Short-circuit current calculation method for metal backflow four-terminal bipolar direct-current power grid

Abstract

The invention belongs to the technical field of DC power grid short-circuit current calculation, and particularly relates to a short-circuit current calculation method for a metal backflow four-terminal bipolar DC power grid, and the method comprises the steps: S1, building an MMC equivalent model; s2, constructing and processing an equivalent circuit of a Bergeron lossy transmission line of the DC line to obtain a Bergeron two-port equivalent model of a single-phase transmission line and a Bergeron equivalent model of a three-phase transmission line; s3, establishing an equivalent model of the metal backflow four-terminal bipolar direct current power grid; s4, establishing an accompanying circuit model of the metal backflow four-terminal bipolar direct current power grid; s5, constructing a conductance matrix G, and forming a node voltage equation; and S6, according to the fault type, modifying a node admittance matrix G in the node voltage equation into an equivalent conductance matrix G ', and then solving the modified node voltage equation to obtain the branch current and the node voltage after the fault. According to the method, the problem that the short-circuit current calculation method of the metal backflow four-terminal bipolar direct-current power grid is insufficient in accuracy can be solved.

Description

Technical Field

[0001] The present invention belongs to the technical field of short-circuit current calculation of direct current (DC) grids, and in particular relates to a short-circuit current calculation method for a metal return four-terminal bipolar DC grid. Background Art

[0002] As the global energy structure accelerates its transition toward a low-carbon future, modular multilevel converter-based multi-terminal DC grids (MMC-MTDCs) have become a key technology for building new power systems due to their flexible and controllable power regulation capabilities and efficient absorption of renewable energy. However, while flexible DC transmission systems using overhead lines are becoming the mainstream choice for long-distance power transmission due to their economical efficiency and large capacity, they also have a significantly higher probability of failure than cable lines. In metallic return four-terminal bipolar DC grids, when a short-circuit fault occurs between poles or between poles, the capacitors of the MMC submodules discharge rapidly due to their low inertia and weak damping characteristics. The fault current can reach tens of times the rated value within milliseconds, far exceeding the tolerance limits of power electronic devices. Failure to promptly lockout or implement current limiting measures can lead to converter station lockout, DC circuit breaker (DCCB) failure to open, and even system-wide cascading failures. Therefore, accurately calculating the dynamic characteristics of short-circuit currents is crucial for optimizing current limiting device parameters, reducing DCCB design costs, and improving system reliability.

[0003] Currently, research on short-circuit current calculation methods still faces the following bottlenecks: 1. Insufficient model refinement. Existing methods generally use lumped parameter models (such as the RL series equivalent circuit), ignoring the distributed parameter characteristics of overhead lines (such as wave impedance and traveling wave propagation delay). This results in an inability to accurately characterize the transient oscillations and wave process characteristics of fault currents. For example, in a bipolar system, the coupling effect between the metallic return line and the pole line can significantly change the impedance distribution of the fault path. However, traditional models often simplify this effect to fixed parameters, making it difficult to reflect the multipath diversion characteristics of the actual short-circuit current. 2. Lack of dynamic coupling between control strategies and fault current limiting. Traditional analytical algorithms (such as time-domain piecewise linearization) separate the converter control strategy (such as capacitor voltage balancing control and circulating current suppression) from the timing of the current limiting device operation, failing to consider the dynamic impact of the source-side current limiting operation on the MMC equivalent impedance. For example, when the current-limiting reactance is activated in stages, the inductance parameters of the MMC equivalent model will change with the operation sequence. However, existing methods do not establish a timing-dependent impedance adjustment mechanism, resulting in significant deviations between the calculated results and the actual fault current. 3. The companion circuit method lacks engineering adaptability: Although the companion circuit method can simulate wave processes by discretizing the distributed parameters of transmission lines, its application to complex topologies (such as four-terminal bipolar systems) still suffers from modeling flaws. For example, the Berelon model must simultaneously address the coupling relationship between the three-phase line and the single-pole return line in a metal return scenario. However, existing methods often use a simplified single-phase model and fail to fully consider the impact of bipolar asymmetry on the node admittance matrix, resulting in limited accuracy in fault current calculations.

[0004] Therefore, how to solve the problem of insufficient accuracy of the short-circuit current calculation method of the metal return four-terminal bipolar DC power grid has become an urgent problem to be solved. Summary of the Invention

[0005] In view of the above-mentioned deficiencies in the prior art, the present invention provides a short-circuit current calculation method for a metal return four-terminal bipolar DC power grid, which can solve the problem of insufficient accuracy of the short-circuit current calculation method for a metal return four-terminal bipolar DC power grid.

[0006] In order to solve the above technical problems, the present invention adopts the following technical solutions:

[0007] A method for calculating short-circuit current for a metal return four-terminal bipolar DC power grid comprises the following steps:

[0008] S1. Based on the fixed timing of the source-side current limiting action of the DC line of the metal return four-terminal bipolar DC grid, the system characteristics at different stages are analyzed and an MMC equivalent model is established;

[0009] S2. Based on the MMC equivalent model of S1, an equivalent circuit of the Berelon lossy transmission line of the DC line is constructed as a simplified distributed parameter model, and the equivalent circuit is processed to obtain the Berelon two-port equivalent model of the single-phase transmission line and the Berelon equivalent model of the three-phase transmission line;

[0010] S3. Based on the MMC equivalent model, the four converter stations of the metallic return four-terminal bipolar DC grid are modeled separately to obtain the MMC equivalent models of the four converter stations. Based on the MMC equivalent models of the four converter stations, the influence of the metallic return line on the short-circuit current is considered, and combined with the Berelon equivalent model of the three-phase transmission line obtained in S2, an equivalent model of the metallic return four-terminal bipolar DC grid is established.

[0011] S4. Discretize the components in the equivalent model of the metallic return four-terminal bipolar DC grid obtained in S3, combine it with the Berelon two-port equivalent model of the single-phase transmission line obtained in S2, discretize all branches of the entire metallic return four-terminal bipolar DC grid, and establish an accompanying circuit model of the metallic return four-terminal bipolar DC grid;

[0012] S5. Based on the adjoint circuit model of the metal return four-terminal bipolar DC grid established in S4, the conductance matrix G is constructed using the adjoint circuit method to form the node voltage equation;

[0013] S6. When a fault occurs in the metal return four-terminal bipolar DC grid, the node admittance matrix G in the node voltage equation is modified to the corresponding equivalent conductance matrix G' according to the fault type. The modified node voltage equation is solved to obtain the branch current and node voltage after the fault.

[0014] Compared with the prior art, the present invention has the following beneficial effects:

[0015] 1. Accurately characterize the transient characteristics of the fault current. The distributed parameters of the DC line are modeled using the Berelon lossy transmission line model (S2), which overcomes the limitations of the traditional lumped parameter model that ignores wave impedance and traveling wave propagation delay, and can more realistically reflect the rapid rise process of the current after the fault, the transient oscillation characteristics and the shunt effect of the metal loop. By accurately simulating the wave process on the overhead line, the dynamic change trend and characteristics of the short-circuit current after the fault can be described in detail. Compared with existing methods, this method has significantly improved the ability to capture the details of the current waveform in the early stage of the fault (microsecond level). In addition, compared with the traditional lumped parameter model, this method significantly improves the calculation accuracy and solves the problem of large errors in short-circuit current estimation.

[0016] 2. Implement dynamic coupling modeling of control strategies and current-limiting actions. Based on the fixed timing of source-side current-limiting actions (S1), an impedance parameter adjustment mechanism dynamically linked to the MMC equivalent model is established, resolving the problem of traditional methods separating the analysis of converter control and current-limiting device actions. For example, when the current-limiting reactance is activated in stages, this method accurately depicts the dynamic process of current decay in the middle and late stages of the fault (millisecond level) through a time-series-linked impedance change model. Traditional analytical algorithms ignore this dynamic coupling, resulting in accumulated errors.

[0017] 3. Optimize the balance between distributed parameter modeling and computational efficiency. The equivalent partitioning strategy of the Berelon model (S2 single-phase / three-phase model hybrid application) and the full-network discretization of the accompanying circuit method (S4-S5) are adopted to retain the details of the wave process while avoiding the matrix dimension explosion problem caused by overly dense grids in traditional electromagnetic transient simulations. Compared with the simplified treatment of the bipolar system topology by the existing accompanying circuit method (such as ignoring the three-phase line coupling), this method improves the model's characterization ability of the coupling effect between the metal loop and the pole line under the same computing resources through a refined discretization strategy. The node voltage equation constructed by the present invention based on the discretization method of the accompanying circuit has a symmetrical, sparse and constant conductivity matrix structure, which greatly improves the computational efficiency of the solution process. This method can significantly reduce the occupancy of computing resources, adapt to the multi-scenario simulation requirements of complex systems, and is particularly suitable for dynamic characteristic analysis of large-scale DC power grids. By optimizing the matrix characteristics, this method not only improves the computational efficiency, but also enhances the stability and reliability of the model in large-scale system simulation.

[0018] 4. Enhance the adaptability to multiple types of fault scenarios. Through independent modeling of the metal loop coupling path (S3) and fault type adaptive admittance matrix correction (S6), complex faults such as inter-pole short circuit and single-pole grounding in the bipolar system can be flexibly handled. Traditional methods often fail to consider the impact of the metal loop potential offset on the fault loop, resulting in deviations in the multi-path current distribution calculation. This method accurately quantifies the role of the metal loop in fault diversion by constructing an equivalent channel. The present invention is based on a distributed parameter model, which can accurately describe the wave process in the overhead line, including dynamic characteristics such as reflection and propagation, and describe in detail the spatiotemporal variation behavior of the short-circuit current. Compared with the traditional concentrated parameter model, this method effectively makes up for the problem of insufficient description of the dynamic process in engineering applications, and significantly improves the applicability of the short-circuit current calculation of the DC transmission system in actual engineering.

[0019] 5. Improve the versatility of short-circuit current calculations. This method, based on a companion circuit calculation method, flexibly adjusts the conductance matrix G to adapt to the short-circuit current calculation requirements for various fault scenarios in DC power grids. Regardless of the fault location or diverse system topologies, this method demonstrates high applicability and calculation accuracy, significantly improving the universality and practicality of short-circuit current calculations in DC power grid fault analysis.

[0020] Preferably, S1 includes:

[0021] For the DC line of a metal return four-terminal bipolar DC grid, when unlimited current is input, the MMC is equivalent to a series circuit of R, L, and C connected in parallel with a variable DC current source. The DC current source is used to represent the control effect of the MMC, thereby representing the impact of the AC-side feed-in current on the short-circuit current.

[0022] Activate the source-side current limiting device according to the fixed current limiting action sequence, and analyze the activation sequence of the current limiting device and the action sequence of the DC circuit breaker (DCCB) after a fault occurs;

[0023] Based on the action sequence of the current limiting device, the parameter duty cycle D is introduced to represent the proportion of the number of MMC sub-modules put into operation. It is used for source-side current limiting, and the state space average equivalent model of the MMC is obtained as the MMC equivalent model.

[0024] This setup can, 1. Improve the dynamic coupling of the MMC control strategy. By equating the MMC to an RLC series circuit in parallel with a variable DC current source (S1), the impact of the AC-side feed-in current on the short-circuit current is dynamically characterized, addressing the drawback of traditional models that ignore the contribution of converter control strategies (such as modulation mode and current closed-loop control) to the fault current. Compared to existing methods that use fixed impedance or simplified voltage source models, this method more accurately reflects the interaction between the AC system and the DC fault through dynamic adjustment of the variable current source, significantly improving calculation accuracy, especially during the rapid current rise stage at the initial stage of the fault.

[0025] 2. Implement refined modeling of current limiting actions and fault sequences. Based on the analysis of the action sequence of current limiting devices and DC circuit breakers (DCCBs) (S1), an MMC equivalent model is established in stages, resolving the error problem caused by the traditional method of simplifying current limiting actions into instantaneous switching. For example, when the current limiting reactance is put into operation in stages, the parameter duty cycle D dynamically characterizes the impact of the number of submodules put into operation on the equivalent impedance. This can accurately characterize the gradual change characteristics of the MMC equivalent inductance and capacitance during the current limiting process. Traditional state-space average models, which ignore timing correlations, have difficulty reflecting the real-time matching relationship between the current limiting strategy and the fault current.

[0026] 3. Enhance the model's adaptability to current limiting strategies. By introducing the duty cycle D as the core parameter (S1) of the state-space average model, the action sequence of the current limiting device is directly mapped to the dynamic adjustment of the MMC equivalent parameters, breaking through the limitations of traditional models that rely on fixed equivalent circuits. For example, when the current limiting device is put into operation in stages, the duty cycle D changes with the action sequence, driving the equivalent impedance parameters (such as the inductance value) to be updated in real time, thereby more realistically simulating the regulation of the current attenuation rate by the post-fault current limiting effect. Compared with the static impedance model in existing methods, this method significantly improves the model's adaptability to complex current limiting strategies.

[0027] Preferably, S2 includes:

[0028] Based on the S1 MMC equivalent model and the role of the distributed parameter model of the DC line in electromagnetic transient simulation, an equivalent circuit of the Berelon lossy transmission line of the DC line is established for use as a simplified distributed parameter model for analysis;

[0029] Based on the equivalent circuit of the Berelon lossy transmission line, the wave equation of the transmission line in the time domain is analyzed, and the analytical expression of the current at both ends of the transmission line is obtained, which is used as the Berelon two-port equivalent model of the single-phase transmission line of the DC line.

[0030] Based on the Berelon two-port equivalent model of the single-phase transmission line, considering the coupling effect between the three-phase transmission lines of the metallic return bipolar DC power grid, the transmission line model of the three-phase Berelon model in the modal domain is derived. Then, the inverse transformation to the time domain is performed to obtain the three-phase current expression of the transmission line in the time domain, which is used as the Berelon equivalent model of the three-phase transmission line.

[0031] This setup 1. Improves the precision and applicability of wave process modeling. By modeling the distributed parameter characteristics of DC lines using the Berelon lossy transmission line equivalent circuit (S2), this method overcomes the limitations of traditional lumped parameter models that ignore the propagation delay and wave impedance of traveling waves, and can accurately characterize the transient oscillation characteristics of fault current propagating on overhead lines. Compared to existing methods (such as RL series equivalent), this method more realistically reflects the rapid rise and reflection process of microsecond-level current at the initial stage of a fault through the analytical solution of the time-domain wave equation, significantly improving the ability to restore waveform details, especially in long-distance lines.

[0032] 2. Solve the modeling problem of the three-phase line coupling effect. Based on the single-phase Berelon two-port model, the complex electromagnetic coupling relationship of the three-phase line is decoupled into independent modal components through modal domain transformation and inverse transformation (S2), and then the time domain three-phase current expression is reconstructed, overcoming the defect of traditional methods that are difficult to solve analytically when directly modeling in the three-phase time domain due to the coupling terms. For example, existing methods often ignore the capacitive coupling between the metal loop and the pole line or simplify the phase-to-phase mutual inductance, resulting in current distribution errors. However, this method uses modal domain decoupling and inverse transformation to achieve closed-loop derivation of analytical expressions while retaining the three-phase coupling details, significantly improving the symmetry of the three-phase current and the calculation accuracy of asymmetric faults.

[0033] 3. Optimize the synergy between the modal domain and time domain models. Through the construction of the three-phase Berelon model in the modal domain and the inverse transformation in the time domain (S2), a balance is achieved between the dimensionality reduction modeling of complex coupled systems and the intuitive expression of physical quantities. Traditional methods often directly use phase domain models, resulting in high dimensions and low solution efficiency for the three-phase simultaneous equations. This method simplifies the computational complexity by reducing the dimensionality of the modal domain, and then retains the physical meaning of the time domain through inverse transformation, taking into account both model accuracy and computational efficiency. For example, in the case of asymmetric faults in metal loops, modal decomposition can effectively separate the common mode and differential mode components, avoiding the numerical oscillation problem caused by potential offset in traditional phase domain models.

[0034] Preferably, in S2, the Berelon two-port equivalent model of the single-phase transmission line is obtained by the following steps:

[0035] According to the equivalent circuit of the Berelon lossy transmission line, the wave equation of the transmission line in the time domain is written as:

[0036]

[0037] Where s = a, b are ports a and b respectively, and a and b are the first and last nodes respectively; x is the position of the traveling wave in the transmission line; R0, L0, C0, and G0 are the resistance, inductance, capacitance, and conductance per unit length respectively;

[0038] Solving the wave equation, we obtain the analytical expression for the current at both ends of the transmission line, which serves as the Berelon two-port equivalent model of a single-phase transmission line:

[0039]

[0040] Where, line wave impedance R=1 / 4R0d, d is the line length; i ha (t-τ), i hb (t-τ) are the equivalent injection current sources of nodes a and b, and the line propagation delay

[0041] This setup can accurately characterize the transient characteristics of traveling wave propagation. By writing and analytically solving the time-domain wave equation of the Berylon lossy transmission line, the line distribution parameters (R0, L0, C0, G0) and the wave impedance Z are clearly defined. c , propagation delay τ, and other key parameters, addressing the shortcomings of traditional lumped parameter models (such as the RL series equivalent) that ignore traveling wave reflections and propagation delays. Compared to existing methods, this model, by leveraging the delay term in the current analytical expression and the wave impedance matching relationship, can more realistically simulate the propagation and reflection of traveling waves on the transmission line during the initial stage of a fault, significantly improving the ability to reproduce the details of the transient current waveform.

[0042] 2. Realize analytical modeling of the traveling wave process. By solving the wave equation, the analytical expression of the current at both ends (such as i a (t) and i b (t) formula), the time domain traveling wave process is converted into an equivalent injection current source (i ha (t-τ), i hb The superposition of the two parameters (t-τ) breaks through the efficiency bottleneck caused by the reliance on mesh discretization of traditional numerical methods (such as the finite difference method). For example, existing methods require dense meshing to capture the wave process when simulating long line faults. However, this model directly relates the current and voltage at both ends through analytical expressions, ensuring accuracy while avoiding the computational burden of numerical iteration.

[0043] 3. Enhance engineering applicability and parameter configurability. By clearly defining the wave impedance The model incorporates physical quantities such as propagation delay τ, and allows for flexible configuration of line length d and distribution parameters R0, L0, and C0, making it adaptable to DC lines of varying voltage levels and wire types. Compared to the traditional Berelon model, which is limited to lossless or uniform lines, this method, by introducing lossy parameters R0 and G0, supports refined modeling of line losses, more closely resonating with real-world engineering scenarios.

[0044] Preferably, in S2, the process of constructing the three-phase current expression of the transmission line in the time domain includes:

[0045] Based on the Berelon two-port equivalent model of a single-phase transmission line, the current at the port on side a in the modal domain is expressed as:

[0046]

[0047] Where i = 0, 1, 2 are the parameters of zero sequence, positive sequence, and negative sequence respectively; j represents the imaginary unit, and ωs represents the angular frequency; Indicates the port voltage on side a; Represents the equivalent injection current source of node a;

[0048] Perform an inverse transformation on the current expression of the port on side a to obtain the three-phase current expression of the transmission line in the time domain:

[0049]

[0050] Where k = m, p, n are the port currents of the metal return line, positive electrode, and negative electrode transmission line respectively; Represents the port voltage on side a; R k =1 / 4R0d; Indicates the line wave impedance;

[0051] T is the transformation matrix between the time domain and the modal domain, expressed as:

[0052]

[0053] Similarly, the expression of the current at the port on the b side is obtained:

[0054]

[0055] Where, Indicates the port voltage on the b side; Represents the equivalent injection current source of node b.

[0056] This setup achieves 1. modal domain decoupling and independent analysis of sequence components in the three-phase coupled system. By introducing zero-sequence, positive-sequence, and negative-sequence parameters in the modal domain (i = 0, 1, 2), the complex electromagnetic coupling relationship of the three-phase transmission line is decoupled into independent sequence components, solving the high-dimensional and difficult-to-analyze problems of simultaneous equations caused by phase mutual inductance and capacitive coupling when directly modeling in the three-phase time domain using traditional methods. For example, existing methods often ignore the zero-sequence current path between the metal loop and the positive and negative poles, resulting in current distribution errors for asymmetric faults (such as single-pole grounding). However, this method significantly improves the ability to characterize the shunt characteristics of the metal loop through modal domain decomposition (such as independent calculation of zero-sequence components).

[0057] 2. Inverse transformation modeling that retains the physical meaning of the time domain. The modal domain current expression is inversely transformed to the time domain through the transformation matrix T, while retaining the wave impedance (Zc ), line loss (R), and other physical parameters, while directly outputting the time-domain current waveforms for the metal return line (j=m), the positive pole (j=p), and the negative pole (j=n). This overcomes the limitation of traditional modal domain methods, which lack a defined inverse transform and cannot intuitively obtain the actual phase current. Compared to existing methods that rely on numerical iteration to solve phase-domain equations, this method balances computational efficiency with engineering interpretability of physical quantities through analytical inverse transforms.

[0058] 3. Supports parametric modeling for complex fault scenarios. By defining independent expressions for metal loops and positive and negative terminal currents and dynamically associating parameters, the boundary conditions of different fault types (such as inter-pole short circuits and single-pole grounding) can be flexibly adapted. Traditional methods often lead to errors in fault path impedance calculations due to fixed parameter assumptions (such as ignoring metal loop potential offsets). This method, through parametric modeling (such as adjusting the weights of the sequence components of the T matrix), achieves accurate quantification of multi-path fault current diversion.

[0059] Preferably, in S4, when discretizing the components, the transient process time of the linear dynamic circuit is discretized into several equal time intervals h, and the differential equation of the component is converted into a difference equation; after all components are discretized, the current equation of each node is listed using Kirchhoff's node current law to obtain the difference equation of the power grid.

[0060] This setup can, 1. Improve the numerical stability and computational efficiency of transient processes. By converting the differential equations of linear dynamic circuits into difference equations (S4) with equal time intervals h, and adopting explicit or implicit discretization strategies (such as the backward Euler method), the numerical oscillation problem caused by variable step-size integration in traditional electromagnetic transient simulations is avoided. Compared with existing methods (such as the trapezoidal method) that are prone to divergence in nonlinear systems, this method significantly improves iterative convergence through fixed-step discretization and linearization, especially reducing computational resource consumption in long-time domain simulations.

[0061] 2. Achieve dimensionality reduction modeling of complex dynamic systems. The dynamic characteristics of components (such as the differential relationship between inductance and capacitance) are converted into algebraic difference equations. Based on Kirchhoff's nodal current law, a full-network differential equation system (S4) is constructed, reducing the dimensionality of the high-order differential equation system to a linear algebraic problem. Traditional methods require solving differential-algebraic equations simultaneously, while this method converts the dynamic process into pure algebraic operations through full discretization, simplifying the matrix construction and solution process. It is particularly suitable for the rapid solution of multi-node systems.

[0062] 3. Enhance the model's ability to capture transient details. By using a discretization strategy with a uniform time step size h, combined with the explicit correlation of the instantaneous current and voltage values ​​through differential equations, we can more precisely characterize the microsecond-level current surges and voltage oscillations following a fault. Existing variable-step methods often sacrifice high-frequency details for efficiency. This method, through a fixed step size and dynamic parameter updates (such as differential iteration of the inductor current), improves the accuracy of waveform detail restoration while maintaining efficiency.

[0063] Preferably, in S4, each element is discretized into a Norton equivalent circuit using the same method; the element includes an inductor element, and the discretization process of the inductor element includes:

[0064] Differential equation based on inductance:

[0065]

[0066] Where, v i (t) and v j (t) are the voltages at the i and j terminals of the inductor L, i ij (t) is the current at port i;

[0067] Reshape the differential equation for inductance:

[0068]

[0069] From the trapezoidal integral formula, we can get the corresponding Norton equivalent circuit:

[0070]

[0071] in:

[0072]

[0073] Where, I L (t-Δt) is the history term of the branch current, represented by a current source; G L is the equivalent conductance.

[0074] This setting, 1. Improve the numerical stability and calculation accuracy of the discretization process. The inductance differential equation is discretized by the trapezoidal integral formula, and the dynamic differential relationship is converted into the algebraic Norton equivalent circuit. Compared with the traditional explicit Euler method or backward Euler method, the trapezoidal integral has the characteristics of second-order accuracy, which can effectively suppress numerical oscillation and truncation errors. For example, the fixed-step explicit integration in the existing method is prone to high-frequency distortion, while this method uses the history term (I L (t-Δt)) and equivalent conductance (G L ) symmetrical design significantly improves the smoothness of the transient current waveform and the calculation stability.

[0075] 2. Realize static equivalent modeling of dynamic components. Discretize the inductor into a Norton equivalent circuit (current source in parallel with conductance), and convert the time domain differential equation into a linear algebraic equation, thus solving the complexity of traditional dynamic component modeling, which requires simultaneous differential-algebraic equations. For example, existing methods need to iteratively solve the differential term at each time step, while this method uses the historical current source I L (t-Δt) absorbs the cumulative effect of the previous moment, combined with the equivalent conductance G L Directly associating with the current voltage difference simplifies the process of building the node admittance matrix, which is particularly suitable for fast simulation of large-scale power grids.

[0076] 3. A unified discretization framework enhances model consistency. All components (such as inductors and capacitors) are discretized into Norton equivalent circuits using the same method, ensuring the uniformity of the branch model across the entire network and the compatibility of the node current equations. Traditional hybrid discretization methods (such as trapezoidal integration for inductors and backward Euler integration for capacitors) are prone to introducing interface errors due to inconsistent integration orders. This method, through a unified trapezoidal integration strategy, avoids conflicts in the discretization parameters of multiple component types and improves the coordination of the entire system simulation.

[0077] 4. Reduce computational complexity and resource consumption. By precalculating the history terms and equivalent conductance of the Norton equivalent circuit, dynamic simulations are transformed into linear algebraic problems, significantly reducing the amount of iterative computation. For example, existing electromagnetic transient simulations require real-time updates of differential terms and iterative convergence. However, this method, through recursive updates of history terms and the constant nature of conductance, requires only matrix forward and backward iterations to solve for node voltages, significantly improving the efficiency of long-time-domain simulations.

[0078] Preferably, in S5 and S6, the node voltage equation is:

[0079] GU(t)=I hist +i sc (t);

[0080] Where G is the equivalent conductance matrix of the circuit; U (t) is the node voltage vector; I hist is the historical current source vector; i sc(t) is the DC current source vector;

[0081] Among them, the equivalent conductivity matrix G is a symmetric matrix, expressed as:

[0082]

[0083] Where, The equivalent conductivity matrices are all symmetric matrices; The equivalent conductivity matrices are all zero matrices; Where n and m are the number of converter stations and joint nodes respectively;

[0084] The elements in the equivalent conductance matrix G are calculated as follows:

[0085]

[0086] Where, is the equivalent conductance matrix of the Berelon model transmission line; are the equivalent conductance matrices of the RL branch and C branch of the MMC respectively; G g is the conductivity matrix of the grounding resistance;

[0087] Historical current source vector I hist for:

[0088]

[0089] Where, are the historical current source vectors of the positive electrode layer, metal loop layer, and negative electrode layer respectively;

[0090] Historical current source vector I hist The calculation method of the elements is as follows:

[0091]

[0092] in:

[0093]

[0094] Where: is the historical current of the Berelon model DC grid ij; and are the historical currents of the equivalent RL branch and C branch of converter i respectively;

[0095] DC current source vector i sc (t) is:

[0096]

[0097] in:

[0098]

[0099] This setup can achieve efficient construction of hierarchical and block matrices of complex power grids. By constructing the equivalent conductivity matrix G by hierarchical and block construction of positive electrode, metal return line and negative electrode, the three-phase coupled system is decomposed into independent sub-matrices (such as G pp , G mm), significantly reducing the computational complexity of matrix filling and inversion. Compared to traditional global matrix unified modeling (e.g., non-layered processing), this method reduces the number of non-zero elements through a matrix partitioning strategy based on physical topology mapping, improving the efficiency of solving large-scale power grids.

[0100] 2. Accurately characterize the cumulative transient effects of dynamic components. Historical current source vector I hist By superimposing the Berelon traveling wave reflected current and the discretized accumulated current of the MMC branch, we can fully characterize the contribution of the historical states of dynamic components such as inductors and capacitors to the current at the current moment. Traditional methods often ignore the temporal coupling between the discharge of the MMC submodule capacitors and the action of the current-limiting reactance. However, this method dynamically adjusts the historical current weights by using the duty cycle D, significantly improving the calculation accuracy of the current decay characteristics in the middle and late stages of a fault.

[0101] 3. Supports flexible modeling and rapid solution of multiple fault types. A dynamic correction mechanism for the node admittance matrix based on the adjoint circuit method modifies the relationship between the fault node admittance and topological connectivity, enabling rapid adaptation to complex fault scenarios such as inter-pole short circuits and single-pole grounding. Compared to traditional methods that require reconstruction of the entire network model, this method only requires local modification of G matrix elements, reducing computational time while maintaining accuracy. It is particularly suitable for real-time simulation testing of protection devices.

[0102] 4. Suppressing numerical errors and improving convergence. The characteristics and hierarchical block structure of the equivalent conductance matrix G, combined with the second-order accurate discretization of the trapezoidal integration method (implicit in the historical current calculation), effectively avoid the numerical oscillation problems of traditional asymmetric matrices or low-order discretization methods (such as the first-order Euler method), ensuring stable convergence of the node voltage equations in long-time domain simulations.

[0103] Preferably, S6 includes:

[0104] After a fault occurs in a metal return four-terminal bipolar DC grid, determine the fault type;

[0105] According to the fault type, the node admittance matrix in the node voltage equation is modified into the corresponding equivalent conductance matrix G';

[0106] Then, by calculating the historical current source I hist And the DC current source i sc , obtain the current change characteristics of the system before and after the fault;

[0107] Finally, the voltage value of each node and the short-circuit current of the fault branch are obtained by recursively solving the modified node voltage equation.

[0108] This setup, through fault-adaptive dynamic correction of the admittance matrix, recursive updating of historical current sources, and recursive solution of node equations, solves the problems of poor generalization of fault scenarios, insufficient characterization of dynamic processes, and low computational efficiency of traditional methods. It significantly improves the accuracy (quantification of shunt paths) and real-time performance (efficient matrix solution) of short-circuit current calculation in four-terminal bipolar DC power grids with metal return, providing reliable support for the rapid verification and optimization of fault protection strategies.

[0109] Preferably, in S6, the fault type includes a single-pole grounding fault P2G, a pole-to-metal return fault P2M, a pole-to-metal return short-circuit grounding fault P2M2G, and an inter-pole short-circuit fault P2P;

[0110] The single-pole grounding fault P2G includes a positive pole grounding short-circuit fault; the equivalent conductance matrix G' of the positive pole grounding short-circuit fault is:

[0111]

[0112] Where R f represents the transition resistance;

[0113] The modification method of G' for other single-pole ground faults P2G is the same as that for positive-pole ground short-circuit faults;

[0114] The pole-to-metal return line fault P2M includes a positive pole-to-metal return line short circuit fault; the equivalent conductance matrix G' of the positive pole-to-metal return line short circuit fault is:

[0115]

[0116] The modification method of G' for other pole-to-metal return fault P2M is the same as that for positive pole-to-metal return short circuit fault;

[0117] The pole-to-metal return line short-circuit grounding fault P2M2G includes the positive pole-to-metal return line short-circuit grounding fault; the equivalent conductance matrix G' of the positive pole-to-metal return line short-circuit grounding fault is:

[0118]

[0119] Where: R gf is the transition resistance between the metal return line and the ground;

[0120] The modification method of G' of other pole-to-metal return short-circuit grounding fault P2M2G is the same as that of positive pole-to-metal return short-circuit grounding fault;

[0121] The inter-pole short circuit fault P2P includes a bipolar short circuit fault. The equivalent conductance matrix G' of the bipolar short circuit fault is:

[0122]

[0123] The modification method of G' for other inter-pole short circuit faults P2P is the same as that for bipolar short circuit faults.

[0124] This setup, through the design of admittance matrix correction rules for multiple types of faults, solves the problems of incomplete fault scenario coverage, over-simplification of transition resistance and metal loop coupling effects, and low computational efficiency in traditional methods. It significantly improves the accuracy (multi-path shunting quantification), efficiency (local correction strategy), and applicability (standardized correction framework) of short-circuit current calculation in four-terminal bipolar DC power grids with metal return, providing reliable technical support for the refined analysis of complex faults and optimization of protection strategies. BRIEF DESCRIPTION OF THE DRAWINGS

[0125] In order to make the purpose, technical solutions and advantages of the invention more clear, the present invention will be further described in detail below with reference to the accompanying drawings, in which:

[0126] Figure 1 Flowchart of this method;

[0127] Figure 2 Schematic diagram of the MMC topology structure of the converter station in the embodiment and the MMC equivalent model when unlimited current is put into use;

[0128] Figure 3 Schematic diagram of the timing of the operation of the protection and current limiting devices of the DC grid in the embodiment;

[0129] Figure 4 Schematic diagram of the MMC state space average equivalent circuit in the embodiment;

[0130] Figure 5 Schematic diagram of an equivalent circuit of a Berelon lossy transmission line in an embodiment;

[0131] Figure 6 Schematic diagram of a Berelon two-port equivalent model of a single-phase transmission line in an embodiment;

[0132] Figure 7 Schematic diagram of the equivalent model of the metal return four-terminal bipolar DC power grid in the embodiment;

[0133] Figure 8 Schematic diagram of the discretization process of the inductor element in the embodiment;

[0134] Figure 9 4 is an implementation flow chart of S5-S6 in the embodiment. DETAILED DESCRIPTION

[0135] The following is a further detailed description through specific implementation methods:

[0136] Example:

[0137] like Figure 1As shown, this embodiment discloses a method for calculating short-circuit current for a metal return four-terminal bipolar DC power grid, comprising the following steps:

[0138] S1. According to the fixed timing of the source-side current limiting action of the DC line of the metal return four-terminal bipolar DC grid, the system characteristics at different stages are analyzed and an MMC equivalent model is established.

[0139] In specific implementation, S1 includes:

[0140] For the DC line of a metal return four-terminal bipolar DC grid, when unlimited current is input, the MMC is equivalent to a series circuit of R, L, and C connected in parallel with a variable DC current source. The DC current source is used to represent the control effect of the MMC, thereby representing the impact of the AC-side feed-in current on the short-circuit current.

[0141] Activate the source-side current limiting device according to the fixed current limiting action sequence, and analyze the activation sequence of the current limiting device and the action sequence of the DC circuit breaker (DCCB) after a fault occurs;

[0142] Based on the action sequence of the current limiting device, the parameter duty cycle D is introduced to represent the proportion of the number of MMC sub-modules put into operation. It is used for source-side current limiting, and the state space average equivalent model of the MMC is obtained as the MMC equivalent model.

[0143] By equating the MMC to an RLC series circuit connected in parallel with a variable DC current source (S1), the impact of the AC-side feed-in current on the short-circuit current is dynamically characterized, addressing the drawback of traditional models that ignore the contribution of converter control strategies (such as modulation method and current closed-loop control) to the fault current. Compared to existing methods that use fixed impedance or simplified voltage source models, this method, through dynamic adjustment of the variable current source, more accurately reflects the interaction between the AC system and the DC fault, significantly improving calculation accuracy during the initial stage of the fault, particularly during the rapid current rise. Furthermore, based on the timing analysis of the current limiting device and the DC circuit breaker (DCCB) (S1), a phased MMC equivalent model is established, addressing the error problem of traditional methods that simplify current limiting operation to instantaneous switching. For example, when the current limiting reactance is activated in stages, the parameter duty cycle D is used to dynamically characterize the impact of the number of activated submodules on the equivalent impedance. This accurately characterizes the gradual changes in the MMC's equivalent inductance and capacitance during the current limiting process. Traditional state-space average models, which ignore timing correlations, struggle to reflect the real-time matching relationship between the current limiting strategy and the fault current. Furthermore, by introducing the duty cycle D as the core parameter (S1) of the state-space average model, the current-limiting device's operating sequence is directly mapped to the dynamic adjustment of the MMC equivalent parameters, breaking through the limitations of traditional models that rely on fixed equivalent circuits. For example, when the current-limiting device is put into operation in stages, the duty cycle D changes with the operating sequence, driving the equivalent impedance parameters (such as the inductance) to update in real time, thereby more realistically simulating the effect of the post-fault current limiting effect on the current decay rate. Compared with the static impedance model used in existing methods, this method significantly improves the model's adaptability to complex current-limiting strategies.

[0144] In order to facilitate those skilled in the art to better understand the content of S1, an example is used for illustration.

[0145] First, the MMC topology is analyzed and an equivalent model of MMC with infinite flow is established.

[0146] When a short circuit occurs in the DC grid line, within 5-10ms, the fault current on the DC side of the MMC is determined by the discharge current of the MMC submodule capacitor and the AC system feed current. The detailed structure before the MMC is locked can be equivalent to an RLC series circuit with a variable DC current source i sc As attached Figure 2 As shown in the figure: R0 and L0 are the bridge arm resistance and bridge arm inductance respectively; L dc is the current limiting reactance; i dc is the DC injection current; u c is the voltage across the capacitor; R c , L c 、C c are the resistance, inductance and capacitance of the equivalent circuit respectively. scThe AC feed-in current determined for the MMC controller varies with the DC grid voltage. This MMC equivalent model with a variable DC current source fully considers the influence of the AC feed-in current and can more accurately estimate the node voltages and branch currents in the circuit.

[0147] Among them, the equivalent parameter R c , L c 、C c for:

[0148]

[0149] Where: R on is the bridge arm on-resistance; N SM is the number of submodules in a bridge arm; C SM is the capacitance of a submodule.

[0150] DC current source i sc It can be expressed as:

[0151]

[0152] Where: P dc is the active power flowing to the DC side of the converter.

[0153] Secondly, an MMC equivalent model based on the current limiting action timing is established.

[0154] After a fault occurs in the DC grid, the DCCB usually takes about 2ms to identify the type of grid fault and starts clearing the fault current and isolating the fault about 10ms after the fault. Since the MMC discharges very quickly after a fault, in order to prevent the MMC from being locked due to overcurrent, it is urgent to put current limiting devices into operation to suppress the amplitude and energy of the fault current during the period from the fault occurrence to the DCCB operation. After a short-circuit fault occurs in the DC grid, a smoothing reactor (current limiting reactor, CLR) is always put into operation in the DC line. In addition, the source-side current limiting device is put into operation according to the fixed current limiting action sequence. After the fault occurs, the current limiting device is put into operation according to the action sequence of the DCCB as shown below. Figure 3 In the figure: t0 is the moment when the fault occurs; t1 is the moment when the source-side current limiting device is put into operation; and t2 is the moment when the DCCB starts to clear the fault current.

[0155] according to Figure 3 The protection and current limiting device action sequence is as follows: At time t0, only the CLR is in operation in the DC line, that is, the smoothing reactor is connected in series in the DC line. Therefore, the MMC equivalent circuit during the period t0–t1 is as follows: Figure 2 As shown. Figure 2 The MMC fault equivalent circuit can be obtained by calculating the differential equations for the fault current in the CLR suppression stage:

[0156]

[0157] At time t1, the source side current limiting is activated. Based on the state space average model, the present invention connects a variable DC current source in parallel to represent the AC side feed current, and introduces the parameter duty cycle D to represent the MMC in a switching cycle T. c The proportion of capacitor input in each phase unit. When D = 1, it means that the MMC is in a fully discharged state and all the capacitors of each phase unit are fully input; when D = 0.5, it means that half of the capacitors of each phase unit are input; when D = 0, it means that no capacitors are input in each phase unit, that is, both the upper and lower bridge arms are bypassed. The equivalent circuit of the MMC state space average model is as follows Figure 4 As shown in the figure: is the average equivalent voltage of the two meta-states.

[0158] S2. Based on the MMC equivalent model of S1, the equivalent circuit of the Berelon lossy transmission line of the DC line is constructed as a simplified distributed parameter model, and it is processed to obtain the Berelon two-port equivalent model of the single-phase transmission line and the Berelon equivalent model of the three-phase transmission line.

[0159] In specific implementation, S2 includes:

[0160] Based on the MMC equivalent model of S1 and the role of the distributed parameter model of the DC line in electromagnetic transient simulation, the equivalent circuit of the Berelon lossy transmission line of the DC line is established, such as Figure 5 As shown, it is used as a simplified distributed parameter model for analysis;

[0161] According to the equivalent circuit of the Berelon lossy transmission line, the transmission line wave equation in the time domain is analyzed, and the analytical expression of the current at both ends of the transmission line is obtained. The Berelon two-port equivalent model of the single-phase transmission line as a DC line is as follows: Figure 6 As shown;

[0162] Based on the Berelon two-port equivalent model of the single-phase transmission line, considering the coupling effect between the three-phase transmission lines of the metallic return bipolar DC power grid, the transmission line model of the three-phase Berelon model in the modal domain is derived. Then, the inverse transformation to the time domain is performed to obtain the three-phase current expression of the transmission line in the time domain, which is used as the Berelon equivalent model of the three-phase transmission line.

[0163] The Berelon two-port equivalent model of a single-phase transmission line is obtained by the following steps:

[0164] According to the equivalent circuit of the Berelon lossy transmission line, the wave equation of the transmission line in the time domain is written as:

[0165]

[0166] Where s = a, b are ports a and b respectively, and a and b are the first and last nodes respectively; x is the position of the traveling wave in the transmission line; R0, L0, C0, and G0 are the resistance, inductance, capacitance, and conductance per unit length respectively;

[0167] Solving the wave equation, we obtain the analytical expression for the current at both ends of the transmission line, which serves as the Berelon two-port equivalent model of a single-phase transmission line:

[0168]

[0169] Where, line wave impedance R=1 / 4R0d, d is the line length; i ha (t-τ), i hb (t-τ) are the equivalent injection current sources of nodes a and b, and the line propagation delay

[0170] In this way, the transient characteristics of traveling wave propagation can be accurately characterized. By writing and analytically solving the time domain wave equation of the Berelon lossy transmission line, the line distribution parameters (R0, L0, C0, G0) and the wave impedance Z are clearly defined. c , propagation delay τ and other key parameters, which solves the defect of traditional lumped parameter models (such as RL series equivalent) that ignores traveling wave reflection and propagation delay. Compared with existing methods, this model can more realistically simulate the propagation and reflection process of traveling waves on the transmission line at the initial stage of fault through the delay term and wave impedance matching relationship in the current analytical expression, and significantly improve the ability to restore the details of transient current waveform. In addition, by solving the wave equation, the analytical expression of the current at both ends (such as i a (t) and i b (t) formula), the time domain traveling wave process is converted into an equivalent injection current source (i ha (t-τ), i hb (t-τ)) breaks through the efficiency bottleneck caused by the reliance on grid discretization of traditional numerical methods (such as the finite difference method). For example, the existing method requires dense grid division to capture the wave process when simulating long line faults, while this model directly associates the current and voltage at both ends through analytical expressions, avoiding the computational burden of numerical iteration while ensuring accuracy. In addition, it can also enhance engineering applicability and parameter configurability. By clearly defining the wave impedance The model incorporates physical quantities such as propagation delay τ, and allows for flexible configuration of line length d and distribution parameters R0, L0, and C0, making it adaptable to DC lines of varying voltage levels and wire types. Compared to the traditional Berelon model, which is limited to lossless or uniform lines, this method, by introducing lossy parameters R0 and G0, supports refined modeling of line losses, more closely resonating with real-world engineering scenarios.

[0171] In specific implementation, the process of constructing the three-phase current expression of the transmission line in the time domain includes:

[0172] Based on the Berelon two-port equivalent model of a single-phase transmission line, the current at the port on side a in the modal domain is expressed as:

[0173]

[0174] Where i = 0, 1, 2 are the parameters of zero sequence, positive sequence, and negative sequence respectively; j represents the imaginary unit, ω s Indicates angular frequency; V a i (t) represents the port voltage on side a; Represents the equivalent injection current source of node a;

[0175] Perform an inverse transformation on the current expression of the port on side a to obtain the three-phase current expression of the transmission line in the time domain:

[0176]

[0177] Where k = m, p, n are the port currents of the metal return line, positive electrode, and negative electrode transmission line respectively; Represents the port voltage on side a; R k =1 / 4R0d; Indicates the line wave impedance;

[0178] T is the transformation matrix between the time domain and the modal domain, expressed as:

[0179]

[0180] Similarly, the expression of the current at the port on the b side is obtained:

[0181]

[0182] Where, Indicates the port voltage on the b side; Represents the equivalent injection current source of node b.

[0183] In this way, by introducing zero-sequence, positive-sequence, and negative-sequence parameters in the modal domain (i=0, 1, 2), the complex electromagnetic coupling relationship of the three-phase transmission line is decoupled into independent sequence components, solving the problem of high dimensionality and difficulty in analyzing the simultaneous equations caused by phase mutual inductance and capacitive coupling when directly modeling in the three-phase time domain using traditional methods. For example, existing methods often ignore the zero-sequence current path between the metal loop and the positive and negative poles, resulting in current distribution errors for asymmetric faults (such as single-pole grounding). This method significantly improves the ability to characterize the shunt characteristics of the metal loop through modal domain decomposition (such as independent calculation of zero-sequence components). In addition, the modal domain current expression is inversely transformed to the time domain through the transformation matrix T, while retaining the wave impedance (Z c ), line loss (R) and other physical parameters, while directly outputting the time domain current waveforms of the metal loop (j=m), positive pole (j=p), and negative pole (j=n), solving the defect of the traditional modal domain method that cannot intuitively obtain the actual phase current due to the undefined inverse transformation. Compared with the existing methods that rely on numerical iteration to solve the phase domain equations, this method takes into account both computational efficiency and engineering interpretability of physical quantities through analytical inverse transformation. In addition, by defining independent expressions for the metal loop, positive and negative pole port currents and dynamic association of parameters, it can flexibly adapt to the boundary conditions of different fault types (such as inter-pole short circuit and single-pole grounding). Traditional methods often lead to calculation deviations of fault path impedance due to fixed parameter assumptions (such as ignoring the potential offset of the metal loop), while this method achieves accurate quantification of multi-path diversion of fault current through parameterized modeling (such as adjustment of the weight of the sequence component of the T matrix).

[0184] The S2 setting models the distributed parameter characteristics of DC lines using the Berelon lossy transmission line equivalent circuit (S2), breaking through the limitations of traditional lumped parameter models that ignore the propagation delay and wave impedance of traveling waves, and can accurately characterize the transient oscillation characteristics of fault current propagating on overhead lines. Compared with existing methods (such as RL series equivalent), this method more realistically reflects the rapid rise and reflection process of microsecond-level current at the beginning of the fault by analytically solving the time-domain wave equation, significantly improving the ability to restore waveform details, especially in long-distance lines. In addition, based on the single-phase Berelon two-port model, through modal domain transformation and inverse transformation (S2), the complex electromagnetic coupling relationship of the three-phase line is decoupled into independent modal components, and the time-domain three-phase current expression is reconstructed. This overcomes the shortcomings of traditional methods that are difficult to analytically solve when directly modeling three-phase time domain coupling terms. For example, existing methods often ignore the capacitive coupling between the metal loop and the pole line or simplify the phase-to-phase mutual inductance, resulting in current distribution errors. However, this method, through modal domain decoupling and inverse transformation, achieves closed-loop derivation of analytical expressions while preserving the details of the three-phase coupling, significantly improving the symmetry of the three-phase current and the computational accuracy of asymmetric faults. Furthermore, by constructing a three-phase Berylon model in the modal domain and performing inverse transformation in the time domain (S2), a balance is achieved between dimensionality reduction modeling of complex coupled systems and intuitive expression of physical quantities. Traditional methods often directly use phase-domain models, resulting in high dimensionality and low solution efficiency for the three-phase simultaneous equations. However, this method simplifies the computational complexity through modal domain dimensionality reduction and then preserves the physical meaning in the time domain through inverse transformation, balancing model accuracy and computational efficiency. For example, in the case of an asymmetric metal loop fault, modal decomposition can effectively separate the common-mode and differential-mode components, avoiding the numerical oscillation problem caused by potential offset in traditional phase-domain models.

[0185] S3. According to the MMC equivalent model, the four converter stations of the metal return four-terminal bipolar DC power grid are modeled respectively to obtain the MMC equivalent models of the four converter stations; based on the MMC equivalent model of the four converter stations, considering the influence of the metal return line on the short-circuit current, combined with the Berelon equivalent model of the three-phase transmission line obtained in S2, an equivalent model of the metal return four-terminal bipolar DC power grid is established.

[0186] S4. Discretize the components in the equivalent model of the metal return four-terminal bipolar DC power grid obtained in S3, combine it with the Berelon two-port equivalent model of the single-phase transmission line obtained in S2, discretize all branches of the entire metal return four-terminal bipolar DC power grid, and establish the accompanying circuit model of the metal return four-terminal bipolar DC power grid.

[0187] Among them, when discretizing the components, the transient process time of the linear dynamic circuit is discretized into several equal time intervals h, and the differential equation of the component is converted into a difference equation; after all components are discretized, Kirchhoff's node current law is used to list the current equation of each node to obtain the difference equation of the power grid.

[0188] By converting the differential equations of linear dynamic circuits into differential equations (S4) with equal time intervals h, and employing explicit or implicit discretization strategies (such as the backward Euler method), this approach avoids the numerical oscillation problem caused by variable-step-size integration in traditional electromagnetic transient simulations. Compared to existing methods (such as the trapezoidal method), which are prone to divergence in nonlinear systems, this method significantly improves iterative convergence through fixed-step-size discretization and linearization, particularly reducing computational resource consumption in long-time-domain simulations. Furthermore, the dynamic characteristics of components (such as the differential relationships between inductance and capacitance) are converted into algebraic difference equations, and a full-network differential equation system (S4) is constructed based on Kirchhoff's nodal current law, reducing the dimensionality of the high-order differential equation system to a linear algebraic problem. While traditional methods require the simultaneous solution of differential-algebraic equations, this method transforms the dynamic process into pure algebraic operations through full discretization, simplifying the matrix construction and solution process and making it particularly suitable for fast solution of multi-node systems. Furthermore, it enhances the model's ability to capture transient details. By using a discretization strategy with a uniform time step size h, combined with the explicit correlation of the instantaneous current and voltage values ​​using differential equations, we can more precisely characterize the microsecond-level current surges and voltage oscillations following a fault. Existing variable-step-size methods often sacrifice high-frequency detail for efficiency. This method, by combining a fixed step size with dynamic parameter updates (such as differential iteration of the inductor current), improves the accuracy of waveform detail restoration while maintaining efficiency.

[0189] In order to help those skilled in the art better understand the technical content of S4, an example is used for illustration.

[0190] According to the equivalent model of MMC and the Berelon equivalent model of transmission line, the equivalent model of metal return four-terminal bipolar DC grid can be obtained as follows: Figure 7 In the figure: 1, 2, 3, and 4 are converter stations 1, 2, 3, and 4 respectively; the DC grid equivalent circuit is divided into three layers: the positive electrode layer, the metal return layer, and the negative electrode layer, which are represented by p, m, and n respectively; are the equivalent resistance, inductance, and capacitance of the k-pole MMC of converter station i (i=1, 2, 3, 4, k=p, m, n); is the inductance of the k-pole smoothing reactor close to converter station i on the transmission line between converter stations i and j (i, j = 1, 2, 3, 4, k = p, m, n); is the k-pole DC current source of converter station i (i=1, 2, 3, 4, k=p, n); R g is the grounding point resistance.

[0191] For example, 2p is the positive busbar of converter station 2, is the positive MMC equivalent resistance of converter station 2, is the positive MMC equivalent inductance of converter station 2, is the positive MMC equivalent capacitance of converter station 2, is the positive DC current source of converter station 2, It is the inductance of the positive smoothing reactor close to converter station 2 on the transmission line between converter stations 2 and 3.

[0192] During specific implementation, each element is discretized into a Norton equivalent circuit using the same method; the elements include inductance elements.

[0193] like Figure 8 As shown, the inductor element can be discretized into a Norton equivalent circuit consisting of a conduction branch and a current source branch in parallel. In the figure: v i (t) and v j (t) are the voltages at the i and j terminals of the inductor L, i ij (t) is the current at port i.

[0194] The discretization process of the inductor element includes:

[0195] Differential equation based on inductance:

[0196]

[0197] Where, v i (t) and v j (t) are the voltages at the i and j terminals of the inductor L, i ij (t) is the current at port i;

[0198] Reshape the differential equation for inductance:

[0199]

[0200] From the trapezoidal integral formula, we can get the corresponding Norton equivalent circuit:

[0201]

[0202] in:

[0203]

[0204] Where, I L (t-Δt) is the history term of the branch current, represented by a current source; G L is the equivalent conductance.

[0205] According to the two-port equivalent model of the DC line and the discretization process of the components, all branches of the entire metal return bipolar DC grid can be discretized to establish the accompanying circuit model of the grid. Assuming that the DC grid has n converter stations and m joint nodes, it can be obtained that Figure 7The positive electrode layer, metal loop layer, and negative electrode layer of the power grid model shown have 2n+m, n+m, and 2n+m nodes respectively.

[0206] In this companion circuit model, the number of nodes in the positive and negative layers is determined by the converter stations at both ends of the grid and the electrical connections of the metallic return lines, respectively. The metallic return line layer considers the electrical characteristics of the return lines. Each node represents an electrical state in the grid, while branches transmit energy through the electrical connections between nodes. This discretization method effectively describes the current distribution, fault propagation, and energy flow in the grid. Therefore, by calculating node voltages and branch currents, the electrical characteristics of the grid under various operating conditions can be solved.

[0207] In this way, the inductance differential equation is discretized by the trapezoidal integral formula, and the dynamic differential relationship is converted into a Norton equivalent circuit in algebraic form. Compared with the traditional explicit Euler method or backward Euler method, the trapezoidal integral has a second-order accuracy characteristic and can effectively suppress numerical oscillation and truncation errors. For example, the fixed-step explicit integration in the existing method is prone to high-frequency distortion, while this method uses the history term (I L (t-Δt)) and equivalent conductance (G L ) symmetric design significantly improves the smoothness of transient current waveform and computational stability. In addition, the inductor is discretized into a Norton equivalent circuit (current source in parallel with conductance), and the time domain differential equation is converted into a linear algebraic equation, which solves the complexity of traditional dynamic component modeling that requires simultaneous differential-algebraic equations. For example, existing methods require iterative solutions to differential terms at each time step, while this method uses the historical current source I L (t-Δt) absorbs the cumulative effect of the previous moment, combined with the equivalent conductance G L Directly linking the current voltage difference simplifies the process of constructing the node admittance matrix, making it particularly suitable for rapid simulation of large-scale power grids. Furthermore, by precalculating the history terms and equivalent conductance of the Norton equivalent circuit, dynamic simulation is transformed into a linear algebra problem, significantly reducing the amount of iterative calculations. For example, existing electromagnetic transient simulations require real-time updates of differential terms and iterative convergence. However, this method, through recursive updates of history terms and the constant nature of conductance, only requires matrix iterations to solve for node voltages, significantly improving the efficiency of long-term simulations.

[0208] S5. Based on the accompanying circuit model of the metal return four-terminal bipolar DC grid established in S4, the conductance matrix G is constructed using the accompanying circuit method to form the node voltage equation. Figure 9 shown.

[0209] In specific implementation, the node voltage equation is:

[0210] GU(t)=I hist +i sc (t);

[0211] Where G is the equivalent conductance matrix of the circuit; U (t) is the node voltage vector; I hist is the historical current source vector; i sc(t) is the DC current source vector;

[0212] Among them, the equivalent conductivity matrix G is a symmetric matrix, expressed as:

[0213]

[0214] Where, The equivalent conductivity matrices are all symmetric matrices; The equivalent conductivity matrices are all zero matrices; Where n and m are the number of converter stations and joint nodes respectively;

[0215] The elements in the equivalent conductance matrix G are calculated as follows:

[0216]

[0217] Where, is the equivalent conductance matrix of the Berelon model transmission line; are the equivalent conductance matrices of the RL branch and C branch of the MMC respectively; G g is the conductivity matrix of the grounding resistance;

[0218] Historical current source vector I hist for:

[0219]

[0220] Where, are the historical current source vectors of the positive electrode layer, metal loop layer, and negative electrode layer respectively;

[0221] Historical current source vector I hist The calculation method of the elements is as follows:

[0222]

[0223] in:

[0224]

[0225] Where: is the historical current of the Berelon model DC grid ij; and are the historical currents of the equivalent RL branch and C branch of converter i respectively;

[0226] DC current source vector i sc(t) is:

[0227]

[0228] in:

[0229]

[0230] This setup constructs the equivalent conductivity matrix G by dividing the positive electrode, metal loop, and negative electrode into layers and blocks, decomposing the three-phase coupled system into independent sub-matrices (such as G pp , G mm ), significantly reducing the computational complexity of matrix filling and inversion. Compared with the traditional unified modeling of the global matrix (such as non-layered processing), this method reduces the number of non-zero elements through the matrix partitioning strategy of physical topology mapping, thereby improving the efficiency of solving large-scale power grids. In addition, the historical current source vector I hist By superimposing the Berelon traveling wave reflected current and the discretized accumulated current of the MMC branch, the contribution of the historical states of dynamic components such as inductors and capacitors to the current at the current moment is fully characterized. Traditional methods often ignore the temporal coupling between the discharge of the MMC submodule capacitors and the action of the current-limiting reactance. However, this method dynamically adjusts the weight of the historical current through the duty cycle D, significantly improving the calculation accuracy of the current decay characteristics in the middle and late stages of the fault. In addition, based on the dynamic correction mechanism of the node admittance matrix of the adjoint circuit method, by modifying the relationship between the fault node admittance and the topological connection, it can quickly adapt to complex fault scenarios such as inter-pole short circuits and single-pole grounding. Compared with traditional methods that require the reconstruction of the entire network model, this method only requires local modification of the G matrix elements, which reduces the computational time while ensuring accuracy, making it particularly suitable for real-time simulation testing of protection devices.

[0231] The short-circuit current calculation method based on the accompanying circuit is highly flexible and accurate. According to different fault types, the corresponding elements in the equivalent conductance matrix are modified and the influence of the transition resistance on the conductance matrix is ​​added, so that the short-circuit current can be calculated quickly and accurately.

[0232] S6. When a fault occurs in the metal return four-terminal bipolar DC grid, the node admittance matrix G in the node voltage equation is modified to the corresponding equivalent conductance matrix G' according to the fault type. The modified node voltage equation is solved to obtain the branch current and node voltage after the fault.

[0233] In specific implementation, S6 includes:

[0234] After a fault occurs in a metal return four-terminal bipolar DC grid, determine the fault type;

[0235] According to the fault type, the node admittance matrix in the node voltage equation is modified into the corresponding equivalent conductance matrix G';

[0236] Then, by calculating the historical current source Ihist And the DC current source i sc , obtain the current change characteristics of the system before and after the fault;

[0237] Finally, the voltage value of each node and the short-circuit current of the fault branch are obtained by recursively solving the modified node voltage equation.

[0238] In this way, through the dynamic correction of the fault-adaptive admittance matrix, the recursive update of the historical current source and the recursive solution of the node equations, the problems of poor generalization of fault scenarios, insufficient dynamic process representation and low computational efficiency of the traditional methods are solved. The accuracy (quantification of the shunt path) and real-time performance (efficient matrix solution) of the short-circuit current calculation of the metal return four-terminal bipolar DC power grid are significantly improved, providing reliable support for the rapid verification and optimization of the fault protection strategy.

[0239] In a specific implementation, the fault types include single-pole grounding fault P2G, pole-to-metal return fault P2M, pole-to-metal return short-circuit grounding fault P2M2G, and inter-pole short-circuit fault P2P;

[0240] The single-pole grounding fault P2G includes a positive pole grounding short-circuit fault; the equivalent conductance matrix G' of the positive pole grounding short-circuit fault is:

[0241]

[0242] Where R f represents the transition resistance;

[0243] The modification method of G' for other single-pole ground faults P2G is the same as that for positive-pole ground short-circuit faults;

[0244] The pole-to-metal return line fault P2M includes a positive pole-to-metal return line short circuit fault; the equivalent conductance matrix G' of the positive pole-to-metal return line short circuit fault is:

[0245]

[0246] The modification method of G' for other pole-to-metal return fault P2M is the same as that for positive pole-to-metal return short circuit fault;

[0247] The pole-to-metal return line short-circuit grounding fault P2M2G includes the positive pole-to-metal return line short-circuit grounding fault; the equivalent conductance matrix G' of the positive pole-to-metal return line short-circuit grounding fault is:

[0248]

[0249] Where: R gf is the transition resistance between the metal return line and the ground;

[0250] The modification method of G' of other pole-to-metal return short-circuit grounding fault P2M2G is the same as that of positive pole-to-metal return short-circuit grounding fault;

[0251] The inter-pole short circuit fault P2P includes a bipolar short circuit fault. The equivalent conductance matrix G' of the bipolar short circuit fault is:

[0252]

[0253] The modification method of G' for other inter-pole short circuit faults P2P is the same as that for bipolar short circuit faults.

[0254] In this way, through the design of admittance matrix correction rules for multiple types of faults, the problems of incomplete fault scenario coverage, over-simplification of transition resistance and metal loop coupling effects, and low calculation efficiency of traditional methods are solved. The accuracy (multi-path shunting quantification), efficiency (local correction strategy) and applicability (standardized correction framework) of the short-circuit current calculation of the four-terminal bipolar DC power grid with metal return are significantly improved, providing reliable technical support for the refined analysis of complex faults and optimization of protection strategies.

[0255] This method models the distributed parameters of the DC line through the Berelon lossy transmission line model (S2), overcoming the limitations of the traditional lumped parameter model that ignores wave impedance and traveling wave propagation delay, and can more realistically reflect the rapid rise process of current after the fault, transient oscillation characteristics and the shunting effect of the metal loop. By accurately simulating the wave process on the overhead line, it can fully describe the dynamic change trend and characteristics of the short-circuit current after the fault. Compared with existing methods, this method has significantly improved the ability to capture the details of the current waveform in the early stage of the fault (microsecond level). In addition, compared with the traditional lumped parameter model, this method significantly improves the calculation accuracy and solves the problem of large short-circuit current estimation error. In addition, based on the fixed timing of the source-side current limiting action (S1), an impedance parameter adjustment mechanism dynamically associated with the MMC equivalent model is established, which solves the problem of separate analysis of converter control and current limiting device action in traditional methods. For example, when the current-limiting reactance is put into operation in stages, this method accurately depicts the dynamic process of current attenuation in the middle and late stages of the fault (millisecond level) through a time-related impedance change model, while the traditional analytical algorithm ignores such dynamic coupling, resulting in error accumulation. In addition, this method adopts the equivalent partitioning strategy of the Berelon model (S2 single-phase / three-phase model hybrid application) and the full-network discretization (S4-S5) of the accompanying circuit method, while retaining the details of the wave process, it avoids the matrix dimension explosion problem caused by over-dense grids in traditional electromagnetic transient simulation. Compared with the existing accompanying circuit method's simplified treatment of bipolar system topology (such as ignoring three-phase line coupling), this method improves the model's ability to characterize the coupling effect between metal loops and pole lines under the same computing resources through a refined discretization strategy. Based on the discretization method of the accompanying circuit, the node voltage equation constructed by the present invention has a symmetrical, sparse and constant conductivity matrix structure, which greatly improves the computational efficiency of the solution process. This method can significantly reduce the occupancy of computing resources, adapt to the multi-scenario simulation requirements of complex systems, and is particularly suitable for the dynamic characteristics analysis of large-scale DC power grids. By optimizing matrix characteristics, this method not only improves computational efficiency but also enhances the stability and reliability of the model in large-scale system simulations.

[0256] In addition, this method can flexibly handle complex faults such as inter-pole short circuits and single-pole grounding in bipolar systems through independent modeling of the metal loop coupling path (S3) and fault type-adaptive admittance matrix correction (S6). Traditional methods often fail to consider the impact of the metal loop potential offset on the fault circuit, resulting in deviations in the multi-path current distribution calculation. However, this method accurately quantifies its role in fault diversion by constructing an equivalent channel for the metal loop. Based on a distributed parameter model, the present invention can accurately describe the wave process in the overhead line, including dynamic characteristics such as reflection and propagation, and describe in detail the spatiotemporal variation of the short-circuit current. Compared with the traditional lumped parameter model, this method effectively compensates for its insufficient description of dynamic processes in engineering applications, and significantly improves the applicability of short-circuit current calculations in DC transmission systems in actual engineering. In addition, based on the calculation method of the accompanying circuit, the present invention can adapt to the short-circuit current calculation requirements of various types of fault scenarios in the DC power grid by flexibly adjusting the conductance matrix G. Regardless of different fault locations or diverse system topologies, this method demonstrates high applicability and calculation accuracy, significantly improving the universality and practicality of short-circuit current calculation in DC grid fault analysis.

[0257] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit the technical solutions. Those skilled in the art should understand that modifications or equivalent replacements of the technical solutions of the present invention that do not depart from the purpose and scope of the technical solutions of the present invention should be included in the scope of the claims of the present invention.

Claims

1. A method for calculating short-circuit current in a metal return four-terminal bipolar DC grid, characterized in that: The following steps are involved: S1. Based on the fixed timing of the source-side current limiting action of the DC line of the metal return four-terminal bipolar DC grid, the system characteristics at different stages are analyzed and an MMC equivalent model is established; S2. Based on the MMC equivalent model of S1, an equivalent circuit of the Berelon lossy transmission line of the DC line is constructed as a simplified distributed parameter model, and the equivalent circuit is processed to obtain the Berelon two-port equivalent model of the single-phase transmission line and the Berelon equivalent model of the three-phase transmission line; S3. Based on the MMC equivalent model, the four converter stations of the metallic return four-terminal bipolar DC grid are modeled separately to obtain the MMC equivalent models of the four converter stations. Based on the MMC equivalent models of the four converter stations, the influence of the metallic return line on the short-circuit current is considered, and combined with the Berelon equivalent model of the three-phase transmission line obtained in S2, an equivalent model of the metallic return four-terminal bipolar DC grid is established. S4. Discretize the components in the equivalent model of the metallic return four-terminal bipolar DC grid obtained in S3, combine it with the Berelon two-port equivalent model of the single-phase transmission line obtained in S2, discretize all branches of the entire metallic return four-terminal bipolar DC grid, and establish an accompanying circuit model of the metallic return four-terminal bipolar DC grid; S5. Based on the adjoint circuit model of the metal return four-terminal bipolar DC grid established in S4, the conductance matrix G is constructed using the adjoint circuit method to form the node voltage equation; S6. When a fault occurs in the metal return four-terminal bipolar DC grid, the node admittance matrix G in the node voltage equation is modified to the corresponding equivalent conductance matrix G' according to the fault type. The modified node voltage equation is solved to obtain the branch current and node voltage after the fault.

2. The method for calculating short-circuit current of a metal return four-terminal bipolar DC power grid according to claim 1, wherein: S1 includes: For the DC line of a metal return four-terminal bipolar DC grid, when unlimited current is input, the MMC is equivalent to a series circuit of R, L, and C connected in parallel with a variable DC current source. The DC current source is used to represent the control effect of the MMC, thereby representing the impact of the AC-side feed-in current on the short-circuit current. Activate the source-side current limiting device according to the fixed current limiting action sequence, and analyze the activation sequence of the current limiting device and the action sequence of the DC circuit breaker (DCCB) after a fault occurs; Based on the action sequence of the current limiting device, the parameter duty cycle D is introduced to represent the proportion of the number of MMC sub-modules put into operation. It is used for source-side current limiting, and the state space average equivalent model of the MMC is obtained as the MMC equivalent model.

3. The method for calculating short-circuit current of a metal return four-terminal bipolar DC power grid according to claim 1, wherein: S2 includes: Based on the S1 MMC equivalent model and the role of the distributed parameter model of the DC line in electromagnetic transient simulation, an equivalent circuit of the Berelon lossy transmission line of the DC line is established for use as a simplified distributed parameter model for analysis; Based on the equivalent circuit of the Berelon lossy transmission line, the wave equation of the transmission line in the time domain is analyzed, and the analytical expression of the current at both ends of the transmission line is obtained, which is used as the Berelon two-port equivalent model of the single-phase transmission line of the DC line. Based on the Berelon two-port equivalent model of the single-phase transmission line, considering the coupling effect between the three-phase transmission lines of the metallic return bipolar DC power grid, the transmission line model of the three-phase Berelon model in the modal domain is derived. Then, the inverse transformation to the time domain is performed to obtain the three-phase current expression of the transmission line in the time domain, which is used as the Berelon equivalent model of the three-phase transmission line.

4. The method for calculating short-circuit current of a metal return four-terminal bipolar DC power grid according to claim 3, wherein: In S2, the Berelon two-port equivalent model of the single-phase transmission line is obtained by the following steps: According to the equivalent circuit of the Berelon lossy transmission line, the wave equation of the transmission line in the time domain is written as: Where s = a, b are ports a and b respectively, and a and b are the first and last nodes respectively; x is the position of the traveling wave in the transmission line; R0, L0, C0, and G0 are the resistance, inductance, capacitance, and conductance per unit length respectively; Solving the wave equation, we obtain the analytical expression for the current at both ends of the transmission line, which serves as the Berelon two-port equivalent model of a single-phase transmission line: Where, line wave impedance R=1 / 4R0d, d is the line length; i ha (t-τ), i hb (t-τ) are the equivalent injection current sources of nodes a and b, and the line propagation delay 5. The method for calculating short-circuit current of a metal return four-terminal bipolar DC power grid according to claim 4, characterized in that: In S2, the process of constructing the three-phase current expression of the transmission line in the time domain includes: Based on the Berelon two-port equivalent model of a single-phase transmission line, the current at the port on side a in the modal domain is expressed as: Where i = 0, 1, 2 are the parameters of zero sequence, positive sequence, and negative sequence respectively; j represents the imaginary unit, ω s represents the angular frequency; Indicates the port voltage on side a; Represents the equivalent injection current source of node a; Perform an inverse transformation on the current expression of the port on side a to obtain the three-phase current expression of the transmission line in the time domain: Where k = m, p, n are the port currents of the metal return line, positive electrode, and negative electrode transmission line respectively; Represents the port voltage on side a; R k =1 / 4R0d; Indicates the line wave impedance; T is the transformation matrix between the time domain and the modal domain, expressed as: Similarly, the expression of the current at the port on the b side is obtained: Where, Indicates the port voltage on the b side; Represents the equivalent injection current source of node b.

6. The method for calculating short-circuit current of a metal return four-terminal bipolar DC power grid according to claim 5, characterized in that: In S4, when discretizing the components, the transient process time of the linear dynamic circuit is discretized into several equal time intervals h, and the differential equations of the components are converted into difference equations; after all components are discretized, Kirchhoff's node current law is used to list the current equations of each node to obtain the difference equation of the power grid.

7. The method for calculating short-circuit current for a metal return four-terminal bipolar DC power grid according to claim 6, wherein: In S4, each component is discretized into a Norton equivalent circuit using the same method; The element includes an inductor element, and the discretization process of the inductor element includes: Differential equation based on inductance: Where, v i (t) and v j (t) are the voltages at the i and j terminals of the inductor L, i ij (t) is the current at port i; Reshape the differential equation for inductance: From the trapezoidal integral formula, we can get the corresponding Norton equivalent circuit: in: Where, I L (t-Δt) is the history term of the branch current, represented by a current source; G L is the equivalent conductance.

8. The method for calculating short-circuit current for a metal return four-terminal bipolar DC power grid according to claim 7, wherein: In S5 and S6, the node voltage equation is: TO(t)=I hist +i sc (t); Where G is the equivalent conductance matrix of the circuit; U (t) is the node voltage vector; I hist is the historical current source vector; i sc(t) is the DC current source vector; Among them, the equivalent conductivity matrix G is a symmetric matrix, expressed as: Where, The equivalent conductivity matrices are all symmetric matrices; The equivalent conductivity matrices are all zero matrices; Where n and m are the number of converter stations and joint nodes respectively; The elements in the equivalent conductance matrix G are calculated as follows: Where, is the equivalent conductance matrix of the Berelon model transmission line; are the equivalent conductance matrices of the RL branch and C branch of the MMC respectively; G g is the conductivity matrix of the grounding resistance; Historical current source vector I hist for: Where, are the historical current source vectors of the positive electrode layer, metal loop layer, and negative electrode layer respectively; Historical current source vector I hist The calculation method of the elements is as follows: in: Where: is the historical current of the Berelon model DC grid ij; and are the historical currents of the equivalent RL branch and C branch of converter i respectively; DC current source vector i sc (t) is: in:

9. The method for calculating short-circuit current for a metal return four-terminal bipolar DC power grid according to claim 8, characterized in that: S6 includes: After a fault occurs in a metal return four-terminal bipolar DC grid, determine the fault type; According to the fault type, the node admittance matrix in the node voltage equation is modified into the corresponding equivalent conductance matrix G'; Then, by calculating the historical current source I hist And the DC current source i sc , obtain the current change characteristics of the system before and after the fault; Finally, the voltage value of each node and the short-circuit current of the fault branch are obtained by recursively solving the modified node voltage equation.

10. The method for calculating short-circuit current of a metal return four-terminal bipolar DC power grid according to claim 9, characterized in that: In S6, the fault types include single-pole grounding fault P2G, pole-to-pole metal return fault P2M, pole-to-pole metal return short-circuit grounding fault P2M2G, and inter-pole short-circuit fault P2P; The single-pole grounding fault P2G includes a positive pole grounding short-circuit fault; the equivalent conductance matrix G' of the positive pole grounding short-circuit fault is: Where R f represents the transition resistance; The modification method of G' for other single-pole ground faults P2G is the same as that for positive-pole ground short-circuit faults; The pole-to-metal return line fault P2M includes a positive pole-to-metal return line short circuit fault; the equivalent conductance matrix G' of the positive pole-to-metal return line short circuit fault is: The modification method of G' for other pole-to-metal return fault P2M is the same as that for positive pole-to-metal return short circuit fault; The pole-to-metal return line short-circuit grounding fault P2M2G includes the positive pole-to-metal return line short-circuit grounding fault; the equivalent conductance matrix G' of the positive pole-to-metal return line short-circuit grounding fault is: Where: R gf is the transition resistance between the metal return line and the ground; The modification method of G' of other pole-to-metal return short-circuit grounding fault P2M2G is the same as that of positive pole-to-metal return short-circuit grounding fault; The inter-pole short circuit fault P2P includes a bipolar short circuit fault. The equivalent conductance matrix G' of the bipolar short circuit fault is: The modification method of G' for other inter-pole short circuit faults P2P is the same as that for bipolar short circuit faults.

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