CN115438461A - Dynamic phasor representation based random transient analysis method for direct current power system - Google Patents

Dynamic phasor representation based random transient analysis method for direct current power system Download PDF

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CN115438461A
CN115438461A CN202210850925.XA CN202210850925A CN115438461A CN 115438461 A CN115438461 A CN 115438461A CN 202210850925 A CN202210850925 A CN 202210850925A CN 115438461 A CN115438461 A CN 115438461A
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power system
direct current
current power
circuit
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陈鹏伟
卢亮
刘念
李欢
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Nanjing University of Aeronautics and Astronautics
CSG Electric Power Research Institute
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Nanjing University of Aeronautics and Astronautics
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    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
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Abstract

The embodiment of the invention discloses a dynamic phasor characterization based random transient analysis method for a direct current power system, relates to the field of power electronization of the direct current power system, and can reflect the contradiction between system characteristics and multi-rate simulation, balance precision and efficiency caused under the source-load random excitation condition. The invention includes: acquiring direct current power system parameters and setting initial parameters; acquiring circuit models of two types of collective elements in a direct current power system; establishing a dynamic phasor model of a converter station in a direct current power system, and obtaining a dynamic accompanying circuit of the converter station; establishing a model of a direct current power system by utilizing circuit models of the two types of integrated elements and a dynamic accompanying circuit of the converter station; acquiring a node voltage equation of the direct current power system; updating a node admittance matrix and an injection current vector according to the change condition of a switching function of the converter station; and converting the dynamic phasor output by the model of the direct current power system into an instantaneous value.

Description

Dynamic phasor characterization based random transient analysis method for direct current power system
Technical Field
The invention relates to the technical field of power electronic systems of direct-current power systems, in particular to a random transient analysis method of a direct-current power system with dynamic phasor representation.
Background
With the development of power semiconductor technology, the economic advantages of a direct current power system are gradually reflected, and the direct current power system becomes one of the development directions of the future and even an energy internet as an important carrier for renewable energy integration, absorption, transformation and capacity increase of an electric vehicle efficiently connected to an alternating current distribution network and a comprehensive energy system. Because both the source and the load of the direct current power system are highly power-electronized, along with the improvement of capacity power level, the increase of the number of converter stations and the improvement of network complexity, the digital simulation of the power system has more challenges from the characteristics of the system.
At present, the electromagnetic transient simulation analysis based on the detailed dynamic characteristic modeling of the element is used for describing the microsecond-level dynamic process of the direct current power system, and the benefit of this is that the method is not limited by the scale and structure of the system. However, as the power electronic converter station and the control protection strategy of the dc power system become more and more complex, the contradiction between the accuracy and the efficiency of the electromagnetic transient simulation analysis becomes more and more prominent due to the increase of the system scale and the increase of the switching frequency: generally, the simulation step length is set to be 1/10 of the switching period or even smaller, and the influence characteristics of random excitation on the system operation are difficult to accurately reflect, so that the existing electromagnetic transient simulation analysis means is difficult to deal with more and more complex control protection strategies.
Disclosure of Invention
The embodiment of the invention provides a dynamic phasor characterization direct current power system random transient analysis method which can accurately reflect the influence characteristics of random excitation on system operation and balance the contradiction between precision and efficiency in dynamic analysis.
In order to achieve the above purpose, the embodiment of the invention adopts the following technical scheme:
s1, acquiring direct current power system parameters and setting initial parameters, wherein the direct current power system parameters are used for representing the structure of a direct current power system;
s2, obtaining a circuit model of two types of collecting elements in the direct current power system, wherein the two types of collecting elements in the direct current power system comprise: a parametric migration lumped element and a deterministic lumped element, a circuit model of the two types of lumped elements comprising: a dynamic accompanying circuit of a parametric migration lumped element and an accompanying circuit of a deterministic lumped element;
s3, establishing a dynamic phasor model of a converter station in the direct current power system, and obtaining a dynamic accompanying circuit of the converter station;
s4, establishing a model of the direct current power system by using the circuit models of the two types of collecting elements obtained in the S2 and the dynamic accompanying circuit of the converter station obtained in the S2, wherein the model of the direct current power system comprises the following steps: a dynamic companion circuit, a node admittance matrix, and an injection current vector of the DC power system;
s5, obtaining a node voltage equation of the direct current power system, wherein a voltage model of a node is GU = I, U represents a node voltage phasor, G represents a temporary admittance matrix at the moment t, and I represents a temporary injection current vector at the moment t;
s6, updating the node admittance matrix and the injection current vector according to the change condition of the switching function of the converter station;
and S7, converting the dynamic phasor output by the model of the direct current power system into an instantaneous value as a random dynamic analysis result of the direct current power system.
The scheme of the embodiment can be applied to a direct current power system under power electronization random excitation, source-load multi-type random excitation of a random system is simulated, and the simulation capability of digital dynamic simulation is improved. The modeling is carried out by adopting a dynamic phasor method, specific harmonic waves can be analyzed, and the contradiction between the precision and the efficiency of dynamic simulation is balanced by adopting large-step simulation. Meanwhile, the direct current power system random transient analysis method characterized by the dynamic phasor can reduce the updating of parameters and reduce the simulation calculation amount.
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In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings required to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a schematic diagram of a process flow provided by an embodiment of the present invention;
FIG. 2 is a schematic diagram of an exemplary embodiment of a deterministic component dynamic phasor form companion circuit and a parametric migration component dynamic phasor form dynamic companion circuit;
FIG. 3 is a VSC circuit, a switching function model of the VSC circuit, and an accompanying circuit provided in an embodiment of the present invention;
FIG. 4 is a node voltage equation for a VSC circuit provided by an embodiment of the present invention;
FIG. 5 is a switching function model and a dynamic companion circuit of a VSC subsystem according to an embodiment of the present invention;
fig. 6 is a node voltage equation of the VSC subsystem provided in an embodiment of the present invention;
FIG. 7 is a schematic diagram of the main logic flow of a hybrid simulation algorithm according to an embodiment of the present invention.
Detailed Description
In order to make the technical solutions of the present invention better understood, the present invention will be described in further detail with reference to the accompanying drawings and specific embodiments. Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the accompanying drawings are exemplary only for explaining the present invention and are not construed as limiting the present invention. As used herein, the singular forms "a", "an", "the" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms "comprises" and/or "comprising," when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof. It will be understood that when an element is referred to as being "connected" or "coupled" to another element, it can be directly connected or coupled to the other element or intervening elements may also be present. Further, "connected" or "coupled" as used herein may include wirelessly connected or coupled. As used herein, the term "and/or" 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 (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the prior art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.
The main problem in the existing solutions is that it is not possible to simulate the external random excitation and the internal parameter random migration of the system. Therefore, it is a problem to be studied to provide a dynamic simulation method capable of accurately reflecting the influence characteristics of random excitation on system operation and balancing the digital simulation precision and efficiency. The design idea of this embodiment lies in: the direct current power system is modeled by adopting dynamic phasor, a dynamic accompanying circuit in a dynamic phasor form is constructed, a node voltage equation of the system at any time is solved, and the function of simulating the dynamic process of the system is realized. The parameter migration element adopts a Stochastic Differential Equation (SDE) to describe the dynamic change process of the parameter migration element, and establishes a dynamic accompanying circuit model in a dynamic phasor form at any time, wherein the dynamic accompanying circuit model comprises an equivalent admittance, a random current source and a historical current source; the deterministic element directly establishes a dynamic adjoint circuit in a dynamic phasor form, and the dynamic adjoint circuit comprises an equivalent admittance and a historical current source; a voltage type converter station in a direct current power system is a nonlinear system and needs to be modeled in a modularized mode, firstly, the voltage type converter station is modeled through a switching function method, then, a switching function model of the converter station is modeled by adopting dynamic phasors, a dynamic phasor model of the converter station is established, and finally, a dynamic accompanying circuit in a dynamic phasor form is established. And (3) constructing a node admittance matrix, an injected current phasor and a node voltage law equation of the dynamic phasor form dynamic accompanying circuit of the whole system by using the parameter migration element, the deterministic element and the dynamic phasor form dynamic accompanying circuit of the converter station, and completing the analysis of random dynamic simulation. The algorithm realizes the random dynamic simulation of the direct current power system, simulates source-load multi-type random excitation, and balances the contradiction between the dynamic simulation precision and the dynamic simulation efficiency. The design concept is further designed and tested to form the following embodiments so as to be applicable by those skilled in the art.
Specifically, an embodiment of the present invention provides a method for analyzing a random transient of a dc power system with dynamic phasor characterization, as shown in fig. 1, including:
s1, acquiring direct current power system parameters and setting initial parameters.
Wherein the DC power system parameter is used to represent a configuration of the DC power system. The direct current power system parameters include: circuit nodes, circuit element parameters (parameter migration and determinism) and converter station parameters; the initial parameters include: time T, step length delta T, total duration T, initial value of injection current vector and dynamic phasor order k. Wherein the initial time t =0; k ∈ N, when k =0, indicates that the dc component of the system is analyzed, and when other values are taken, indicates that the k-order harmonic of the system is analyzed.
And S2, obtaining circuit models of two types of collecting elements in the direct current power system.
Wherein, two types of collecting elements in the direct current power system comprise: a parametric migration lumped element and a deterministic lumped element, a circuit model of the two types of lumped elements comprising: a dynamic accompanying circuit of parametric migration lumped elements and an accompanying circuit of deterministic lumped elements. Wherein the parameters of the deterministic element are fixed, corresponding to the companion circuit, which is composed of the admittance (deterministic value) and the historical current source; and the parameter of the parameter migration element is changed, and the corresponding dynamic accompanying circuit is composed of an admittance (random), a historical current source and a random current source.
And S3, establishing a dynamic phasor model of the converter station in the direct current power system, and obtaining a dynamic accompanying circuit of the converter station.
The direct current power system specifically adopts a voltage source type converter station.
And S4, establishing a model of the direct current power system by using the circuit models of the two types of collecting elements obtained in the S2 and the dynamic accompanying circuit of the converter station obtained in the S2.
Wherein, the model of the direct current power system comprises: a dynamic companion circuit, a node admittance matrix, and an injection current vector of the direct current power system. And constructing the dynamic adjoint circuit in the form of the dynamic phasor of the direct current power system by using the obtained converter station, the adjoint circuit in the form of the dynamic phasor of the deterministic element and the dynamic adjoint circuit in the form of the dynamic phasor of the parameter migration element. The initial node admittance matrix and injection current vector are written by the column. Updating the current time t = t 0 +Δt。
And S5, acquiring a node voltage equation of the direct current power system.
The voltage model of the node is GU = I, U represents a node voltage phasor, G represents a temporary admittance matrix at the time t, and I represents a temporary injection current vector at the time t, which corresponds to the injection current of each node. And solving to obtain the node voltage and the branch current at the time t, and storing the values of the node admittance matrix and the injection current vector which need to be output and updated. Meanwhile, because dynamic phasor modeling is utilized, the dynamic phasor is a complex number, and a node voltage equation cannot be directly calculated, wherein G = G R +jG I ，U＝U R +jU I ，I＝I R +jI I . The node voltage equation needs to be split into a real part and an imaginary part, namely G R U R -G I U I ＝I R And G R U I +G I U R ＝I I . Calculating the dynamic phasor form of each node voltage and each branch current at the time t, wherein j represents a complex unit, G R Representing the real part matrix, G, of the nodal admittance matrix I Representing the imaginary matrix, U, of the node admittance matrix R Representing the real part of the node voltage matrix, U I Representing the imaginary matrix of the node voltage matrix, I R Display sectionReal part matrix of dot voltage matrix, I I Representing the imaginary matrix of the node voltage matrix.
S6, updating the node admittance matrix and the injection current vector according to the change condition of the switching function of the converter station;
and S7, converting the dynamic phasor output by the model of the direct current power system into an instantaneous value as a random dynamic analysis result of the direct current power system.
In this case, after S6 is performed, data in the form of dynamic phasor values are obtained, and thus the obtained dynamic phasor values need to be converted into instantaneous values.
The scheme of the embodiment can be applied to a direct current power system under power electronics random excitation, source-load multi-type random excitation of a random system is simulated, and the simulation capability of digital dynamic simulation is improved. The modeling is carried out by adopting a dynamic phasor method, specific harmonic waves can be analyzed, and the contradiction between the precision and the efficiency of dynamic simulation is balanced by adopting large-step simulation. Meanwhile, the dynamic phasor representation based random transient analysis method for the direct current power system can reduce parameter updating and reduce simulation calculation amount. Therefore, the direct-current power system under the random excitation can be efficiently simulated, the dynamic process of the system caused by external excitation and internal parameter migration can be analyzed, specific harmonic waves can be analyzed, and the contradiction between the dynamic simulation precision and the efficiency can be balanced.
In this embodiment, the step S2 includes: determining a parameter migration element and a deterministic element in the DC power system. If the parameters of the elements are fixed and constant, the elements belong to deterministic elements, and if the parameters of the elements are time-varying, the elements belong to parameter migration elements; differential modeling is carried out on the deterministic element by adopting an implicit trapezoidal method, and differential modeling is carried out on the parameter migration element by adopting a Milstein format; respectively utilizing the modeling results of the deterministic element and the parametric migration element to obtain a dynamic accompanying circuit in the form of a dynamic phasor of the parametric migration lumped element and a dynamic accompanying circuit in the form of a dynamic phasor of the deterministic lumped element, wherein the types of the lumped element comprise: resistance, capacitance and inductance.
In particular, deterministic lumped elementsThe dynamic companion circuit of the dynamic phasor form of the unit is:
Figure BDA0003754630130000071
G LR the equivalent admittance of the RL branch is indicated,
Figure BDA0003754630130000072
representing a k-order dynamic phasor of the inductance voltage at the moment n, wherein n represents the moment t, and k represents the order of the dynamic phasor;
Figure BDA0003754630130000073
is the historical current source for the RL leg.
Figure BDA0003754630130000074
G L The equivalent admittance of the inductance is represented,
Figure BDA0003754630130000075
denotes the k-order dynamic phasor of the inductor voltage at time n-1, j denotes the unit of a complex number, L denotes the deterministic inductance, R denotes the deterministic resistance, Δ t denotes the time step, ω s Representing angular frequency.
Further, the dynamic adjoint circuit of the parameter migration lumped element in the form of dynamic phasor is as follows:
Figure BDA0003754630130000081
and
Figure BDA0003754630130000082
respectively the voltage of the inductor and the voltage of the capacitor,
Figure BDA0003754630130000083
and
Figure BDA0003754630130000084
respectively the equivalent admittance of the random migration inductance and capacitance,
Figure BDA0003754630130000085
and
Figure BDA0003754630130000086
historical current sources of random transfer inductance and capacitance, respectively;
Figure BDA0003754630130000087
and
Figure BDA0003754630130000088
is a random current source for randomly migrating inductance and capacitance, n represents the time t,
Figure BDA0003754630130000089
which is indicative of the current of the inductor,
Figure BDA00037546301300000810
representing the capacitive current.
Figure BDA00037546301300000811
Figure BDA00037546301300000812
Wherein n represents time t, L n The inductance is shifted for the parameter at time t,
Figure BDA00037546301300000813
for the estimation of the parameter migration inductance at time t, α, β represent the migration process and diffusion process of the random differential equation (SDE), respectively, Δ t represents the time step, j represents the unit of the complex number, k represents the order of the dynamic phasor, ω s The angular frequency is represented by the angular frequency,
Figure BDA00037546301300000814
denotes the inductor current at the corresponding time t- Δ t, wherein n-1 represents t- Δ t, Δ W n-1 Represents the increment, Δ D, of the n-1 time in a standard Wiener process n-1 Is an intermediate quantity
Figure BDA00037546301300000815
For the time t parameter migration inductance estimated value, C n The inductance is shifted for the parameter at time t,
Figure BDA00037546301300000816
representing the capacitor voltage at the corresponding time t-deltat.
For example, establishing a deterministic element and a parametric shift element dynamic phasor equivalent circuit is shown in fig. 2 a) and 2 c), and establishing a deterministic element dynamic phasor form dynamic companion circuit and a parametric shift element dynamic phasor form dynamic companion circuit is shown in fig. 2 b) and 2 d), wherein the parametric shift element and the deterministic element are distinguished as to whether lumped element (resistance, capacitance and inductance) parameters are time-varying or not, and if the parameters are fixed, they are not changed into deterministic elements, and otherwise they are parameter shift elements.
For deterministic resistance, the node i and node j resistance dynamic phasor equations can be expressed as:
Figure BDA0003754630130000091
in the formula:
Figure BDA0003754630130000092
k-order dynamic phasor representing current at the moment t of the resistor; r represents a deterministic resistance; v i k (t) and
Figure BDA0003754630130000093
representing k-order dynamic phasors of the voltages of the node i and the node j at the time t; g R Representing the equivalent admittance of the deterministic resistance.
Since the deterministic resistance contains no differential terms, it can be directly discretized into
Figure BDA0003754630130000094
In the formula: n is a discrete index corresponding to time t. G R Represents time tEquivalent admittance of the qualitative resistance.
For deterministic inductance, the node i and node j inductance dynamic phasor equations can be expressed as:
Figure BDA0003754630130000095
in the formula:
Figure BDA0003754630130000096
representing k-order dynamic phasor of current at the moment t of the inductor; j is the unit of a complex number; l represents a deterministic inductance. Omega s And T is the fundamental wave period, and is 2 pi/T.
The method is characterized by utilizing a trapezoidal method to obtain:
Figure BDA0003754630130000097
in the formula: n and n-1 correspond to discrete subscripts at time t and t- Δ t, respectively;
Figure BDA0003754630130000098
and
Figure BDA0003754630130000099
respectively representing k-order dynamic phasors of the inductive current at the n moment and the n-1 moment;
Figure BDA00037546301300000910
and
Figure BDA00037546301300000911
representing k-order dynamic phasors of the voltages of the node i and the node j at the moment n;
Figure BDA00037546301300000912
and
Figure BDA00037546301300000913
representing the k-order dynamic phasors for the voltages at node i and node j at time n-1.
For deterministic capacitance, the capacitance dynamic phasor equation can be expressed as:
Figure BDA00037546301300000914
in the formula:
Figure BDA00037546301300000915
representing k-order dynamic phasor of current at the moment t of the capacitor;
Figure BDA00037546301300000916
representing the k-order dynamic phasor of the voltage at the moment t of the capacitor; c represents the deterministic capacitance.
The dispersion can be obtained by a trapezoidal method:
Figure BDA00037546301300000917
in the formula:
Figure BDA0003754630130000101
and
Figure BDA0003754630130000102
respectively representing k-order dynamic phasors of the inductive current at the n moment and the n-1 moment;
Figure BDA0003754630130000103
and
Figure BDA0003754630130000104
representing the k-order dynamic phasors of the inductor voltage at time n and at time n-1, respectively.
In order to be able to construct the node voltage equation, a dynamic companion circuit is required that converts deterministic inductance and capacitance into a dynamic phasor form, and equations (4) and (6) are rewritten and are available:
Figure BDA0003754630130000105
Figure BDA0003754630130000106
Figure BDA0003754630130000107
in the formula:
Figure BDA0003754630130000108
and
Figure BDA0003754630130000109
respectively representing the equivalent admittance of the inductor and the capacitor; u. of L And u C Representing the voltages of the inductor and the capacitor, respectively;
Figure BDA00037546301300001010
and
Figure BDA00037546301300001011
historical current sources representing inductance and capacitance, respectively.
Meanwhile, in order to reduce the simulation calculation amount, the lumped element can be combined and modeled, and the RL branch is taken as an example to obtain:
Figure BDA00037546301300001012
in the formula:
Figure BDA00037546301300001013
representing the k-order dynamic phasor of the current at time t of the RL branch.
In order to construct a dynamic adjoint circuit in a dynamic phasor form, the following formula (10) is obtained by adopting a trapezoidal method for discrete arrangement:
Figure BDA00037546301300001014
in the formula:
Figure BDA00037546301300001015
represents the equivalent admittance of the RL branch;
Figure BDA00037546301300001016
a k-order dynamic phasor representing the inductor voltage at time n (time t);
Figure BDA00037546301300001017
is the historical current source for the RL leg.
Figure BDA0003754630130000111
In this embodiment, as shown in fig. 2 c), the creating of the dynamic companion circuit in the form of the dynamic phasor of the parameter migration element includes:
the parameter migration element can describe the parameter migration process through a random differential equation.
Figure BDA0003754630130000112
In the formula: r (t), L (t) and C (t) represent the random migration resistance, capacitance and inductance, respectively. α, β represent the migration process and the diffusion process of the random differential equation (SDE), respectively. α (R, t), α (L, t) and α (C, t) represent the offset processes of the parameters migration resistance parameter, inductance parameter and capacitance parameter, respectively. β (R, t), β (L, t) and β (C, t) represent diffusion processes of the parameters migration resistance parameter, inductance parameter and capacitance parameter, respectively. W R (t)、W L (t) and W C (t) is an independent standard Wiener process.
For the parameter migration resistance, only considering the slow process of the parameter migration resistance, the dynamic phasor equation of the node i and the node j can be expressed as follows:
Figure BDA0003754630130000113
in the formula:
Figure BDA0003754630130000114
representing k-order dynamic phasor of current at time t of the parameter transfer resistance; g R (t) represents the admittance of the parametric migration resistance at time t.
Discretizing a node dynamic phasor equation of the parameter migration resistance to obtain:
Figure BDA0003754630130000115
in the formula: r is n And G R,n Respectively representing the parameter migration resistance value and the equivalent admittance at the time t. R n It needs to be updated synchronously with the simulation time and is available discretely in the backward Milstein format.
Figure BDA0003754630130000121
In the formula: r n-1 Representing the parameter migration resistance value at the time of t-delta t;
Figure BDA0003754630130000122
Figure BDA0003754630130000123
W n ＝W(t n ) N (0, 1) represents a standard normal distribution;
Figure BDA0003754630130000124
the resistance shift estimate is moved for the time t parameter.
For the parametric shift inductance, only the slow course of the parametric shift inductance is considered (i.e. only the 0 th order dynamic phasor is considered,
Figure BDA0003754630130000125
since the change of the inductive flux causes the voltage change, it can be obtained from Faraday's law of electromagnetic induction and dynamic phasor properties, wherein the dynamic phasor differential properties are
Figure BDA0003754630130000126
<·> k Represents an operator for extracting k-order dynamic phasor, and has a convolution property of
Figure BDA0003754630130000127
x and y represent variables, and K represents a selected dynamic phasor set.
Figure BDA0003754630130000128
In the formula: psi L (t) represents the flux linkage at time t; l (t) represents the parametric migration inductance.
The random process of the parameter shift inductance is substituted into formula (17), and the dynamic current of the parameter shift inductance can be expressed as:
Figure BDA0003754630130000129
discretization using the backward Milstein format gave:
Figure BDA00037546301300001210
in the formula:
Figure BDA00037546301300001211
estimation of inductance for time t parameter migration
Figure BDA00037546301300001212
For the parametric transfer capacitance, only the slow course of the parametric transfer inductance is considered (i.e. only the 0 th order dynamic phasor,<Q C (t)> k ≈C(t)<u C (t)> k ) Since the change of the capacitance charge can cause the current to change, the charge equation and the dynamic phasor property can obtain that:
Figure BDA0003754630130000131
in the formula: q C (t) represents the charge at time t.
The stochastic process for the parametric shift capacitor is substituted into equation (20), and the dynamic voltage of the parametric shift capacitor can be expressed as:
Figure BDA0003754630130000132
discretization using the backward Milstein format gave:
Figure BDA0003754630130000133
in the formula:
Figure BDA0003754630130000134
estimation of inductance for time t parameter migration
Figure BDA0003754630130000135
In order to be able to construct the node voltage equation, a dynamic companion circuit in the form of a dynamic phasor is required to convert the parameter transfer inductance and capacitance, and equations (19) and (22) are rewritten as follows:
Figure BDA0003754630130000136
in the formula:
Figure BDA0003754630130000137
and
Figure BDA0003754630130000138
the voltages of the inductor and capacitor, respectively;
Figure BDA0003754630130000139
and
Figure BDA00037546301300001310
are respectively random migrationEquivalent admittances of an inductance and a capacitance;
Figure BDA00037546301300001311
and
Figure BDA00037546301300001312
historical current sources of random migration inductance and capacitance respectively;
Figure BDA00037546301300001313
and
Figure BDA00037546301300001314
is a random current source that randomly migrates inductance and capacitance.
Figure BDA00037546301300001315
Figure BDA0003754630130000141
Meanwhile, in order to reduce the simulation calculation amount, the lumped element can be combined for modeling, taking an RL branch as an example, and the model can be obtained by faraday's law of electromagnetic induction and dynamic phasor properties:
Figure BDA0003754630130000142
after adopting a backward Milstein format for dispersing and finishing, the product can be obtained:
Figure BDA0003754630130000143
in the formula:
Figure BDA0003754630130000144
is the random current source of the RL branch.
Figure BDA0003754630130000145
In this embodiment, the step S3 includes: and 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 by a switching function (representing a switching state), which is an instantaneous value model, and the switching function model is converted into a dynamic phasor model through dynamic phasor definition and properties. The complexity of the dynamic phasor model is determined by the dynamic phasor order k, and the larger the value of k is, the higher the simulation precision is. And carrying out differential modeling on a parameter migration element and a deterministic element in the dynamic phasor model of the converter station by respectively adopting an implicit trapezoidal method and a Milstein format to obtain a dynamic accompanying circuit in the dynamic phasor form of the converter station. The dynamic phasor model of the converter station comprises a parameter migration element and a deterministic element, the deterministic element is subjected to implicit trapezoidal differential modeling, the parameter migration element is subjected to Milstein format differential modeling, and a dynamic accompanying circuit in the form of the dynamic phasor of the converter station is established. For example: the step S3 includes: the accompanying circuit for establishing the dynamic phasor form of the voltage source type converter station in the direct current power system is shown in fig. 3 c), and comprises the following components: a voltage type converter station in a direct current power system has a switch model, is a nonlinear system, is inconvenient to solve a converter station circuit by using a node voltage method, takes an alternating current side inductor, a switch and a direct current side capacitor as a whole, establishes a three-input and two-output port equivalent model, and couples an alternating current side and a direct current side into a subsystem through a controlled source. In order to establish an accompanying circuit in a dynamic phasor form of a voltage type converter station of a direct current power system, firstly, a switching function method is utilized for modeling, and the following steps can be obtained:
Figure BDA0003754630130000151
in the formula: u. of dc And i dc Respectively representing the direct-current side voltage and current of the VSC; r p And L p Respectively representing equivalent resistance and inductance of the bridge arm; v. of N Represents the voltage of node N; p is an element { a, b, c } representing three phases; whereins a 、s b And s c Characterizing the switching function, S, of each phase of the bridge arm respectively 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。
Then, dynamic phasor modeling is utilized to obtain:
Figure BDA0003754630130000152
in the formula:
Figure BDA0003754630130000153
the dynamic phasor forms respectively represent a, b and c three-phase alternating-current side currents;
Figure BDA0003754630130000154
representing the dynamic phasor form of the voltage at two ends of the direct current side capacitor;
Figure BDA0003754630130000155
representing the output current of the direct current side capacitor; s 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。
The companion circuit in the form of a dynamic phasor is established by a model of a switching function in the form of a dynamic phasor. The current-voltage characteristics of the two ends of the alternating current side inductor and the injection quantity of the direct current side capacitor are as follows:
Figure BDA0003754630130000156
Figure BDA0003754630130000157
from the equations (27) and (28), the AC side and the DC side of the converter station model are coupled to each other, and one end of the inductor is connectedNode voltage is D p u dc The injection current of the direct current side capacitor is formed by combining three-phase current of an alternating current side. Through the established companion circuit, a node voltage equation of the companion circuit can be obtained
Figure BDA0003754630130000161
As shown in fig. 4.
In this embodiment, in step S4, a dynamic companion circuit in the form of a dynamic phasor of the dc power system, a node admittance matrix, and an injection current vector need to be constructed, where the dynamic companion circuit includes:
a dynamic companion circuit of the system is constructed using the parameter migration element, the deterministic element and the dynamic companion circuit in the form of a dynamic phasor of the converter station, the column write node admittance matrix and the injection current vector. Taking the VSC subsystem as an example, the ac side is connected to the randomly processed grid, as shown in figure 5 a),
Figure BDA0003754630130000162
and
Figure BDA0003754630130000163
is a k-order dynamic phasor of a three-phase power supply and a three-phase node voltage,
Figure BDA0003754630130000164
is the equivalent admittance of the parametric shift inductor-resistor branch. However, as can be seen from fig. 4, the node admittance matrix of the VSC
Figure BDA0003754630130000165
The node voltage equation is a nonlinear equation, cannot be directly solved, and needs to be corrected in order to carry out iterative solution in simulation.
Figure BDA0003754630130000166
The method can be split into direct current side voltage and amplification admittance:
Figure BDA0003754630130000167
in the formula:
Figure BDA0003754630130000168
is that
Figure BDA0003754630130000169
And
Figure BDA00037546301300001610
and (4) increasing the admittance.
Similarly, using circuit fundamentals, three-phase currents are represented by node voltages at time n and other known parameters,
Figure BDA00037546301300001611
can be rewritten as:
Figure BDA00037546301300001612
in the formula: u. of Rp Is an equivalent resistance R p Pressure drop of (d);
Figure BDA00037546301300001613
is that
Figure BDA00037546301300001614
And
Figure BDA00037546301300001615
an amplification admittance;
Figure BDA00037546301300001616
is that
Figure BDA00037546301300001617
And
Figure BDA00037546301300001618
and (4) increasing the admittance.
By equations (29) and (30), a node voltage equation of the VSC subsystem is constructed, as shown in fig. 6.
In this embodiment, the step S5 includes: calculating and storing node voltage and branch current, comprising:
and constructing a node voltage equation GU = I. The method comprises the steps of obtaining a node voltage phasor at a time point t, obtaining a branch current and a node voltage phasor at the time point t, obtaining a branch current and obtaining a current vector, wherein U represents the node voltage phasor, G represents a t-delta t temporary admittance matrix, and I represents a t-delta t temporary injection current vector, solving to obtain the node voltage and the branch current at the time point t, and storing values of the node admittance matrix and the injection current vector which need to be output and updated.
Meanwhile, because dynamic phasor modeling is utilized, the dynamic phasor is a complex number, and a node voltage equation cannot be directly calculated, wherein G = G R +jG I ，U＝U R +jU I ，I＝I R +jI I . The node voltage equation needs to be split into a real part and an imaginary part as follows: g R U R -G I U I ＝I R And G R U I +G I U R ＝I I . Calculating the dynamic phasor form of each node voltage and each branch current at the time t, wherein j represents a complex unit, G R Representing the real part matrix, G, of the nodal admittance matrix I Representing the imaginary matrix, U, of the node admittance matrix R Representing the real part of the node voltage matrix, U I Representing the imaginary matrix of the node voltage matrix, I R Representing the real part of the node voltage matrix, I I Representing the imaginary matrix of the node voltage matrix.
In this embodiment, the step S6 includes:
if the switching function of the converter station changes, the node admittance matrix is corrected, then the voltage of each node and the branch current are taken (which can be temporarily stored in a computer or a database of an operation program), and then the historical current source of the dynamic phasor form dynamic companion circuit at the moment t of the converter station is updated, wherein the finally obtained branch current is the current flowing through the element and is determined according to the admittance, the node voltage, the random current source and the historical current source. It is detected whether a change of the switching function of the converter station in the system has occurred. If the switching function is not changed, the node admittance matrix does not need to be corrected, the voltage of each node and the branch current stored in the system are called, and the historical current source of the dynamic accompanying circuit at the moment t of the converter station in the dynamic phasor form is updated. If the switching function changes, the node admittance matrix needs to be corrected, the voltage of each node and the branch current stored in the system are called, and the historical current source of the dynamic phasor dynamic accompanying circuit of the converter station at the moment t is updated.
After the node voltages and branch current stored in the system are fetched, the method comprises the following steps: for the parameter migration element, updating the admittance, the random current source and the historical current source of the dynamic companion circuit in the form of the dynamic phasor of the parameter migration element, and correcting the node admittance matrix; for deterministic elements, the current sources of the dynamic companion circuit in the form of dynamic phasors of the deterministic elements are updated. Generating row and column parameters corresponding to the node admittance matrix to be updated by using the updated admittance, the random current source and the historical current source, wherein the row and column parameters comprise a temporary admittance matrix G and a temporary injection current vector I at the time t, and t = t 0 +Δt，t 0 An initial time.
In practical applications, this embodiment may be further refined and implemented by a computer program, as shown in fig. 7, and the specific implementation process of the program may be as shown in steps 1-14, which include:
step 1: inputting direct current power system parameters and setting initial parameters. The input dc power system parameters shown include: circuit nodes, circuit element parameters (parameter migration and determinism) and converter station parameters; the initial parameters shown include: time T, step length delta T, total duration T, initial value of injection current vector and dynamic phasor order k.
Step 2: parametric migration elements and deterministic elements are modeled differentially. And establishing dynamic phasor models of the parameter migration element and the deterministic element, and differentiating to form an accompanying circuit of the parameter migration lumped element and a dynamic accompanying circuit of the deterministic lumped element in a dynamic phasor form.
And step 3: and carrying out differential modeling on the converter station modules. And establishing a dynamic phasor model of the voltage type converter station of the direct current power system, and differentiating to form an accompanying circuit in the form of the dynamic phasor of the converter station.
And 4, step 4: simulation time update t = t 0 +Δt。
And 5: a node admittance matrix G and an injection current vector I are generated.
Step 6: and calculating and storing the node voltage and the branch current at the time t.
And 7: and (4) judging whether the simulation is finished or not, ending and entering step 14, otherwise, entering step 8.
And 8: and updating the random current source and the historical current source of the parameter migration element by using the node voltage and the branch current calculated in the step 6.
And step 9: and (4) updating the parameter migration element admittance by using the node voltage and the branch current calculated in the step (6), and correcting the node admittance matrix.
Step 10: the historical current source of the deterministic element is updated with the node voltage and branch current calculated in step 6.
Step 11: and judging whether the control is changed, namely whether the switching function is changed, if so, entering a step 12, and if not, entering a step 4.
Step 12: and updating the switching function and correcting the node admittance matrix.
Step 13: and updating the random current source and the historical current source of the converter station module.
Step 14: and (5) calling the dynamic phasor to be output, converting the dynamic phasor into an instantaneous value for output, and ending the simulation.
The scheme designed by the embodiment can be applied to a direct current power system under power electronic random excitation, a parameter migration element, a deterministic element and a dynamic phasor form dynamic companion circuit of a voltage type converter station are established, a node voltage equation is constructed, source-charge multi-type random excitation of a random system is simulated, and the simulation capability of digital dynamic simulation is improved. The modeling is carried out by adopting a dynamic phasor method, specific harmonic waves can be analyzed, and the contradiction between the precision and the efficiency of dynamic simulation is balanced by adopting large-step simulation. Meanwhile, the dynamic phasor representation based random transient analysis method for the direct current power system can reduce parameter updating and reduce simulation calculation amount.
All the embodiments in the present specification are described in a progressive manner, and the same and similar parts among the embodiments are referred to each other, and each embodiment focuses on the differences from other embodiments. In particular, the apparatus embodiments are substantially similar to the method embodiments and therefore are described in a relatively simple manner, and reference may be made to some of the description of the method embodiments for relevant points. The above description is only for the specific embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.

Claims (10)

1. A random transient analysis method for a dynamic phasor representation direct current power system is characterized by comprising the following steps:
s1, acquiring direct current power system parameters and setting initial parameters, wherein the direct current power system parameters are used for representing the structure of a direct current power system;
s2, obtaining circuit models of two types of collecting elements in the direct current power system, wherein the two types of collecting elements in the direct current power system comprise: a parametric migration lumped element and a deterministic lumped element, a circuit model of the two types of lumped elements comprising: a dynamic accompanying circuit of a parametric migration lumped element and an accompanying circuit of a deterministic lumped element;
s3, establishing a dynamic phasor model of a converter station in the direct current power system, and obtaining a dynamic accompanying circuit of the converter station;
s4, establishing a model of the direct current power system by using the circuit models of the two types of collecting elements obtained in the S2 and the dynamic accompanying circuit of the converter station obtained in the S2, wherein the model of the direct current power system comprises the following steps: a dynamic companion circuit, a node admittance matrix, and an injection current vector of the DC power system;
s5, obtaining a node voltage equation of the direct current power system, wherein a voltage model of a node is GU = I, U represents a node voltage phasor, G represents a temporary admittance matrix at the moment t, and I represents a temporary injection current vector at the moment t;
s6, updating the node admittance matrix and the injection current vector according to the change condition of the switching function of the converter station;
and S7, converting the dynamic phasor output by the model of the direct current power system into an instantaneous value as a random dynamic analysis result of the direct current power system.
2. The method according to claim 1, wherein step S1 comprises:
the direct current power system parameters include: circuit nodes, circuit element parameters and converter station parameters in the direct current power system;
the initial parameters include: time T, step length delta T, total duration T, initial value of injection current vector and dynamic phasor order k, wherein:
t =0 at the initial time;
and k belongs to N, when k =0, the direct current quantity of the system is analyzed, and when k ≠ 0, the k-order harmonic of the direct current power system is analyzed.
3. The method according to claim 1, wherein the step S2 comprises:
determining a parameter migration element and a deterministic element in the direct current power system, wherein the element belongs to the deterministic element if the parameter of the element is fixed, and the element belongs to the parameter migration element if the parameter of the element is time-varying;
differential modeling is carried out on the deterministic element by adopting an implicit trapezoidal method, and differential modeling is carried out on the parameter migration element by adopting a Milstein format;
respectively obtaining a dynamic accompanying circuit in the form of a dynamic phasor of a parameter migration lumped element and an accompanying circuit in the form of a dynamic phasor of a deterministic lumped element by using the modeling results of the deterministic element and the parameter migration element, wherein the types of the lumped element comprise: resistance, capacitance and inductance.
4. The method according to claim 1, wherein the step S3 comprises:
establishing a switching function model of the converter station, and converting the switching function model into a dynamic phasor model of the converter station;
and carrying out differential modeling on a parameter migration element and a deterministic element in the dynamic phasor model of the converter station by respectively adopting an implicit trapezoidal method and a Milstein format to obtain a dynamic accompanying circuit in the dynamic phasor form of the converter station.
5. A method according to claim 3, characterized in that the accompanying circuit in the form of a dynamic phasor of a deterministic lumped element is:
Figure FDA0003754630120000031
Figure FDA0003754630120000032
the equivalent admittance of the RL branch is indicated,
Figure FDA0003754630120000033
the method comprises the steps that k-order dynamic phasor of RL branch voltage at n moment is shown, n represents t moment, and k represents the order of the dynamic phasor;
Figure FDA0003754630120000034
is the historical current source for the RL leg.
6. The method of claim 5, comprising:
Figure FDA0003754630120000035
Figure FDA0003754630120000036
the equivalent admittance of the RL branch is indicated,
Figure FDA0003754630120000037
representing the dynamic phasor of order k of the inductor voltage at the instant n-1, j representing the unit of a complex number, L representing the deterministic inductance, RRepresenting deterministic resistance, at represents a time step, ω s Representing angular frequency.
7. The method of claim 3, wherein the dynamic companion circuit in the form of a dynamic phasor for the parameter migration lumped element is:
Figure FDA0003754630120000038
Figure FDA0003754630120000039
and
Figure FDA00037546301200000310
respectively the voltage of the inductor and the voltage of the capacitor,
Figure FDA00037546301200000311
and
Figure FDA00037546301200000312
respectively the equivalent admittance of the random mobility inductance and capacitance,
Figure FDA00037546301200000313
and
Figure FDA00037546301200000314
historical current sources of random transfer inductance and capacitance, respectively;
Figure FDA00037546301200000315
and
Figure FDA00037546301200000316
is a random current source for randomly migrating inductance and capacitance, n represents the time t,
Figure FDA00037546301200000317
which is representative of the inductor current,
Figure FDA00037546301200000318
representing the capacitive current.
8. The method of claim 7, comprising:
Figure FDA00037546301200000319
Figure FDA00037546301200000320
where n corresponds to time t, L n The inductance is shifted for the parameter at time t,
Figure FDA0003754630120000041
for the estimation of the parameter migration inductance at time t, α, β represent the migration process and diffusion process of the random differential equation (SDE), respectively, Δ t represents the time step, j represents the unit of the complex number, k represents the order of the dynamic phasor, ω s The angular frequency is represented by the angular frequency,
Figure FDA0003754630120000042
representing the inductor current, Δ W, at a time corresponding to t- Δ t n-1 Representing the increment at time n-1 in a standard Wiener process,
Figure FDA0003754630120000043
Figure FDA0003754630120000044
for time t parameter migration inductance estimate, C n The inductance is shifted for the parameter at time t,
Figure FDA0003754630120000045
representing the capacitor voltage at the corresponding time t-deltat.
9. The method according to claim 1, wherein step S6 comprises:
and if the switching function of the converter station changes, correcting the node admittance matrix, then calling the voltage of each node and the branch current, and updating the historical current source and the random current source of the dynamic adjoint circuit of the converter station in the form of dynamic phasor at the moment t.
10. The method of claim 9, after retrieving each node voltage and branch current stored in the system, comprising:
for the parameter migration element, updating the admittance, the random current source and the historical current source of the dynamic companion circuit in the form of the dynamic phasor of the parameter migration element, and correcting the node admittance matrix; for deterministic elements, the current sources of the companion circuits in the form of dynamic phasors of the deterministic elements are updated.
Generating row and column parameters corresponding to the node admittance matrix to be updated by using the updated admittance, the random current source and the historical current source, wherein the row and column parameters comprise a temporary admittance matrix G and a temporary injection current vector I at the time t, and t = t 0 +Δt，t 0 An initial time.
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