance per unit length, the following wave equation can be established: Rewritten as a second-order wave equation: The d'Alembert solution is: Where u f (tx / v) is the forward voltage wave propagating in the positive direction, u b (t+x / v) is the reverse voltage wave propagating in the reverse direction, i f (tx / v) is the forward current wave propagating in the positive direction, i b (t+x / v) is the reverse current wave propagating in the reverse direction; is the propagation speed of the traveling wave along the line, and the wave impedance is Combining (19) and (20) and transforming them, we get (21) At the m and n ends of the line, x = 0 and x = 1 respectively, and let Substituting it into formula (21), we can get the relationship between the voltage and current at both ends of the line; u m (t-τ)+Z c i m (t-τ)=u n (t)-Z c i n (t) (22) By rearranging formula (22), we can obtain the port current expressed by wave impedance and equivalent current source: Among them, the corresponding equivalent current sources are: That is, the wave process in the distributed line parameter model can be represented by a lumped parameter model of wave impedance and equivalent current source, thereby constructing a two-port model of the transmission line. In this model, there is no direct physical connection between the two ports. Instead, the two ports are connected by the action of the current source, which is determined by the voltage and current at a previous moment. This approach achieves natural decoupling of the line. For actual transmission lines, the line resistance can be treated as a concentrated resistance and introduced in series in sections. The line length l is divided into two sections, each section is l / 2 long, and a concentrated resistance R / 4 is connected in series at both ends, and a concentrated resistance R / 2 is connected in series in the middle section, where R is the resistance of the entire line length. An equivalent two-port network considering resistance loss is obtained. Two half-split line models are obtained by separating along the dotted line. Port current: The corresponding equivalent current sources are: The two half-split lines are cascaded and simplified to obtain the Berelon transmission line model considering resistance loss.

2. An efficient electromagnetic transient modeling system for hybrid HVDC transmission systems containing IGCTs, characterized by: The efficient electromagnetic transient modeling system applies the efficient electromagnetic transient modeling method of the hybrid high-voltage direct current transmission system containing IGCT according to claim 1 to perform efficient electromagnetic transient modeling.

3. A storage medium, characterized in that: The storage medium stores a computer program, which, when executed, executes the efficient electromagnetic transient modeling method for a hybrid HVDC power transmission system containing IGCTs according to claim 1.

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