A dynamic phasor representation method for stochastic transient analysis of DC power systems

Abstract

The embodiment of the application discloses a dynamic phasor representation DC power system random transient analysis method, relates to the power electronic field of the DC power system, and can reflect system characteristics caused by source-load random excitation conditions and multi-rate simulation, and balance the contradiction between precision and efficiency. The application comprises the following steps: obtaining DC power system parameters and setting initial parameters; obtaining circuit models of two types of lumped elements in the DC power system; establishing a dynamic phasor model of a converter station in the DC power system and obtaining a dynamic companion circuit of the converter station; using the circuit models of the two types of lumped elements and the dynamic companion circuit of the converter station, establishing a model of the DC power system; obtaining node voltage equations of the DC power system; updating a node admittance matrix and an injected current vector according to changes in a switching function of the converter station; and converting dynamic phasors output by the model of the DC power system into instantaneous values.

Description

Technical Field

[0001] This invention relates to the field of power electronic systems technology for DC power systems, and more particularly to a method for stochastic transient analysis of DC power systems with dynamic phasor characterization. Background Technology

[0002] With the development of power semiconductor technology, the economic advantages of DC power systems are gradually becoming apparent. As an important carrier for renewable energy integration and consumption, efficient access of electric vehicles to AC distribution networks, capacity expansion and upgrading, and integrated energy systems, it has become one of the future development directions of the energy internet. Due to the high degree of power electronics at both the source and load ends of DC power systems, with the increase in capacity and power levels, the increase in the number of converter stations, and the increase in network complexity, digital simulation of power systems faces more challenges from the characteristics of the system itself.

[0003] Currently, electromagnetic transient simulation analysis based on detailed dynamic characteristic modeling of components is used to characterize the microsecond-level dynamic processes of DC power systems. The advantage of this approach is that it is not limited by system size or structure. However, as the power electronic converter stations and control and protection strategies of DC power systems become increasingly complex, the increased system size and switching frequency exacerbate the contradiction between accuracy and efficiency in electromagnetic transient simulation analysis. For example, the simulation step size is typically set to 1 / 10 or even smaller of the switching cycle, making it difficult to accurately reflect the impact of random excitations on system operation. Consequently, existing electromagnetic transient simulation analysis methods are struggling to cope with increasingly complex control and protection strategies. Summary of the Invention

[0004] The embodiments of the present invention provide a method for stochastic transient analysis of DC power systems with dynamic phasor characterization, which can accurately reflect the influence characteristics of stochastic excitation on system operation and balance the contradiction between accuracy and efficiency in dynamic analysis.

[0005] To achieve the above objectives, the embodiments of the present invention adopt the following technical solutions:

[0006] S1. Obtain DC power system parameters and set initial parameters, wherein the DC power system parameters are used to represent the structure of the DC power system;

[0007] S2. Obtain the circuit models of the two types of lumped elements in the DC power system, wherein the two types of lumped elements in the DC power system include: parameter migration lumped elements and deterministic lumped elements, and the circuit models of the two types of lumped elements include: the dynamic accompanying circuit of the parameter migration lumped elements and the accompanying circuit of the deterministic lumped elements.

[0008] S3. Establish the dynamic phasor model of the converter station in the DC power system and obtain the dynamic accompanying circuit of the converter station.

[0009] S4. Using the circuit models of the two types of lumped elements obtained in S2, and the dynamic accompanying circuit of the converter station obtained in S2, establish the model of the DC power system. The model of the DC power system includes: the dynamic accompanying circuit of the DC power system, the node admittance matrix, and the injected current vector.

[0010] S5. Obtain the node voltage equations of the DC power system, wherein the node voltage model is GU=I, U represents the node voltage phasor, G represents the temporary admittance matrix at time t, and I represents the temporary injected current vector at time t.

[0011] S6. Update the node admittance matrix and injected current vector according to the changes in the switching function of the converter station;

[0012] S7. Convert the dynamic phasors output by the model of the DC power system into instantaneous values, which are used as the results of the stochastic dynamic analysis of the DC power system.

[0013] The scheme in this embodiment can be applied to DC power systems under stochastic excitation with power electronics, simulating multiple types of source-load stochastic excitations in stochastic systems and improving the simulation capability of digital dynamic simulation. Using dynamic phasor modeling allows for analysis of specific harmonics, and employing large-step simulation balances the trade-off between accuracy and efficiency in dynamic simulation. Furthermore, the stochastic transient analysis method for DC power systems represented by dynamic phasors reduces parameter updates and computational load. Attached Figure Description

[0014] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0015] Figure 1 A schematic diagram of the method flow provided in an embodiment of the present invention;

[0016] Figure 2 A schematic diagram of the accompanying circuit in the form of a deterministic element dynamic phasor and the dynamic accompanying circuit in the form of a parameter migration element dynamic phasor, provided for embodiments of the present invention;

[0017] Figure 3 The VSC circuit, the switching function model of the VSC circuit, and the accompanying circuit provided in the embodiments of the present invention;

[0018] Figure 4 The node voltage equations for the VSC circuit provided in this embodiment of the invention;

[0019] Figure 5 The switching function model and dynamic accompanying circuit of the VSC subsystem provided in the embodiments of the present invention;

[0020] Figure 6 The node voltage equations for the VSC subsystem provided in this embodiment of the invention;

[0021] Figure 7 A schematic diagram of the main logic flow of the hybrid simulation algorithm for a specific example provided in the embodiments of the present invention. Detailed Implementation

[0022] To enable those skilled in the art to better understand the technical solutions of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. Embodiments of the present invention will be described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention. Those skilled in the art will understand that, unless specifically stated otherwise, the singular forms “a,” “an,” “the,” and “the” used herein may also include the plural forms. It should be further understood that the term “comprising” as used in the specification of the present invention means the presence of the stated features, integers, steps, operations, elements, and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof. It should be understood that when we say an element is “connected” or “coupled” to another element, it can be directly connected or coupled to the other element, or there may be intermediate elements. Furthermore, “connected” or “coupled” as used herein can include wireless connections or couplings. The term "and / or" as used herein includes any and all combinations of one or more of the associated listed items. It will be understood by those skilled in the art that, unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. It should also be understood that terms such as those defined in general dictionaries should be understood to have the meaning consistent with their meaning in the context of the prior art, and should not be interpreted in an idealized or overly formal sense unless defined as herein.

[0023] The main problem with existing solutions is their inability to simulate the external random excitations and internal parameter random migrations of the system. Therefore, proposing a dynamic simulation method that accurately reflects the impact of random excitations on system operation while balancing the accuracy and efficiency of digital simulation has become a research objective. The design concept of this embodiment is as follows: Dynamic phasor modeling is used for the DC power system to construct a dynamic phasor-form dynamic accompanying circuit, solving the node voltage equations at any given time to simulate the dynamic process of the system. The parameter migration element uses stochastic differential equations (SDEs) to describe its dynamic changes, establishing a dynamic phasor-form dynamic accompanying circuit model at any given time, including equivalent admittance, random current sources, and historical current sources. Deterministic elements directly establish a dynamic phasor-form dynamic accompanying circuit, including equivalent admittance and historical current sources. The voltage-type converter station in the DC power system is a nonlinear system requiring modular modeling. First, it is modeled using the switching function method. Then, the switching function model of the converter station is modeled using dynamic phasors to establish its dynamic phasor model, and finally, its dynamic phasor-form dynamic accompanying circuit is established. By utilizing parameter migration components, deterministic components, and the dynamic phasor form of the converter station's dynamic accompanying circuit, the nodal admittance matrix, injected current phasor, and nodal voltage normal equations at any given time of the overall system's dynamic phasor form dynamic accompanying circuit are constructed, enabling the analysis of stochastic dynamic simulation. This algorithm achieves stochastic dynamic simulation of DC power systems, simulating multiple types of source-load stochastic excitations, and balancing the trade-off between dynamic simulation accuracy and efficiency. Further design and experimentation have yielded the following specific implementation method, which can be applied by those skilled in the art.

[0024] Specifically, embodiments of the present invention provide a method for stochastic transient analysis of DC power systems using dynamic phasor characterization, such as... Figure 1 As shown, it includes:

[0025] S1. Obtain DC power system parameters and set initial parameters.

[0026] The DC power system parameters are used to represent the structure of the DC power system. These parameters include: circuit node parameters, circuit element parameters (parameter migration and determinism), and converter station parameters. Initial parameters include: time t, step size Δt, total duration T, initial value of the injected current vector, and dynamic phasor order k. The initial time t = 0; k ∈ N. When k = 0, it indicates analysis of the DC components of the system; other values ​​indicate analysis of the k-th harmonic of the system.

[0027] S2. Obtain the circuit models of the two types of lumped elements in the DC power system.

[0028] The DC power system includes two types of lumped elements: parameter migration lumped elements and deterministic lumped elements. The circuit models for these two types of lumped elements include: dynamic accompanying circuits for parameter migration lumped elements and accompanying circuits for deterministic lumped elements. The parameters of deterministic elements are fixed, corresponding to their accompanying circuits, which consist of admittance (a deterministic value) and historical current sources. The parameters of parameter migration elements are variable, corresponding to dynamic accompanying circuits, which consist of admittance (random), historical current sources, and random current sources.

[0029] S3. Establish the dynamic phasor model of the converter station in the DC power system and obtain the dynamic accompanying circuit of the converter station.

[0030] Specifically, the DC power system adopts a voltage source converter station.

[0031] S4. Using the circuit models of the two types of lumped elements obtained in S2, and the dynamic accompanying circuit of the converter station obtained in S2, establish the model of the DC power system.

[0032] The model of the DC power system includes: the dynamic accompanying circuit, the node admittance matrix, and the injected current vector. Using the obtained accompanying circuits in dynamic phasor form for converter stations, deterministic components, and parameter migration components, the dynamic accompanying circuit in dynamic phasor form for the DC power system is constructed. The initial node admittance matrix and injected current vector are written. The current time t = t0 + Δt is updated.

[0033] S5. Obtain the node voltage equations of the DC power system.

[0034] The node voltage model is GU = I, where U represents the node voltage phasor, G represents the temporary admittance matrix at time t, and I represents the temporary injected current vector at time t, corresponding to the injected current at each node. The node voltage and branch current at time t are solved, and the values ​​of the node admittance matrix and injected current vector that need to be output and updated are stored. However, since dynamic phasor modeling is used, and the dynamic phasor is a complex number, the node voltage equation cannot be directly calculated, where G = G... R +jG I U = U R +jU I , I = I R +jI I The node voltage equations need to be decomposed into real and imaginary parts, i.e., G R U R -G I U I =I R and G R U I+G I U R =I I The dynamic phasor forms of the node voltages and branch currents at time t can be obtained through calculation, where j represents the complex unit, and G... R G represents the real part of the nodal admittance matrix. I U represents the imaginary part of the nodal admittance matrix. R U represents the real part of the node voltage matrix. I I represents the imaginary part of the node voltage matrix. R I represents the real part of the node voltage matrix. I This represents the imaginary part of the node voltage matrix.

[0035] S6. Update the node admittance matrix and injected current vector according to the changes in the switching function of the converter station;

[0036] S7. Convert the dynamic phasors output by the model of the DC power system into instantaneous values, which are used as the results of the stochastic dynamic analysis of the DC power system.

[0037] After S6 is executed, the result is data in the form of dynamic phasor values. Therefore, it is necessary to convert the obtained dynamic phasor values ​​into instantaneous values.

[0038] The scheme in this embodiment can be applied to DC power systems under stochastic excitation with power electronics, simulating multiple types of source-load stochastic excitations in stochastic systems and improving the simulation capability of digital dynamic simulation. Using dynamic phasor modeling allows for analysis of specific harmonics, and employing large-step simulation balances the trade-off between dynamic simulation accuracy and efficiency. Simultaneously, the stochastic transient analysis method for DC power systems represented by dynamic phasors reduces parameter updates and computational load. This achieves efficient simulation of DC power systems under stochastic excitation, analyzing the system dynamics caused by external excitations and internal parameter migrations, and enabling analysis of specific harmonics while balancing the trade-off between dynamic simulation accuracy and efficiency.

[0039] In this embodiment, step S2 includes: determining the parameter migration elements and deterministic elements in the DC power system. Elements with fixed parameters are considered deterministic elements, while those with time-varying parameters are considered parameter migration elements. Deterministic elements are modeled using implicit trapezoidal geometry, while parameter migration elements are modeled using Milstein geometry. Using the modeling results of the deterministic and parameter migration elements, the dynamic phasor form of the dynamic accompanying circuit for the parameter migration lumped element and the dynamic phasor form of the dynamic accompanying circuit for the deterministic lumped element are obtained. The types of lumped elements include resistors, capacitors, and inductors.

[0040] Specifically, the dynamic accompaniment circuit in the dynamic phasor form of deterministic lumped elements is as follows: G LR This represents the equivalent admittance of the RL branch. This represents the k-th order dynamic phasor of the inductor voltage at time n, where n represents time t and k represents the order of the dynamic phasor. It is the historical current source of the RL branch.

[0041] G L This represents the equivalent admittance of the inductor. The k-th order dynamic phasor represents the inductor voltage at time n-1, j represents the unit of the complex number, L represents the deterministic inductance, R represents the deterministic resistance, Δt represents the time step, and ω represents the time step. s It represents angular frequency.

[0042] Furthermore, the dynamic accompaniment circuit in the dynamic phasor form of the parameter migration lumped element is as follows: and These are the voltage across the inductor and the voltage across the capacitor, respectively. and These are the equivalent admittances of the random migration inductor and capacitor, respectively. and These are the historical current sources of randomly migrated inductors and capacitors, respectively. and It is a random current source that randomly migrates inductors and capacitors, where n represents time t. Indicates inductor current. This represents the capacitor current.

[0043]

[0044]

[0045] Where n represents time t, L n Let the parameter transfer inductance be at time t. Let α and β represent the migration inductance estimate at time t, where α and β represent the migration and diffusion processes of the stochastic differential equation (SDE), respectively, Δt represents the time step, j represents the unit of the complex number, k represents the dynamic phasor order, and ω represents the time step. s Represents angular frequency. This represents the inductor current at time t-Δt, where n-1 represents t-Δt, and ΔW n-1 ΔD represents the increment at time n-1 in the standard Wiener process. n-1 It is an intermediate quantity For the parameter migration inductance prediction at time t, C n Let the parameter transfer inductance be at time t. This represents the capacitor voltage at time t-Δt.

[0046] For example, constructing dynamic phasor-shaped equivalent circuits for deterministic elements and parameter migration elements, such as... Figure 2 a) and Figure 2 As shown in c), the dynamic phasor form of deterministic element dynamic phasor circuit and the dynamic phasor form of parameter migration element dynamic phasor circuit are established as follows: Figure 2 b) and Figure 2 As shown in d), the difference between parameter migration elements and deterministic elements is whether the parameters of lumped elements (resistors, capacitors, and inductors) are time-varying. If the parameters are fixed, they are deterministic elements; otherwise, they are parameter migration elements.

[0047] For deterministic resistors, the dynamic phasor equations for the resistors at nodes i and j can be expressed as:

[0048]

[0049] In the formula: The k-th order dynamic phasor represents the current through the resistor at time t; R represents the deterministic resistance; V i k (t) and G represents the k-th order dynamic phasor of the voltages at node i and node j at time t; R The equivalent admittance represents the deterministic resistance.

[0050] Since deterministic resistors do not contain differential terms, they can be directly discretized as follows:

[0051]

[0052] In the formula: n is the discrete index of the corresponding time t. G R It represents the equivalent admittance of the deterministic resistance at time t.

[0053] For a deterministic inductor, the dynamic phasor equations for the inductors at nodes i and j can be expressed as:

[0054]

[0055] In the formula: ω represents the k-th order dynamic phasor of the inductor current at time t; j is the unit of the complex number; L represents the deterministic inductance. s = 2π / T, where T is the fundamental period.

[0056] Discretization using the trapezoidal method yields:

[0057]

[0058] In the formula: n and n-1 correspond to the discrete subscripts at time t and t-Δt, respectively; and These represent the k-th order dynamic phasors of the inductor current at time n and time n-1, respectively. and The k-th order dynamic phasor represents the voltages at node i and node j at time n; and The k-th order dynamic phasor represents the voltages at node i and node j at time n-1.

[0059] For a deterministic capacitor, the dynamic phasor equation of the capacitor can be expressed as:

[0060]

[0061] In the formula: The k-th order dynamic phasor represents the current in the capacitor at time t; The k-th order dynamic phasor represents the voltage of the capacitor at time t; C represents the deterministic capacitance.

[0062] Discretization using the trapezoidal method yields:

[0063]

[0064] In the formula: and These represent the k-th order dynamic phasors of the inductor current at time n and time n-1, respectively. and These represent the k-th order dynamic phasors of the inductor voltage at time n and time n-1, respectively.

[0065] In order to construct the node voltage equations, the deterministic inductance and capacitance need to be transformed into dynamic phasor forms of dynamic accompanying circuits. Rewriting equations (4) and (6) yields:

[0066]

[0067]

[0068]

[0069] In the formula: and These represent the equivalent admittances of the inductor and capacitor, respectively; u L and u C These represent the voltage across the inductor and capacitor, respectively. and These represent the historical current sources for inductors and capacitors, respectively.

[0070] Meanwhile, to reduce the amount of simulation computation, lumped elements can be combined for modeling. Taking an RL branch as an example, we can obtain:

[0071]

[0072] In the formula: The k-th order dynamic phasor represents the current in the RL branch at time t.

[0073] To construct a dynamic phasor form of a dynamic adjoint circuit, equation (10) can be discretized and rearranged using the trapezoidal rule to obtain:

[0074]

[0075] In the formula: The equivalent admittance of the RL branch; The k-th order dynamic phasor represents the inductor voltage at time n (time t); It is the historical current source of the RL branch.

[0076]

[0077] In this embodiment, a dynamic accompanying circuit in the form of a dynamic phasor for parameter migration elements is established as follows: Figure 2 As shown in c), it includes:

[0078] The parameter migration process of a parameter migration element can be described by stochastic differential equations.

[0079]

[0080] In the formula: R(t), L(t), and C(t) represent the random migration resistance, capacitance, and inductance, respectively. α and β represent the migration and diffusion processes of the stochastic differential equation (SDE), respectively. α(R,t), α(L,t), and α(C,t) represent the migration of resistance, inductance, and capacitance parameters, respectively. β(R,t), β(L,t), and β(C,t) represent the diffusion processes of resistance, inductance, and capacitance parameters, respectively. W R (t), W L (t) and W C (t) is an independent standard Wiener process.

[0081] For the parameter migration resistance, considering only the slow process of parameter migration resistance, the dynamic phasor equations for nodes i and j can be expressed as:

[0082]

[0083] In the formula: The k-th order dynamic phasor of the current at time t represents the parameter migration resistance; G R (t) represents the admittance of the parameter migration resistance at time t.

[0084] Discretizing the nodal dynamic phasor equations of the parameter migration resistance yields:

[0085]

[0086] In the formula: R n and G R,n R represents the parameter migration resistance and equivalent admittance at time t, respectively. n It needs to be updated synchronously with the simulation time, and can be obtained by discretization according to the backward Milstein scheme.

[0087]

[0088] In the formula: R n-1 This represents the parameter migration resistance value at time t-Δt; W n =W(t) n N(0,1) represents the standard normal distribution; The estimated value of the migration resistance of the parameter at time t.

[0089] For parameter migration inductance, only the slow process of parameter migration inductance is considered (i.e., only the 0th order dynamic phasor is considered). Since changes in inductance flux lead to changes in voltage, according to Faraday's law of electromagnetic induction and the dynamic phasor property, the differential property of the dynamic phasor is: <·> k The operator representing the extraction of k-th order dynamic phasors has the following convolution properties: x and y represent variables, and K represents the selection of a dynamic phasor set.

[0090]

[0091] In the formula: ψ L L(t) represents the flux linkage at time t; L(t) represents the parameter migration inductance.

[0092] Substituting the stochastic process of the parameter-transferring inductor into equation (17), we can obtain that the dynamic current of the parameter-transferring inductor can be expressed as:

[0093]

[0094] Discretized using the backward Milstein scheme, we can obtain:

[0095]

[0096] In the formula: Predicted value of parameter migration inductance at time t

[0097] For parameter migration capacitors, only the slow process of parameter migration inductors is considered (i.e., only the 0th-order dynamic phasor is considered). C (t)> k ≈C(t) C (t)>​​k Since changes in capacitance charge lead to changes in current, we can derive the following from the charge equation and dynamic phasor properties:

[0098]

[0099] In the formula: Q C (t) represents the charge at time t.

[0100] Substituting the stochastic process of the parameter migration capacitor into equation (20), we can obtain the dynamic voltage of the parameter migration capacitor as follows:

[0101]

[0102] Discretized using the backward Milstein scheme, we can obtain:

[0103]

[0104] In the formula: Predicted value of parameter migration inductance at time t

[0105] In order to construct the node voltage equations, the parameter migration inductance and capacitance need to be transformed into a dynamic phasor form of a dynamic accompanying circuit. Rewriting equations (19) and (22) yields:

[0106]

[0107] In the formula: and These are the voltages of the inductor and capacitor, respectively. and These are the equivalent admittances of the random migration inductor and capacitor, respectively. and These are the historical current sources of randomly migrated inductors and capacitors, respectively. and It is a random current source that randomly migrates inductors and capacitors.

[0108]

[0109]

[0110] Meanwhile, to reduce the computational load of simulation, lumped elements can be combined for modeling. Taking the RL branch as an example, based on Faraday's law of electromagnetic induction and the properties of dynamic phasors, we can obtain:

[0111]

[0112] Discretized using the backward Milstein scheme and rearranged, we obtain:

[0113]

[0114] In the formula: It is a random current source for the RL branch.

[0115]

[0116] In this embodiment, step S3 includes: establishing a switching function model of the converter station and converting the switching function model into a dynamic phasor model of the converter station. The voltage source converter station is modeled using a switching function (representing the switching state), which is an instantaneous value model. The switching function model is transformed into a dynamic phasor model through the definition and properties of dynamic phasors. The complexity of the dynamic phasor model is determined by the dynamic phasor order k; the larger the value of k, the higher the simulation accuracy. For the parameter migration elements and deterministic elements in the dynamic phasor model of the converter station, implicit trapezoidal method and Milstein scheme are used for differential modeling, respectively, to obtain the dynamic phasor form of the dynamic accompanying circuit of the converter station. The converter station's dynamic phasor model contains parameter migration elements and deterministic elements. Implicit trapezoidal method differential modeling is used for deterministic elements, and Milstein scheme differential modeling is used for parameter migration elements to establish the dynamic phasor form of the dynamic accompanying circuit of the converter station. For example, step S3 above includes: establishing the dynamic phasor form of the accompanying circuit of a voltage source converter station in a DC power system, such as... Figure 3 As shown in c), the voltage-source converter station in a DC power system has a switching model, making it a nonlinear system. Therefore, it is not convenient to solve the converter station circuit using the nodal voltage method. The AC-side inductance, switches, and DC-side capacitors are considered as a whole, and a three-input and two-output port equivalent model is established. The AC and DC sides are coupled into a subsystem through controlled sources. To establish the accompanying circuit in the dynamic phasor form of the voltage-source converter station in the DC power system, the switching function method is first used for modeling, resulting in:

[0117]

[0118] In the formula: u dc and i dc These represent the DC-side voltage and current of VSC, respectively; R p and L p These represent the equivalent resistance and inductance of the bridge arms, respectively; v N The voltage at node N represents the voltage; p∈{a,b,c} represents the three phases; where s a s b and s c S represents the switching function of each phase arm. a =(2s a -s b -s c ) / 3, S b =(2sb -s a -s c ) / 3, S c =(2s c -s a -s b ) / 3.

[0119] Then, by using dynamic phasor modeling, we can obtain:

[0120]

[0121] In the formula: These represent the dynamic phasor forms of the AC currents on the three phases a, b, and c, respectively. The dynamic phasor form representing the voltage across the DC-side capacitor; S represents the DC-side capacitor output current; a =(2s a -s b -s c ) / 3, S b =(2s b -s a -s c ) / 3, S c =(2s c -s a -s b ) / 3.

[0122] The accompanying circuit in dynamic phasor form is established using a switching function model in dynamic phasor form. The current-voltage characteristics across the AC-side inductor and the injection amount of the DC-side capacitor are given by:

[0123]

[0124]

[0125] From equations (27) and (28), it can be seen that the AC side and DC side are coupled to each other in the converter station model, and the node voltage at one end of the inductor is D. p u dc The injected current into the DC-side capacitor is composed of the combined currents of the three phases on the AC side. By establishing the accompanying circuit, its node voltage equations can be obtained. like Figure 4 As shown.

[0126] In this embodiment, step S4 above requires constructing the dynamic phasor form of the dynamic accompanying circuit, the node admittance matrix, and the injected current vector of the DC power system, including:

[0127] The dynamic accompanying circuit of the system is constructed using parameter migration elements, deterministic elements, and the dynamic phasor form of the converter station's dynamic accompanying circuit. The nodal admittance matrix and injected current vector are then described. Taking the VSC subsystem as an example, the AC side is connected to a grid with a stochastic process, such as... Figure 5 As shown in a), and It is the k-th order dynamic phasor of the three-phase power supply and the three-phase node voltage. It is the equivalent admittance of the parameter migration inductor-resistor branch. However, due to... Figure 4 It can be seen that the nodal admittance matrix of VSC is... It is a nonlinear equation that cannot be solved directly. In order to perform iterative solutions in simulation, the nodal voltage equation needs to be modified. It can be broken down into DC-side voltage and augmented admittance:

[0128]

[0129] In the formula: yes and Increased admittance.

[0130] Similarly, using basic circuit principles, the three-phase current is represented by the node voltage at time n and other known parameters. It can be rewritten as:

[0131]

[0132] In the formula: u Rp It is the equivalent resistance R p The pressure drop; yes and Increased admittance; yes and Increased admittance.

[0133] Using equations (29) and (30), the node voltage equations of the VSC subsystem are constructed as follows: Figure 6 As shown.

[0134] In this embodiment, step S5 includes: calculating and storing node voltages and branch currents, including:

[0135] Construct the node voltage equation GU = I. Here, U represents the node voltage phasor, G represents the temporary admittance matrix at time t-Δt, and I represents the temporary injected current vector at time t-Δt. Solve for the node voltage and branch current at time t, and store the values ​​of the node admittance matrix and injected current vector that need to be output and updated.

[0136] Meanwhile, since dynamic phasor modeling is used, and the dynamic phasor is a complex number, the nodal voltage equations cannot be directly calculated, where G = G R +jG I U = U R +jU I , I = I R +jI I The node voltage equation needs to be decomposed into real and imaginary parts as follows: G R U R -G I U I =I R and G R U I +G I U R =I I The dynamic phasor forms of the node voltages and branch currents at time t can be obtained through calculation, where j represents the complex unit, and G... R G represents the real part of the nodal admittance matrix. I U represents the imaginary part of the nodal admittance matrix. R U represents the real part of the node voltage matrix. I I represents the imaginary part of the node voltage matrix. R I represents the real part of the node voltage matrix. I This represents the imaginary part of the node voltage matrix.

[0137] In this embodiment, step S6 includes:

[0138] If the switching function of the converter station changes, the node admittance matrix is ​​corrected. Then, the node voltages and branch currents (which can be temporarily stored in the running program's computer or database) are retrieved, and the historical current sources of the converter station's dynamic phasor-form dynamic accompanying circuit at time t are updated. The final obtained branch current is the current flowing through the component, determined by the admittance, node voltages, random current sources, and historical current sources. The system detects whether the switching function of the converter station has changed. If the switching function has not changed, there is no need to correct the node admittance matrix; instead, the stored node voltages and branch currents are retrieved, and the historical current sources of the converter station's dynamic phasor-form dynamic accompanying circuit at time t are updated. If the switching function has changed, the node admittance matrix needs to be corrected, and the stored node voltages and branch currents are retrieved, and the historical current sources of the converter station's dynamic phasor-form dynamic accompanying circuit at time t are updated.

[0139] After retrieving the stored node voltages and branch currents in the system, the following steps are performed: For parameter migration elements, update the admittance, random current source, and historical current source of the dynamic phasor form of the dynamic accompanying circuit of the parameter migration element, and correct the node admittance matrix; for deterministic elements, update the current source of the dynamic accompanying circuit of the deterministic element in dynamic phasor form. Using the updated admittance, random current source, and historical current source, generate the row and column parameters corresponding to the node admittance matrix that needs to be updated, including the temporary admittance matrix G and the temporary injected current vector I at time t, where t = t0 + Δt, and t0 is the initial time.

[0140] In practical applications, this embodiment can be further refined and implemented through computer programs, such as... Figure 7 As shown, the specific execution process of the program can be illustrated in steps 1-14, which includes:

[0141] Step 1: Input the DC power system parameters and set the initial parameters. The input DC power system parameters shown include: circuit node parameters, circuit element parameters (parameter migration and determinism), and converter station parameters; the initial parameters shown include: time t, step size Δt, total duration T, initial value of injected current vector, and dynamic phasor order k.

[0142] Step 2: Differential Modeling of Parameter Migration Elements and Deterministic Elements. Establish dynamic phasor models for parameter migration elements and deterministic elements, and after differential modeling, construct the adjoint circuit of the parameter migration lumped element and the dynamic adjoint circuit in dynamic phasor form of the deterministic lumped element.

[0143] Step 3: Differential Modeling of Converter Station Modules. A dynamic phasor model of the voltage-type converter station in the DC power system is established, and after differential modeling, it forms the accompanying circuit in the dynamic phasor form of the converter station.

[0144] Step 4: Simulate the time interval update t = t0 + Δt.

[0145] Step 5: Generate the node admittance matrix G and the injected current vector I.

[0146] Step 6: Calculate and store the node voltage and branch current at time t.

[0147] Step 7: Determine if the simulation has ended. If it has ended, proceed to step 14; otherwise, proceed to step 8.

[0148] Step 8: Use the node voltages and branch currents calculated in Step 6 to update the random current sources and historical current sources of the parameter migration elements.

[0149] Step 9: Use the node voltages and branch currents calculated in Step 6 to update the parameter migration element admittance and correct the node admittance matrix.

[0150] Step 10: Update the historical current sources of deterministic elements using the node voltages and branch currents calculated in Step 6.

[0151] Step 11: Determine if the control has changed, i.e., whether the switching function has changed. If it has changed, proceed to step 12; otherwise, proceed to step 4.

[0152] Step 12: Update the switching function and correct the nodal admittance matrix.

[0153] Step 13: Update the random current source and historical current source of the converter station module.

[0154] Step 14: Retrieve the dynamic phasor to be output, convert it into an instantaneous value output, and the simulation ends.

[0155] The scheme designed in this embodiment can be applied to DC power systems under stochastic excitation with power electronics. It establishes dynamic phasor-form dynamic accompanying circuits for parameter migration elements, deterministic elements, and voltage-type converter stations, constructs nodal voltage equations, and simulates multiple types of source-load stochastic excitations in stochastic systems, thus improving the simulation capability of digital dynamic simulation. The use of dynamic phasor modeling allows for analysis of specific harmonics, and the large step size simulation balances the trade-off between accuracy and efficiency in dynamic simulation. Furthermore, the stochastic transient analysis method for DC power systems represented by dynamic phasors reduces parameter updates and the amount of simulation computation.

[0156] The various embodiments in this specification are described in a progressive manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on its differences from other embodiments. In particular, the device embodiments are basically similar to the method embodiments, so the description is relatively simple; relevant parts can be referred to the descriptions in the method embodiments. The above descriptions are merely specific embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for stochastic transient analysis of DC power systems using dynamic phasor characterization, characterized in that, include: S1. Obtain DC power system parameters and set initial parameters, wherein the DC power system parameters are used to represent the structure of the DC power system; S2. Obtain the circuit models of the two types of lumped elements in the DC power system, wherein the two types of lumped elements in the DC power system include: parameter migration lumped elements and deterministic lumped elements, and the circuit models of the two types of lumped elements include: the dynamic accompanying circuit of the parameter migration lumped elements and the accompanying circuit of the deterministic lumped elements. S3. Establish the dynamic phasor model of the converter station in the DC power system and obtain the dynamic accompanying circuit of the converter station. S4. Using the circuit models of the two types of lumped elements obtained in S2, and the dynamic accompanying circuit of the converter station obtained in S2, establish the model of the DC power system. The model of the DC power system includes: the dynamic accompanying circuit of the DC power system, the node admittance matrix, and the injected current vector. S5. Obtain the node voltage equations of the DC power system, wherein the node voltage model is GU=I, U represents the node voltage phasor, G represents the temporary admittance matrix at time t, and I represents the temporary injected current vector at time t. S6. Update the node admittance matrix and injected current vector according to the changes in the switching function of the converter station; S7. Convert the dynamic phasors output by the model of the DC power system into instantaneous values, and use them as the results of the stochastic dynamic analysis of the DC power system. Step S2 includes: The parameter migration element and deterministic element in the DC power system are determined. If the parameter of the element is fixed, it is a deterministic element. If the parameter of the element is time-varying, it is a parameter migration element. For deterministic components, the implicit trapezoidal method is used for differential modeling, and for parameter-transfer components, the Milstein scheme is used for differential modeling. Using the modeling results of deterministic elements and parameter migration elements respectively, we obtain the dynamic phasor form of the dynamic accompanying circuit of the parameter migration lumped element and the dynamic phasor form of the dynamic accompanying circuit of the deterministic lumped element. The types of lumped elements include: resistors, capacitors and inductors. Step S3 includes: Establish a switching function model for the converter station, and convert the switching function model into a dynamic phasor model for the converter station; For the parameter migration elements and deterministic elements in the dynamic phasor model of the converter station, differential modeling is performed using the implicit trapezoidal method and Milstein scheme, respectively, to obtain the dynamic phasor form of the dynamic accompanying circuit of the converter station. The dynamic phasor form of the parameter migration lumped element is the dynamic accompanying circuit: , and These are the voltage across the inductor and the voltage across the capacitor, respectively. and These are the equivalent admittances of the random migration inductor and capacitor, respectively. and These are the historical current sources of randomly migrated inductors and capacitors, respectively. and It is a random current source that randomly migrates inductors and capacitors, where n represents time t. Indicates inductor current. This represents the capacitor current.

2. The method according to claim 1, characterized in that, Step S1 includes: The DC power system parameters include: circuit node parameters, circuit element parameters, and converter station parameters in the DC power system; The initial parameters shown include: time t, step size ∆t, total duration T, initial value of the injected current vector, and dynamic phasor order k, where: At the initial time t=0; k∈N, when k=0, it means to analyze the DC power of the system, and when k≠0, it means to analyze the k-th harmonic of the DC power system.

3. The method according to claim 1, characterized in that, The accompanying circuit in the dynamic phasor form of a deterministic lumped element is: , This represents the equivalent admittance of the RL branch. Let represent the k-th order dynamic phasor of the RL branch voltage at time n, where n represents time t and k represents the order of the dynamic phasor. It is the historical current source of the RL branch.

4. The method according to claim 3, characterized in that, include: , Let represent the k-th order dynamic phasor of the inductor voltage at time n-1, j denote the unit of the complex number, L represent the deterministic inductance, R represent the deterministic resistance, and ∆t represent the time step. It represents angular frequency.

5. The method according to claim 1, characterized in that, include: , Where n corresponds to time t, Let the parameter transfer inductance be at time t. Let be the predicted parameter migration inductance at time t, where α and β represent the migration and diffusion processes of the stochastic differential equation (SDE), respectively, ∆t represents the time step, j represents the unit of the complex number, and k represents the dynamic phasor order. Represents angular frequency. This represents the inductor current at time t-∆t. This represents the increment at time n-1 in the standard Wiener process. , The estimated value of the parameter migration inductance at time t, Let the parameter transfer inductance be at time t. This represents the capacitor voltage at time t-∆t.

6. The method according to claim 1, characterized in that, Step S6 includes: If the switching function of the converter station changes, the node admittance matrix is ​​corrected, then the voltage and branch current of each node are retrieved, and the historical current source and random current source of the dynamic phasor form of the converter station at time t are updated.

7. The method according to claim 6, characterized in that, After retrieving the node voltages and branch currents stored in the system, the following is included: For parameter migration elements, update the admittance, random current source, and historical current source of the dynamic phasor form of the parameter migration element's dynamic accompanying circuit, and correct the nodal admittance matrix; for deterministic elements, update the current source of the dynamic phasor form of the deterministic element's accompanying circuit. Using the updated admittance, random current source, and historical current source, the row and column parameters corresponding to the node admittance matrix that needs to be updated are generated, including the temporary admittance matrix G and the temporary injected current vector I at time t, where t = t0 + ∆t, and t0 is the initial time.

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