Steady-state characteristic analysis method for diode-rectified dc collection power system

Abstract

The application discloses a steady-state characteristic analysis method of a diode rectifier direct-current collection power system, which comprises the following steps: constructing a point-to-point system topology model, wherein the point-to-point system comprises an alternating-current subsystem, a diode rectifier and a direct-current subsystem; respectively establishing an alternating-current subsystem holomorphic embedding model and a direct-current subsystem holomorphic embedding model based on a self-selected power series initial point holomorphic embedding load flow calculation method (A-HELM); establishing an interface model of the diode rectifier based on the conversion relationship among alternating-current voltage, direct-current voltage and power; adopting an alternating iteration method, coordinating the alternating-current and direct-current interfaces through outer iteration, and sequentially solving the direct-current subsystem holomorphic embedding model, the interface model of the diode rectifier and the alternating-current subsystem holomorphic embedding model in the inner layer until global convergence is achieved; and analyzing the steady-state operation characteristics of the point-to-point system according to the output results after convergence. The method can accurately capture the dynamic influence of commutation reactance on the voltage drop of the direct-current side and the reactive power consumption of the alternating-current side, and realizes accurate description of the physical mechanism of the DRU.

Description

Technical Field

[0001] This invention relates to the field of DC power system analysis technology, and specifically to a method for analyzing the steady-state characteristics of a diode-rectified DC collection power system. Background Technology

[0002] In specific application scenarios such as offshore wind power cluster integration and ultra-long-distance power transmission, high-voltage direct current (HVDC) transmission technology has become a key carrier for achieving optimized cross-regional energy allocation due to its significant advantages in transmission capacity, line loss, and asynchronous interconnection. Currently, the DC converter solutions widely adopted in industry mainly focus on voltage source converters (VSCs) and traditional line commutated converters (LCCs). However, the complex control architecture, expensive semiconductor device costs, and relatively significant operating losses of VSC technology greatly limit its economic applicability in large-scale, long-lifecycle projects. Traditional LCC solutions are prone to commutation failures during operation and lack autonomous fault ride-through capabilities when dealing with system faults, making it difficult to meet increasingly stringent grid stability requirements.

[0003] Against this backdrop, diode rectifier units (DRUs), with their inherent technological advantages such as small size, extremely high reliability, low operating losses, and low construction costs, have gradually become the focus of attention in academia and engineering. Organically combining DRUs with grid-based energy storage systems to construct compact and lightweight DC transmission solutions has become an important direction for promoting the evolution of future new energy DC aggregation technologies. However, as AC / DC hybrid transmission systems develop towards large-scale, multi-terminal, and complex topologies, a deep technical contradiction has arisen between the passive characteristics of DRUs and the diversity of system control modes. Furthermore, the algebraic equations of new systems exhibit extremely high non-convexity and transcendental characteristics, making the calculation process highly sensitive to the selection of initial values. Moreover, when dealing with complex AC / DC interface matching, the frequent occurrence of singularities in the Jacobian matrix often leads to iterative divergence or getting trapped in locally ill-conditioned solutions with no physical meaning.

[0004] Reference [1]: Wei Zhinong, Ji Cong, Sun Guoqiang. Optimal power flow calculation of AC / DC system with VSC-HVDC using interior point method [J]. Proceedings of the CSEE, 2012, 32(19): 89-95+190. DOI: 10.13334 / j.0258-8013.pcsee.2012.19.014. By improving the traditional interior point method, a VSC-HVDC steady-state model for solving the optimal power flow using the original dual interior point method and the predictive correction interior point method is proposed, which greatly reduces the number of iterations.

[0005] Reference [2]: Lin Junjie, Hu Hanye, Wang Xinwu, et al. Fully embedded power flow calculation method for AC / DC system of flexible traction power supply in subway considering the control characteristics of bidirectional converter [J / OL]. Power System Technology, 1-17 [2026-03-17]. https: / / doi.org / 10.13335 / j.1000-3673.pst.2025.1121. For AC / DC system of flexible traction power supply in subway, a fully embedded power flow method based on self-selected power series initial point is proposed to achieve more stable and efficient calculation.

[0006] Reference [3]: Jiang Tao, Zhang Yong, Li Xue, et al. Fully embedded calculation of AC / DC power flow in power system [J]. Journal of Electrical Engineering, 2021, 36(21):4429-4443+4481.DOI:10.19595 / j.cnki.1000-6753.tces.201306. Focusing on the master-slave control mode of VSC converter station, a fully embedded method for AC / DC power flow calculation is proposed.

[0007] The numerical calculation methods mentioned above are mainly for VSC-HVDC system design or applications in other fields. However, they lack a robust and reliable computational benchmark for novel DC-DC power systems composed of diode rectifiers (DRUs) and grid-type energy storage systems, which face challenges in power flow distribution acquisition, including complex topologies, diverse control modes, high nonlinearity, and the sensitivity of traditional Newton-Raphson algorithms to initial conditions and the tendency for iteration to diverge. Therefore, there is an urgent need to introduce more rigorous mathematical analysis theories to compensate for the shortcomings of existing technologies and ensure the safe and reliable operation of future energy systems. Summary of the Invention: This invention provides a steady-state characteristic analysis method for diode-rectified DC-DC power systems. This method can accurately capture the dynamic influence of commutation reactance on DC-side voltage drop and AC-side reactive power consumption, and achieves a precise characterization of the physical mechanism of DRU. When dealing with novel systems containing DRU and grid-type energy storage with strong nonlinear characteristics and diverse constraints, this method can completely solve the inherent problems of Jacobian matrix singularity and computational non-convergence.

[0008] The technical solution adopted in this invention is as follows: The steady-state characteristic analysis method for diode-rectified DC-DC power systems includes the following steps: Step 1: Construct a point-to-point system topology model, which includes an AC subsystem, a diode rectifier, and a DC subsystem; Step 2: Based on the fully embedded power flow calculation method with self-selected power series initial points (A-HELM), establish fully embedded models for the AC subsystem and the DC subsystem respectively; Step 3: Based on the conversion relationship between AC voltage and DC voltage and power, establish the interface model of the diode rectifier; Step 4: Using the alternating iterative method, the AC / DC interface is coordinated through outer-layer iteration, and the fully embedded DC subsystem model, the diode rectifier interface model, and the fully embedded AC subsystem model are solved sequentially in the inner layer until global convergence is achieved. Step 5: Analyze the steady-state operating characteristics of the point-to-point system based on the converged output results.

[0009] In step 1, the constructed point-to-point system topology model includes: grid-type energy storage, new energy power stations, AC buses, diode rectifiers, DC lines, and receiving-end constant DC voltage converter stations, with the following connection relationships: The grid-type energy storage and new energy power stations are connected in parallel to the AC bus. The AC bus is connected to the AC side of the diode rectifier, and the DC side of the diode rectifier is connected to the receiving-end constant DC voltage converter station through a DC line.

[0010] in: Grid-based energy storage acts as a balancing node, providing stable voltage to the AC bus. and frequency support; The renewable energy power station acts as a PQ node, injecting active power into the AC bus. and reactive power ; AC bus (PCC): The common connection point connecting grid-type energy storage and new energy power stations; Diode rectifier: Converts alternating current to direct current using a six-pulse uncontrolled rectifier topology; DC line: Connecting the diode rectifier output and the receiving-end DC voltage converter station, establish a π-type equivalent circuit model of the DC submarine cable, including the DC line resistance. Inductance and capacitance to ground; Receiving-end constant DC voltage converter station: A modular multilevel converter (MMC) is used as the V-node to maintain a constant DC voltage. .

[0011] In step 2, the fully embedded power flow calculation method with self-selected power series initial points (A-HELM) is used to establish fully embedded models for the AC subsystem and the DC subsystem, that is, by introducing complex analytical embedding parameters. The nonlinear power flow equations of the AC / DC system are transformed into equations about holomorphic functions. Specifically, these include: The AC subsystem includes grid-type energy storage nodes and new energy power station nodes. The fully embedded model of the constructed AC subsystem is as follows: 1) The grid-type energy storage node acts as a balancer node (SL node). The fully embedded model of the grid-type energy storage node is as follows: (1); in, Indicates the embedded parameters The holomorphic function of the energy storage node voltage. To embed complex variables, when α=0: V=1, i.e., the initial solution, corresponding to no-load or flat start; when α=1: V= That is, the target solution, the rated voltage; The rated voltage of the energy storage node is given, i.e., the control target. An analytical initial value is provided for HELM by constructing a known voltage change path.

[0012] 2) The new energy power station node is used as a PQ node. The fully embedded model of the new energy power station node is as follows: (2); in, It's about nodes. i and j Line admittance, It is a node i The ground-based self-admittance is as follows: (3); in, This indicates the node number currently being examined, and it will iterate through all PQ nodes; It is the self-admittance of node i, including all branches. It is the branch admittance between nodes i and j.

[0013] (4); in, It is the conductance of the k-th branch to ground. It is the susceptance of the k-th ground branch. The imaginary unit is used for reactive power. .

[0014] This indicates that node j is embedded in the parameters. The pure voltage function under these conditions; Represents the initial state quantity of the voltage function; Represents the voltage conjugate function; express The conjugate complex variable, where the "*" operator represents the conjugate operation; Represents the holomorphic voltage function of node i under the embedding parameter α; This represents a fully embedded variable, which is a complex parameter that changes continuously from 0 to 1, controlling the power from 0 to the target value; Represents the complete admittance between nodes i and j; The initial state quantity representing the voltage function ( The solution when =0).

[0015] S is a node i Net injected power, For nodes i The complex power conjugate of the net injected power is as follows: (5); in, and These are the active and reactive power outputs of new energy sources, respectively. This refers to the active power absorbed by the rectifier from the AC bus.

[0016] The DC subsystem includes the sending-end rectifier output node and the receiving-end constant voltage node. The fully embedded model of the DC subsystem is as follows: 1) The output node of the sending-end rectifier is taken as node P (with known power). The fully embedded model of the output node of the sending-end rectifier is as follows: (6); in, This is a DC conductance matrix; Inject DC power into the sending end; 2) The receiving-end constant voltage node is controlled by a constant DC voltage and is used as a V node (with known voltage). The fully embedded model of the receiving-end constant voltage node is as follows: (7); in, Indicates the embedded parameters The holomorphic function of the receiving-end node voltage; The given value of the DC voltage at the receiving node is the control target.

[0017] In step 3, the diode rectifier serves as an interface module, and is described using the following power flow model: 3.1: Diode voltage transformation equation: Given DC current Based on the diode voltage-current characteristics, the following is obtained: (8); in, This represents the AC side voltage value of the diode rectifier. This represents the DC-side voltage value of the diode rectifier. For commutation reactance, it can sometimes be disregarded.

[0018] 3.2: Diode Loss Equation: Given DC current The converter loss formula is: (9); in, This represents the loss value of the diode rectifier; a, b, and c are loss coefficients, which can be calculated based on the rated parameters of the rectifier.

[0019] 3.3: Power Balance Equation: (10); in, This represents the active power delivered to the rectifier by the AC system, i.e., the total input power; This represents the active power delivered by the DC system from the converter station after conversion, i.e., the useful power that has been successfully converted and output. This indicates the power loss throughout the entire conversion and transmission process, such as the conduction loss of the converter valve and the transformer loss.

[0020] In step 4, the system model is solved using an alternating iterative method, and the specific steps include: S4.1: Initialization, setting the initial DC power value and initial value of AC voltage ; S4.2: The outer iteration begins, and the following calculation steps are performed: S4.2.1: Invoke the DC fully embedded solver for a given DC power. The coefficients of each power series of the DC node voltage are solved recursively, and the DC voltage at the sending end is obtained by analytical extension using Bauer's Eta algorithm. ; S4.2.2: Calculate the DC current based on Ohm's law and the DC circuit resistance: ; in:, This represents the DC voltage at the sending end (rectifier side) calculated in the k-th iteration. This is the far-end voltage calculated by the DC HELM solver and obtained through analytical extension. This indicates the given value of the DC voltage at the receiving end (inverter side); The resistance of the DC line; S4.2.3: Perform diode rectifier interface calculations based on DC current. Combining diode voltage transformation equation To deduce the required AC voltage ; S4.2.4: Calculate the power absorbed by the diode rectifier from the AC side. Direct current Combining the diode loss equation: The AC absorption power is obtained. ; in, express The active power absorbed by the rectifier from the AC system; express Initially, assume the desired DC power to be transmitted; This indicates that the diode rectifier is operating at the current DC current. The power loss generated below; S4.2.5: Update the net power of the AC node, combining it with the obtained AC absorbed power. The net power of the AC node is obtained. ; S4.2.6: Invoke the AC fully embedded solver to update the AC node net power. Substituting the values ​​into the equations, the coefficients of each power series of the AC node voltages are recursively solved, and then analytically extended using Bauer's Eta algorithm to obtain the AC bus voltages. ; S4.2.7: Perform convergence judgment, if | - | If the result is achieved, the system converges globally, and the result is output; otherwise, the AC voltage is updated. , k=k+1, and return to step S4.2; where This is the preset convergence tolerance.

[0021] The specific steps for calling the DC fully embedded solver in S4.2.1 include: a1: Parameter Input and Preprocessing. Input DC network parameters, including: number of nodes. Conductivity matrix G, node type array, specified power Specified voltage ; a2: Constructing the system matrix Because HELM requires solving a system of linear equations of identical form for each order of power series when recursively solving for the coefficients of each power series, i.e., the coefficient matrix... Only the right-hand side term b differs. For a DC grid, the node voltage equation can be written as: In the recursive process of HELM, for the nth order coefficient, the system of linear equations that need to be solved is: ,in, It is a constant during the iteration process, and can be built once and reused repeatedly; It depends on the first n-1 order coefficients and the power injection term. Therefore, the coefficient matrix... DC node admittance matrix It can be written as: ,form × The DC conductance matrix is ​​given, and the row containing node V is set as a unit vector, where, This represents the number of DC nodes. a3: For the system matrix Performing a single LU decomposition yields a lower triangular matrix L, an upper triangular matrix U, and a permutation matrix P, such that... The decomposition result is reused for solving the coefficients of subsequent power series. a4: Set initial point The solution of the previous section in the point-to-point system is used as the self-selected initial point; a5: Solve for the ground state solution V[0], construct the right-hand side b[0], and use the lower triangular matrix L, upper triangular matrix U, and permutation matrix P obtained from the decomposition to solve the linear equation system. ; a6: Recursively solve for the coefficients of higher-order power series, starting from the order... n =1 to the maximum order For each order Construct the right-hand side term b[n] and solve using the decomposition results. The voltage coefficient V[n] is obtained, and the auxiliary coefficient is updated according to the following formula. : ; a7: Perform Bauer's Eta analytic continuation. Based on the obtained power series coefficient sequence, construct the Eta table, fill it with a recursive formula, and calculate the sum of the first row of the Eta table: ; Obtain the DC voltage value of the sending end after analytical extension. .

[0022] The specific steps for calling the AC fully null embedded solver in S4.2.6 include: b1: Parameter Input and Preprocessing. Input the AC network parameters, including: number of nodes. Conductivity matrix G, node type array, specified power Specified voltage ; b2: Constructing the system matrix , it is × The real matrix is ​​used to separate the real and imaginary parts of the complex equation, where Set the number of nodes to be exchanged, and set the diagonal elements of the row containing the balanced node to 1, and the other off-diagonal elements to 0; b3: For the system matrix Performing a single LU decomposition yields a lower triangular matrix L, an upper triangular matrix U, and a permutation matrix P, such that... The decomposition result is reused for solving the coefficients of subsequent power series. b4: Set the initial point V(0), take the solution of the previous section in the point-to-point system as the self-selected initial point, and take the specified voltage value for the balancing node; b5: Solve for the ground state solution , build 3D real right-hand side vector The system of linear equations is solved using the lower triangular matrix L, upper triangular matrix U, and permutation matrix P obtained from the decomposition. ; b6: Recursively solve for the coefficients of higher-order power series, starting from the order... n =1 to the maximum order For each order Construct the right-hand item And solve using the decomposition results. The voltage coefficient is obtained. And update the auxiliary coefficients according to the following formula. : ; b7: Perform Bauer's Eta analytic continuation. Based on the obtained complex power series coefficient sequence, extract the real and imaginary part coefficient sequences respectively, and construct Eta tables for each. After filling the tables with recursive formulas, calculate the sum of the first row of each table, and finally synthesize the complex number result. The AC bus voltage value after analytical extension is obtained. .

[0023] The recursive formula used to fill the Eta table in Bauer's Eta analytical continuation is: like Odd number: ; If k is even: ; in, In the table Eta, the first... Column, No. The elements of a row.

[0024] The voltage value after analytical extension is: .

[0025] In step S5, the steady-state operating characteristics of the system are analyzed based on the converged output results, specifically including: Obtain the following steady-state operating parameters: the complex form of the AC bus voltage output by the AC fully pure embedded solver. The rectifier output voltage in real form, output by a fully embedded DC solver. ,according to Calculated DC current ,according to Calculated DC power and according to Calculated rectifier losses ; To assess the system's operational status, the assessment metrics should include at least: Power transfer efficiency Voltage stability indicators reflecting the amplitude of AC bus voltage, and the output of different new energy sources. Comparison of system characteristics under operating conditions.

[0026] This invention provides a steady-state characteristic analysis method for a diode-rectified DC-DC power system, with the following technical advantages: 1) The HELM-based power flow solution method in this invention is applied to a DC collection and transmission system based on grid-type energy storage and diode rectification. Its greatest advantage is that each HELM solution in the inner layer is a non-iterative linear recursion, and the computational efficiency is greatly improved through the "self-selected initial point" and "Bauer's Eta" techniques, making it very suitable for handling a large number of continuous cross-sectional calculations caused by fluctuations in new energy output.

[0027] 2) This invention transforms the power flow calculation problem from a nonlinear iterative search problem in the real number domain into an analytical extension problem of holomorphic functions in the complex plane, thus mathematically avoiding the high dependence of the traditional Newton method on initial values. Since holomorphic embedded paths can theoretically uniquely and deterministically guide the solution vector smoothly from the zero-power state to the physical operating state, this invention's method can completely solve the inherent problems of Jacobian matrix singularity and computational non-convergence when dealing with novel systems containing DRUs and grid-type energy storage systems with strong nonlinear characteristics and diverse constraints. It possesses excellent global convergence performance and computational robustness.

[0028] 3) The power series recursive solution mechanism employed in this invention transforms the originally complex nonlinear operator operations into solving a system of linear equations for a constant admittance matrix. During the calculation, matrix decomposition only needs to be performed once, and subsequent acquisition of higher-order coefficients involves only vector multiplication and addition operations, significantly reducing the numerical computation overhead in large-scale, multi-node AC / DC hybrid systems. Simultaneously, the application of Bauer's Eta algorithm ensures extremely high computational accuracy and execution efficiency even with a limited number of truncated series terms.

[0029] 4) The interface model constructed in this invention deeply integrates the voltage-current nonlinear constraints of diode passive commutation, achieving an accurate characterization of the physical mechanism of the DRU. It can accurately capture the dynamic influence of commutation reactance on DC-side voltage drop and AC-side reactive power consumption. Through the coordination of inner and outer iterative structures, a high degree of matching of physical quantities on both AC and DC sides is achieved, eliminating the physical mechanism distortion errors that may occur when traditional methods process the DRU interface.

[0030] 5) The fully embedded solver structure provided by this invention has a high degree of consistency and can seamlessly adapt to changes in various DC topologies and control logics. It has strong engineering adaptability and scalability, providing a reliable steady-state analysis benchmark not only for compact DC transmission schemes including DRUs, but also providing key technical support for subsequent system planning, stability judgment, and reliability assessment of large-scale new energy DC aggregation, and has significant engineering application value. Attached Figure Description

[0031] The present invention will be further described below with reference to the accompanying drawings and examples; Figure 1 This is a schematic diagram of the point-to-point system based on diode rectification and grid-type energy storage described in this invention.

[0032] Figure 2 This is a schematic diagram of the modules of the method described in this invention.

[0033] Figure 3 This is a schematic diagram of node modeling for the point-to-point system described in this invention.

[0034] Figure 4 This is a flowchart of the overall solution process described in this invention.

[0035] Figure 5 This is a flowchart of the HELM solver described in this invention.

[0036] Figure 6 This function performs steady-state calculations for point-to-point systems and outputs comparison results between theoretical and simulated values.

[0037] Figure 7 To achieve different power output levels of new energy sources Below, AC bus voltage amplitude DC power output and rectifier losses The comparison curve between the calculation results and the electromagnetic transient simulation results. Detailed Implementation

[0038] This invention proposes a steady-state characteristic analysis method for DC-DC power collection systems based on diode rectifiers. This method addresses the power flow calculation challenges arising from the deep technical contradiction between the passive characteristics of DRUs and the diversity of system control modes in novel DC-DC power collection systems incorporating diode rectifier units (DRUs) and grid-based energy storage. By transforming the power flow calculation problem from a nonlinear iterative search problem in the real number domain into an analytical extension problem of holomorphic functions in the complex plane, this method mathematically circumvents the limitations of traditional Newtonian methods. The Raphson algorithm's high dependence on initial values ​​can completely solve the inherent problems of Jacobian matrix singularity and computational non-convergence when facing strong nonlinearity and diverse constraints, providing a reliable steady-state analysis benchmark for compact DC transmission schemes that include DRUs.

[0039] The specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0040] Step 1: Construct a point-to-point system topology model: The constructed point-to-point system topology model is as follows Figure 1 As shown, the system includes: grid-type energy storage, new energy power plants, AC bus, diode rectifiers, DC lines, and a receiving-end constant DC voltage converter station. This model covers the core components of an AC / DC hybrid transmission system, with the following connections: the grid-type energy storage and new energy power plants are connected in parallel to the AC bus; the AC bus is connected to the AC side of the diode rectifier; and the DC side of the diode rectifier is connected to the receiving-end constant DC voltage converter station via a DC line.

[0041] In this point-to-point system, the functional definitions and node type classifications of each component are as follows: Grid-based energy storage, acting as a slack node (SL node), functions to provide a stable voltage to the AC bus. The frequency support serves as the voltage reference for the entire AC subsystem. The renewable energy power station acts as a PQ node, injecting active power into the AC bus. and reactive power This represents the output characteristics of renewable energy sources such as wind power and photovoltaics; The AC bus is the common connection point (PCC) connecting grid-type energy storage and new energy power plants, and it is also the power exchange interface between the AC subsystem and the diode rectifier. The diode rectifier adopts a six-pulse uncontrolled rectifier topology, which converts AC power into DC power. It has inherent technical advantages such as small size, extremely high reliability, low operating loss and low construction cost. These are the core features that distinguish this system from traditional VSC or LCC converter schemes. The DC line connects the diode rectifier output and the receiving-end DC voltage converter station. This invention establishes a π-type equivalent circuit model of the DC submarine cable, including the DC line resistance. Parameters such as inductance and capacitance to ground; The receiving-end DC voltage converter station uses a modular multilevel converter (MMC) as the V-node, whose control function is to maintain the DC voltage constant at the set value. .

[0042] Figure 3 A schematic diagram of node modeling that maps the above physical system to a fully embedded computing model is further shown. Figure 3 The diagram clearly shows that the AC subsystem contains a ballast node and a PQ node; the DC subsystem contains a P node and a V node; and the diode rectifier, as the AC / DC interface, connects the two subsystems and plays a crucial role in the conversion of AC and DC physical quantities.

[0043] Step 2: Establish models for each subsystem based on the fully pure embedded power flow calculation method with self-selected power series initial points: This step is based on the A-HELM (Alternate Power Series Initial Point) fully embedded power flow calculation method, establishing fully embedded models for both the AC and DC subsystems. The core idea of ​​this method is to introduce complex analytical embedding parameters. The nonlinear power flow equations of the AC / DC system are transformed into equations about The holomorphic function. Since the holomorphic embedding path can theoretically uniquely and deterministically guide the solution vector to smoothly migrate from the zero-power state to the physical operating state, the global convergence performance of the computation can be guaranteed from a mathematical mechanism.

[0044] (a) Fully Embedded Model of the Communication Subsystem: The AC subsystem includes grid-type energy storage nodes and new energy power station nodes. The fully embedded model of the constructed AC subsystem is as follows: 1) Grid-type energy storage nodes act as balancing nodes, providing analytical initial values ​​by constructing a known voltage change path. Their fully embedded model is: ; in, Indicates the embedded parameters A holomorphic function of the equilibrium node voltage under given conditions. For embedding complex variables, its physical meaning can be interpreted as: when When the voltage is 1, it corresponds to the initial solution for no-load or flat start; when When, the voltage equals The target solution corresponding to the rated voltage; The rated voltage of the balancing node is given, i.e., the control target.

[0045] 2) The fully embedded model of the new energy power station node as a PQ node is as follows: ; in, It's about nodes. and Line admittance, It is a node The ground-based self-admittance is defined as follows: ; ; in, It is the first The electrical conductivity of the branch circuit to ground, It is the first The electrical discharge of a branch circuit to the ground Represents the imaginary unit. .

[0046] In the above formulas, the physical meaning of each parameter is as follows: Represents a node In embedded parameters The pure voltage function under these conditions; Represents the initial state quantity of the voltage function; Represents the voltage conjugate function. express The conjugate complex variable, where the "*" operator represents the conjugate operation; Represents a node In embedded parameters The pure voltage function under these conditions; This represents a fully embedded variable, which is a complex parameter that changes continuously from 0 to 1, controlling the power to transition continuously from 0 to the target value; Represents a node and Complete admittance between; The initial state quantity representing the voltage function, i.e. Solution at that time.

[0047] For nodes The complex power conjugate of net injected power reflects the balance between the actual power delivered to the AC bus by the renewable energy power plant and the power absorbed by the rectifier: ; in, and These are the active and reactive power outputs of new energy sources, respectively. This represents the active power absorbed by the diode rectifier from the AC bus.

[0048] (II) Fully Embedded Model of DC Subsystem: The DC subsystem includes the sending-end rectifier output node and the receiving-end constant voltage node. The fully embedded model of the constructed DC subsystem is as follows: 1) The output node of the sending-end rectifier is taken as node P (the known power node), and its fully embedded model is: ; in, This is the DC conductance matrix, which characterizes the admittance properties of the DC network; DC power injected into the sending node.

[0049] 2) The receiving-end constant voltage node adopts constant DC voltage control and is used as the V node (a known voltage node). Its fully embedded model is as follows: ; in, Indicates the embedded parameters The holomorphic function of the V-node voltage; The DC voltage setpoint for node V is the control target.

[0050] Step 3: Establish the interface model of the diode rectifier: As a core interface module in AC / DC systems, the diode rectifier's interface model needs to accurately describe the nonlinear constraints between AC voltage and DC voltage and power during passive commutation. The interface model established in this invention deeply integrates the voltage characteristics of diode passive commutation. The current nonlinear constraint accurately captures the dynamic influence of commutation reactance on DC-side voltage drop and AC-side reactive power consumption, thus achieving a precise characterization of the DRU physical mechanism. This interface model includes the following three equations: 1) Diode voltage transformation equation: Based on diode voltage Current characteristics are used to establish the transformation relationship between AC side voltage and DC side voltage: ; in, This represents the AC side voltage value of the diode rectifier. This represents the DC-side voltage value of the diode rectifier. Let be the commutation reactance. This equation accurately reflects the effect of the commutation reactance on the DC output voltage drop. In some simplified analysis scenarios, if the effect of the commutation reactance can be ignored, then... The value can be zero.

[0051] 2) Diode loss equation: Converter losses include conduction losses and switching losses, which are fitted using a quadratic polynomial: ; in, This indicates the loss value of the diode rectifier; , , These are the loss coefficients, which can be calculated from the rectifier's rated parameters. This equation accurately reflects the nonlinear characteristics of losses as a function of load current.

[0052] 3) Power balance equation: The AC input power, DC output power, and commutation losses satisfy the power conservation relationship: ; in, This represents the active power delivered from the AC system to the diode rectifier, i.e., the total input power; This represents the active power delivered by the DC system from the converter station after conversion, i.e., the useful power that has been successfully converted and output. This represents the power loss throughout the entire conversion and transmission process, including the conduction loss of the converter valve and the transformer loss.

[0053] Step 4: Solve the system model using the alternating iterative method: The overall solution process is as follows: Figure 4 As shown. This invention employs an alternating iterative method, coordinating the AC / DC interface through outer-layer iteration, while sequentially calling the DC fully embedded solver, performing rectifier interface calculations, and calling the AC fully embedded solver in the inner layer until global convergence. This method, through the coordination of the inner and outer iterative structures, achieves a high degree of matching between physical quantities on both the AC and DC sides, eliminating the physical mechanism distortion errors that may occur when traditional methods handle DRU interfaces. The specific steps are described below: S4.1: Initialization. Set the initial DC power value. and initial value of AC voltage This provides a starting point for the iterative process.

[0054] S4.2: The outer iteration begins, and the following sub-steps are executed: 1) Use the fully embedded DC subsystem solver to solve the fully embedded DC subsystem model. That is, for a given DC power... The power series coefficients of the DC node voltage are solved recursively. The power series recursive solution mechanism adopted in this invention transforms the originally complex nonlinear operator operations into solving a system of linear equations for a constant admittance matrix. In the calculation process, matrix decomposition only needs to be performed once, and the subsequent acquisition of higher-order coefficients only involves vector multiplication and addition operations, which greatly reduces the numerical computation overhead.

[0055] Assuming DC node voltage It's about embedded parameters. The power series: ; Expanding the power series, we can derive the recursive matrix of the DC system in the following form. Where the DC conductance matrix on the left side... It depends only on the network topology and node type, and remains unchanged during iteration; the right-hand vector It is by The constant term obtained from the calculation of the power series coefficients reflects the cumulative effect of the current state of the system: ; The matrix equations are further simplified into linear algebraic equations: ; In the formula: This is the system parameter matrix, whose structure depends only on the network parameters and the type of network nodes. When the network structure remains unchanged, this matrix will not change. For demand The coefficient vector of a power series; For orders not greater than The result of the recursive calculation of the power series coefficients.

[0056] The specific solution steps of the DC fully embedded solver are as follows: Figure 5 As shown, it includes: a1: Parameter Input and Preprocessing. Input DC network parameters, including: number of nodes. Conductivity matrix Node type array, specified power Specified voltage ; a2: Constructing the system matrix ,form Matrix. For node V (constant voltage node), since the voltage is known, its row is set as a unit vector, i.e., in the coefficient matrix. In the code, set the diagonal elements of the row containing the node to 1, and set the remaining off-diagonal elements to 0. and .

[0057] a3: LU Decomposition: Perform LU decomposition on the system matrix to linearize it. Only one decomposition is needed, followed by only forward and backward substitution operations. Specifically: first, decompose the matrix... Performing a single LU decomposition yields... ,in: It is a unit lower triangular matrix. It is an upper triangular matrix. It is a permutation matrix. Because the coefficient matrix... While remaining unchanged throughout the fully embedded recursive process, this "pre-decomposition" strategy can significantly improve computational efficiency for each distinct right-hand side term. All can be reused.

[0058] a4: Set the initial point The present invention is characterized by the use of the "self-selected initial point" technique, which takes the solution of the previous cross section as the self-selected initial point and uses the continuity between adjacent cross sections to accelerate the convergence process.

[0059] a5: Solve for the ground state solution V[0] ( Construct the right-hand term b[0] and solve it using the decomposed LU. First replace the right-hand term. Perform a previous generation solution. Finally, back substitution is performed to solve the problem. Thus, the ground state solution V[0] is obtained.

[0060] a6: Recursively solve for the coefficients of higher-order power series, from up to the maximum order For each order First, construct the right-hand side term b[n]. Then, use the already decomposed LU to solve the system of linear equations to obtain V[n]. Specifically, first, permutate the right-hand side term. Then the previous generation is solved. Finally, substitute back to solve. We obtain V[n]. Then we update the auxiliary coefficient W[n], which is used to construct the right-hand side of the next order: ; a7: Convergence check. If the calculated voltage and the target voltage satisfy... If the sum is equal to 1, then the series converges, and the power series solution is complete.

[0061] a8: Perform Bauer's Eta analytic continuation. Since the power series obtained through the above recursion only exists in... It is effective in the vicinity, limited by the convergence radius, and the final physical working point solution is required in... The location is likely to fall outside the convergence radius, so direct substitution is not possible. This can lead to inaccurate or non-convergent results. Therefore, it is necessary to perform analytic extension using Bauer's Eta algorithm to transform the power series into a rational function (Padé approximation), whose effective range is much larger than the original power series. The application of Bauer's Eta algorithm ensures that extremely high computational accuracy and execution efficiency can still be achieved even with a finite number of truncated terms in the series.

[0062] The specific steps are as follows: ① Obtain the power series coefficient sequence of the nodes: ; ② Initialize the Eta table, with dimension 1. ; ③From arrive Loop, from arrive The Eta table is filled recursively by calculating the coefficients of the numerator and denominator polynomials of the rational approximation using the following recursive formula: like Odd number: ; like Even numbers: ; ④ Calculate the sum of all elements in the first row of the Eta table, starting from column 0: ; This sum is the voltage value after analytical extension, corresponding to... The precise value at that point, that is, the DC voltage at the sending end. .

[0063] a9: Output results. Output includes: voltage at each node. Actual power of each P node (for verification), injected current of each V node, power flow distribution of the line, and convergence information: maximum order of use, maximum number of iterations.

[0064] It is important to note that in the DC fully embedded solver, the system matrix construction and LU decomposition are part of the "initialization" step, which only needs to be executed once, unlike the iteration process. The change is irrelevant. During each round of execution of the outer iteration, for different... First, based on the current situation The right-hand side is reconstructed, and then the coefficients of each order are quickly solved using the decomposed LU matrix. Finally, the bus voltage is obtained by analytical extension using Bauer's Eta algorithm. .

[0065] 2) Calculate the DC current. Calculate the current distribution in the DC subsystem based on Ohm's law and the DC line resistance: ; in, Indicates the first The DC line current calculated in the next iteration; Indicates the first The next iteration calculates the DC voltage on the rectifier side of the sending end by an analytical extension of the DC fully embedded solver; This represents the given value of the DC voltage on the inverter side at the receiving end, which is a known and constant reference value.

[0066] 3) Diode rectifier interface calculation. Based on the DC current results and the diode voltage transformation equation: ; Back-calculation required AC voltage .

[0067] This step enables the conversion from DC-side electrical quantities to AC-side electrical quantities.

[0068] 4) Calculate the power absorbed by the diode rectifier from the AC side. Based on the DC current results combined with the diode loss equation and power balance equation: ; Obtain AC absorption power .in, Indicates the first The active power absorbed by the diode rectifier from the AC system is calculated in the next iteration; Indicates the first Initially, it is assumed that the desired DC power will be transmitted. This indicates that the diode rectifier is operating at the current DC current. The power loss generated below.

[0069] 5) Update the net power of the AC node. Combine this with the obtained AC absorbed power. Calculate the net power of the AC nodes, reflecting the actual net power injected into the AC bus by the new energy power plant: ; 6) Call the AC fully embedded solver to solve the AC subsystem fully embedded model. The AC subsystem includes grid-type energy storage nodes and new energy power station nodes. First, recursively solve the power series coefficients of the AC node voltages. The process has the same methodology as the DC fully embedded solver.

[0070] Assume the AC node voltage is related to the embedded parameters. The power series: ; Expanding the power series and separating the real and imaginary parts, we obtain the recurrence matrix of the AC system in the following form: ; Similarly, the matrix equations are further simplified into linear algebraic equations: ; Updated node net power Substituting the equations constructed using the fully embedded model of the communication, and comparing... Given coefficients of the same power, recursively solve for all coefficients. .

[0071] The specific solution steps of the fully embedded solver are as follows: Figure 5 As shown, it includes: b1: Parameter Input and Preprocessing. Input the AC network parameters, including: number of nodes. Admittance matrix Node type array, specified power of new energy source Grid-type energy storage with specified voltage .

[0072] b2: Constructing the system matrix ,for Real matrix, The number of AC nodes corresponds to the separation of the real and imaginary parts of the complex equation, respectively. The elements of the coefficient matrix are derived from the AC node admittance matrix. It consists of the real and imaginary parts, where the diagonal part is the self-admittance and the off-diagonal part is the mutual admittance, i.e. (node (self-guided a) (node and (mutual admittance between them).

[0073] Processing the slack node: Since the voltage of the slack node is known, in the coefficient matrix... In the code, set the diagonal elements of the row containing the node to 1, and the remaining off-diagonal elements to 0. That is... ; .

[0074] b3: Perform LU decomposition on the system matrix: the specific decomposition form is as follows ,include: Matrix (unit lower triangular matrix) Matrix (upper triangular matrix) Matrix (orthogonal permutation matrix). Due to the coefficient matrix The process remains unchanged during the whole pure embedding recursion, requiring only one decomposition. All orders share the decomposition result storage, and subsequent operations only involve back-generation operations, thereby greatly improving computational efficiency.

[0075] b4: Set initial point The feature of this invention is that it adopts the "self-selected initial point" technology, which takes the solution of the previous section as the self-selected initial point and takes a specified voltage value for the equilibrium node.

[0076] b5: Solve for the ground state solution V[0] (n=0): First construct The right-hand side vector b[0] is used to solve the linear equation system using pre-decomposition LU, and then W[0] is calculated: .

[0077] b6: Recursively solve for higher-order coefficients, from... arrive For each order : 1) Construct the right-hand item Special processing is required for PV nodes to meet voltage amplitude constraints; 2) Solve using pre-decomposed LU For each order Solve separately First, perform the replacement. Then the previous generation is solved. Finally, return to the solution. ,get And update : ; b7: Convergence check. If... Then it converges.

[0078] b8: Perform Bauer's Eta analytical continuation (complex version): Since the AC system voltage is a complex number, the real and imaginary parts need to be processed separately. Extract the real part coefficient sequence. and imaginary part coefficient sequence Construct Eta tables for the real and imaginary parts of the sequence respectively; calculate the sum of the first row of the real and imaginary parts respectively, and finally synthesize the complex number result. .

[0079] b9: Output Results: The output results are the voltages of each node. (Complex form, including amplitude and phase angle), power injected at each node, reactive power output of PV nodes. Line power flow distribution and convergence information (maximum order of use, maximum number of iterations).

[0080] Analytical extension was performed using Bauer's Eta algorithm, ultimately yielding... The precise value at that point, that is, the AC bus voltage. .

[0081] 7) Convergence check: Observe whether the convergence condition is met. ,in: This represents the convergence tolerance, a very small positive number used to determine whether the calculation result is sufficiently accurate. If this condition is met, global convergence is achieved, and the result is output; otherwise, the AC voltage is updated. , Return to step 2) and continue the outer iteration.

[0082] The AC fully embedded solver and the DC fully embedded solver follow the same core methodology. The fully embedded solver structure provided by this invention has a high degree of consistency, can seamlessly adapt to various DC topologies and control logic changes, and has strong engineering adaptability and scalability. This shared methodology specifically includes: (1) One-time decomposition of the system matrix: All orders are reused; (2) Power series recursion: solve successively from lower to higher orders; (3) Coefficient convolution update: ; (4) Bauer's Eta analytic extension: extending the power series to ; (5) Select initial point: use the solution from the previous section to accelerate convergence.

[0083] The main difference between AC fully embedded solvers and DC fully embedded solvers lies in the greater complexity of AC solvers. Specifically, in AC systems, voltage, power, and admittance are all complex numbers, requiring handling of complex quantities; after separating the real and imaginary parts, a more complex solution is formed. The matrix dimension increases exponentially; PV nodes must simultaneously satisfy amplitude constraints, and the reactive power of PV nodes... It is a quantity to be determined, and the recursive calculation of reactive power needs to be handled separately.

[0084] Each fully pure embedding solution in the inner layer is a non-iterative linear recursion, and the combination of "self-selected initial point" and "Bauer's Eta" technology greatly improves the computational efficiency, making it very suitable for handling a large number of continuous cross-section calculations caused by fluctuations in new energy power output.

[0085] Step 5: Analyze the steady-state operating characteristics of the system based on the converged output results: Once the algorithm converges, the output includes: AC side: Stable bus voltage Active power output of grid-type energy storage and reactive power ,in, The output is in complex form, provided by a fully embedded AC solver, and includes magnitude and phase angle. As a balancing node, it is calculated.

[0086] Interface: Operating point of diode rectifier ( , and losses .

[0087] DC side: Power distribution on the line And voltage drop, voltage drop is the receiving end voltage With rectifier output voltage The difference.

[0088] The specific meanings and calculation methods of the above convergence results are as follows: AC bus voltage It is the final output of the fully embedded AC solver, which is a complex number containing magnitude and phase information; Grid-based energy storage output , The equilibrium nodes are obtained by solving the AC fully embedded solver, where: , Injected current Calculated from node voltages and admittance matrices: ; rectifier output voltage It is the final output (sender outlet node P) of the DC fully embedded solver, and is a real number; Receiving end voltage It is the known set voltage value (V node) of the receiving-end DC voltage converter station. DC current Calculated from DC voltage and line resistance: ; DC power Calculated from DC voltage and current: ; rectifier losses Calculated from the loss equation: ; Rectifier power absorption Calculated based on DC power and losses according to the power balance relationship: .

[0089] The convergence results can be used to comprehensively evaluate the system's operational status. The main evaluation indicators include: Voltage stability assessment includes: whether the AC bus voltage amplitude is within the allowable range, typically ±5% of the rated value; whether the DC voltage level meets the equipment requirements; and the smoothness of voltage fluctuation characteristics as power changes.

[0090] Power transfer efficiency: .

[0091] Rectifier loss characteristics: .

[0092] Comparative analysis under different operating conditions: The method of this invention can be widely applied to the analysis of system characteristics under different operating conditions, including different load rates. Variations within the range of 0.1-1.2 pu; different power factors: Positive and negative values ​​were taken; different control parameters: droop coefficient, voltage setpoint; different network parameters: line length, rectifier parameter changes; and system response characteristics analysis under fault / normal operating conditions, line disconnection, and equipment shutdown.

[0093] System module composition: like Figure 2 As shown, the steady-state characteristic analysis system that implements the above analysis method includes the following modules: The topology modeling module is used to construct the topology of a point-to-point system and set the types and parameters of each node. The DC fully embedded solver module is used to realize fully embedded modeling and solving of the rectifier outlet at the sending end and the constant DC voltage converter station node at the receiving end. The rectifier interface module is used to realize voltage conversion and power loss calculation of diode rectifiers; The fully embedded solver module is used to realize fully embedded modeling and solving of nodes in grid-type energy storage and new energy power stations; The outer iterative control module is used to coordinate the AC / DC interface and determine global convergence. The results output module is used to output and visualize the steady-state operating characteristics of the system.

[0094] Verification Example: The following example demonstrates a typical point-to-point system for transmitting offshore wind power via high-voltage direct current (HVDC). The sending end consists of a grid-following (GFL) doubly-fed wind turbine and a grid-forming (GFM) energy storage system. These are combined via an AC submarine cable, connected to a diode rectifier, and then transmitted via a DC submarine cable to the onshore receiving end. The receiving end uses a modular multilevel converter (MMC) connected to the main AC power grid. The system modeling structure is as follows: Figure 1 As shown.

[0095] After the model is run, the steady-state characteristic values ​​are compared with the calculated steady-state power flow values ​​obtained based on the method of this invention. Figure 6 As shown, the verification results are as follows: DC output voltage: Theoretical calculation value is 2311.49V, simulation measurement value is 2271V; DC power transmission current: Theoretical calculation value is 20.77A, simulation measurement value is 18.04A; AC PCC peak voltage: theoretically calculated value is 551.22V, simulated measurement value is 567.9V; Total DC power: Theoretical calculation value is 48000.00W, target setting value is 50000W.

[0096] The comparison results show that the theoretical calculation values ​​and the actual simulation measurements are in good agreement, and the calculation accuracy meets the requirements of engineering applications. This verification result demonstrates that the method of this invention can accurately solve the steady-state power flow distribution of a DC-DC power system based on diode rectification. It not only provides a reliable steady-state analysis benchmark for compact DC transmission schemes including DRUs, but also provides crucial technical support for subsequent system planning, stability assessment, and reliability evaluation of large-scale renewable energy DC-DC aggregation, demonstrating significant engineering application value.

[0097] Based on the above method, a simulation model of the point-to-point system is built in the MATLAB environment, and the method of this invention is applied to perform steady-state power flow calculation. Figure 7 It gives the output levels of different new energy sources Below, AC bus voltage amplitude DC power output and rectifier losses The comparison curve between the calculation results and the electromagnetic transient simulation results.

[0098] from Figure 7 It can be seen that the steady-state quantities such as AC bus voltage, DC power, and rectifier losses obtained by the steady-state characteristic analysis method of the diode rectifier DC collection power system proposed in this invention are in good agreement with the detailed electromagnetic transient simulation results, and the deviation between the two is within the allowable range for engineering. As the output of new energy sources increases from 0.2 pu to 1.0 pu, the AC bus voltage shows a gradual decreasing trend, which is consistent with the physical characteristic that the commutation voltage drop of the diode rectifier increases with the increase of current; the DC power output increases approximately linearly, indicating that the system can maintain a stable power transmission capability over a wide power range; and the rectifier losses increase according to a quadratic function law, verifying the loss equation. The accuracy.

[0099] The above results further demonstrate that the method of the present invention can accurately capture the dynamic influence of commutation reactance on DC-side voltage drop and AC-side reactive power consumption, and achieve a precise characterization of the physical mechanism of DRU. At the same time, when facing large-scale changes in the output of new energy sources, the inner fully embedded solver, with its self-selected initial point and Bauer's Eta analytical extension technique, always maintains non-iterative linear recursion, avoiding the problems of Jacobian matrix singularity and initial value sensitivity, and fundamentally ensuring the global convergence and engineering applicability of the calculation.

Claims

1. A method for analyzing the steady-state characteristics of a diode-rectified DC-DC power system, characterized in that... Includes the following steps: Step 1: Construct a point-to-point system topology model, which includes an AC subsystem, a diode rectifier, and a DC subsystem; Step 2: Based on the fully embedded power flow calculation method with self-selected power series initial points (A-HELM), establish fully embedded models for the AC subsystem and the DC subsystem respectively; Step 3: Based on the conversion relationship between AC voltage and DC voltage and power, establish the interface model of the diode rectifier; Step 4: Using the alternating iterative method, the AC / DC interface is coordinated through outer-layer iteration, and the fully embedded DC subsystem model, the diode rectifier interface model, and the fully embedded AC subsystem model are solved sequentially in the inner layer until global convergence is achieved. Step 5: Analyze the steady-state operating characteristics of the point-to-point system based on the converged output results.

2. The steady-state characteristic analysis method for a diode-rectified DC-DC power system according to claim 1, characterized in that: In step 1, the constructed point-to-point system topology model includes: grid-type energy storage, new energy power stations, AC buses, diode rectifiers, DC lines, and receiving-end constant DC voltage converter stations, with the following connection relationships: The grid-type energy storage and new energy power stations are connected in parallel to the AC bus. The AC bus is connected to the AC side of the diode rectifier, and the DC side of the diode rectifier is connected to the receiving-end constant DC voltage converter station through a DC line. in: Grid-based energy storage acts as a balancing node, providing stable voltage to the AC bus. and frequency support; The renewable energy power station acts as a PQ node, injecting active power into the AC bus. and reactive power ; Receiving-end constant DC voltage converter station: A modular multilevel converter (MMC) is used as the V-node to maintain a constant DC voltage. .

3. The steady-state characteristic analysis method for a diode-rectified DC-DC power system according to claim 2, characterized in that: In step 2, the fully embedded power flow calculation method with self-selected power series initial points (A-HELM) is used to establish fully embedded models for the AC subsystem and the DC subsystem, that is, by introducing complex analytical embedding parameters. The nonlinear power flow equations of the AC / DC system are transformed into equations about holomorphic functions specifically include: The AC subsystem includes grid-type energy storage nodes and new energy power station nodes. The fully embedded model of the constructed AC subsystem is as follows: 1) The grid-type energy storage node acts as a balancer node. The fully embedded model of the grid-type energy storage node is as follows: （1）； in, Indicates the embedded parameters The holomorphic function of the energy storage node voltage. To embed complex variables, when α=0: V=1, i.e., the initial solution, corresponding to no-load or flat start; when α=1: V= That is, the target solution, the rated voltage; The rated voltage of the energy storage node is given, i.e., the control target.

4. The steady-state characteristic analysis method for a diode-rectified DC-DC power system according to claim 3, characterized in that: The new energy power station node is used as a PQ node, and the fully embedded model of the new energy power station node is as follows: （2）； in, It's about nodes. i and j Line admittance, It is a node i The ground-based self-admittance is as follows: （3）； in, Indicates the node number currently being examined; It is the self-admittance of node i, including all branches. It is the branch admittance between nodes i and j; （4）； in, It is the conductance of the k-th branch to ground. It is the susceptance of the k-th ground branch. The imaginary unit is used for reactive power; This indicates that node j is embedded in the parameters. The pure voltage function under these conditions; Represents the initial state quantity of the voltage function; Represents the voltage conjugate function; express The conjugate complex variable, where the "*" operator represents the conjugate operation; Represents the holomorphic voltage function of node i under the embedding parameter α; This represents a fully embedded variable, which is a complex parameter that changes continuously from 0 to 1, controlling the power from 0 to the target value; Represents the complete admittance between nodes i and j; The initial state quantity representing the voltage function; S is a node i Net injected power, For nodes i The complex power conjugate of the net injected power is as follows: （5）； in, and These are the active and reactive power outputs of new energy sources, respectively. This refers to the active power absorbed by the rectifier from the AC bus.

5. The steady-state characteristic analysis method for a diode-rectified DC-DC power system according to claim 4, characterized in that: The DC subsystem includes the sending-end rectifier output node and the receiving-end constant voltage node. The fully embedded model of the DC subsystem is as follows: 1) The output node of the sending-end rectifier is taken as node P. The fully embedded model of the output node of the sending-end rectifier is as follows: （6）； in, This is a DC conductance matrix; Inject DC power into the sending end; 2) The receiving-end constant voltage node adopts constant DC voltage control and is used as the V node. The fully embedded model of the receiving-end constant voltage node is as follows: （7）； in, Indicates the embedded parameters The holomorphic function of the receiving-end node voltage; The given value of the DC voltage at the receiving node is the control target.

6. The steady-state characteristic analysis method for a diode-rectified DC-DC power system according to claim 5, characterized in that: In step 3, the diode rectifier serves as an interface module, and is described using the following power flow model: 3.1: Diode voltage transformation equation: Given DC current Based on the diode voltage-current characteristics, the following is obtained: （8）； in, This represents the AC side voltage value of the diode rectifier. This represents the DC-side voltage value of the diode rectifier. For commutation reactance; 3.2: Diode Loss Equation: Given DC current The converter loss formula is: （9）； in, This represents the loss value of the diode rectifier; a, b, and c are the loss coefficients, which can be calculated based on the rated parameters of the rectifier. 3.3: Power Balance Equation: （10）； in, This represents the active power delivered to the rectifier by the AC system, i.e., the total input power; This represents the active power delivered by the DC system from the converter station after conversion, i.e., the useful power that has been successfully converted and output. This indicates the power loss during the entire conversion and transmission process.

7. The steady-state characteristic analysis method for a diode-rectified DC-DC power system according to claim 6, characterized in that: In step 4, the system model is solved using an alternating iterative method, and the specific steps include: S4.1: Initialization, setting the initial DC power value and initial value of AC voltage ; S4.2: The outer iteration begins, and the following calculation steps are performed: S4.2.1: Invoke the DC fully embedded solver for a given DC power. The coefficients of each power series of the DC node voltage are solved recursively, and the DC voltage at the sending end is obtained by analytical extension using Bauer's Eta algorithm. ; S4.2.2: Calculate the DC current based on Ohm's law and the DC circuit resistance: ； in:, This represents the sending-end DC voltage calculated in the kth iteration; it is the far-end voltage calculated by the DC HELM solver and obtained through analytical extension. This indicates the given value of the DC voltage at the receiving end; The resistance of the DC line; S4.2.3: Perform diode rectifier interface calculations based on DC current. Combining diode voltage transformation equation To deduce the required AC voltage ; S4.2.4: Calculate the power absorbed by the diode rectifier from the AC side. Direct current Combining the diode loss equation: The AC absorption power is obtained. ; in, express The active power absorbed by the rectifier from the AC system; express Initially, assume the desired DC power to be transmitted; This indicates that the diode rectifier is operating at the current DC current. The power loss generated below; S4.2.5: Update the net power of the AC node, combining it with the obtained AC absorbed power. The net power of the AC node is obtained. ; S4.2.6: Invoke the AC fully embedded solver to update the AC node net power. Substituting the values ​​into the equations, the coefficients of each power series of the AC node voltages are recursively solved, and then analytically extended using Bauer's Eta algorithm to obtain the AC bus voltages. ; S4.2.7: Perform convergence judgment, if | - | If the result is achieved, the system converges globally, and the result is output; otherwise, the AC voltage is updated. , k=k+1, and return to step S4.2; where This is the preset convergence tolerance.

8. The steady-state characteristic analysis method for a diode-rectified DC-DC power system according to claim 7, characterized in that: The specific steps for calling the DC fully embedded solver in S4.2.1 include: a1: Parameter input and preprocessing, input DC network parameters; a2: Constructing the system matrix ,form × The DC conductance matrix is ​​given, and the row containing node V is set as a unit vector, where, This represents the number of DC nodes. a3: For the system matrix Performing a single LU decomposition yields a lower triangular matrix L, an upper triangular matrix U, and a permutation matrix P, such that... The decomposition result is reused for solving the coefficients of subsequent power series. a4: Set initial point The solution of the previous section in the point-to-point system is used as the self-selected initial point; a5: Solve for the ground state solution V[0], construct the right-hand side b[0], and use the lower triangular matrix L, upper triangular matrix U, and permutation matrix P obtained from the decomposition to solve the linear equation system. ; a6: Recursively solve for the coefficients of higher-order power series, starting from the order... n =1 to the maximum order For each order Construct the right-hand side term b[n] and solve using the decomposition results. The voltage coefficient V[n] is obtained, and the auxiliary coefficient is updated according to the following formula. : ； a7: Perform Bauer's Eta analytic continuation. Based on the obtained power series coefficient sequence, construct the Eta table, fill it with a recursive formula, and calculate the sum of the first row of the Eta table: ； Obtain the DC voltage value of the sending end after analytical extension. .

9. The steady-state characteristic analysis method for a diode-rectified DC-DC power system according to claim 8, characterized in that: The specific steps for calling the AC fully null embedded solver in S4.2.6 include: b1: Parameter input and preprocessing, inputting AC network parameters; b2: Constructing the system matrix , it is × The real matrix is ​​used to separate the real and imaginary parts of the complex equation, where Set the number of nodes to be exchanged, and set the diagonal elements of the row containing the balanced node to 1, and the other off-diagonal elements to 0; b3: For the system matrix Performing a single LU decomposition yields a lower triangular matrix L, an upper triangular matrix U, and a permutation matrix P, such that... The decomposition result is reused for solving the coefficients of subsequent power series. b4: Set the initial point V(0), take the solution of the previous section in the point-to-point system as the self-selected initial point, and take the specified voltage value for the balancing node; b5: Solve for the ground state solution , build 3D real right-hand side vector The system of linear equations is solved using the lower triangular matrix L, upper triangular matrix U, and permutation matrix P obtained from the decomposition. ; b6: Recursively solve for the coefficients of higher-order power series, starting from the order... n =1 to the maximum order For each order Construct the right-hand item And solve using the decomposition results. The voltage coefficient is obtained. And update the auxiliary coefficients according to the following formula. : ； b7: Perform Bauer's Eta analytic continuation. Based on the obtained complex power series coefficient sequence, extract the real and imaginary part coefficient sequences respectively, and construct Eta tables for each. After filling the tables with recursive formulas, calculate the sum of the first row of each table, and finally synthesize the complex number result. The AC bus voltage value after analytical extension is obtained. .

10. The steady-state characteristic analysis method for a diode-rectified DC-DC power system according to claim 9, characterized in that: In step S5, the steady-state operating characteristics of the system are analyzed based on the converged output results, specifically including: Obtain the following steady-state operating parameters: the complex form of the AC bus voltage output by the AC fully pure embedded solver. The rectifier output voltage in real form, output by a fully embedded DC solver. ,according to Calculated DC current ,according to Calculated DC power and according to Calculated rectifier losses ; To assess the system's operational status, the assessment metrics should include at least: Power transfer efficiency Voltage stability indicators reflecting the amplitude of AC bus voltage, and the output of different new energy sources. Comparison of system characteristics under operating conditions.

Images