CN110889210B - Frequency shift transient simulation method, system, medium and device based on root matching method - Google Patents

Frequency shift transient simulation method, system, medium and device based on root matching method Download PDF

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CN110889210B
CN110889210B CN201911125899.9A CN201911125899A CN110889210B CN 110889210 B CN110889210 B CN 110889210B CN 201911125899 A CN201911125899 A CN 201911125899A CN 110889210 B CN110889210 B CN 110889210B
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frequency shift
current
transient
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CN110889210A (en
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谭镇东
宋炎侃
陈颖
于智同
黄少伟
沈沉
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Tsinghua University
Sichuan Energy Internet Research Institute EIRI Tsinghua University
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Abstract

The application relates to the transient model simulation field, and provides a frequency shift transient simulation method based on a root matching method and the like, wherein the method comprises the step of calculating a historical current item I of a root matching frequency shift transient equation of each elementh(t); and matching the historical current item I of the frequency shift transient equation according to the roots of all the elementshAnd an AC electrical system topology structure forming a network node injection current complex envelope vector In(ii) a Calculating network node voltage equation UnCalculating the node voltage complex envelope Un(ii) a Calculating the time t, wherein each element root is matched with the voltage complex envelope U (t) of the internal electric element of the frequency shift transient equation, and each element root is matched with the current complex envelope I (t) of the internal electric element of the frequency shift transient equation; t is t + delta t, if the current time t is larger than the ending time tendIf not, the historical current item is continuously calculated. The method solves the problem that the traditional frequency shift transient model is inaccurate in simulation when the electric quantity fluctuation is large, improves the simulation accuracy of the transient model, and has higher efficiency.

Description

Root matching method-based frequency shift transient simulation method, system, medium and equipment
Technical Field
The application relates to the field of transient model simulation, in particular to a frequency shift transient simulation method, system, medium and equipment based on a root matching method.
Background
In a traditional time domain simulation program, the application is widely mainly composed of an electromechanical Transient Simulation Program (TSP) and an electromagnetic transient simulation program (EMTP), wherein the two programs have respective advantages and disadvantages: the modeling of the electrical transient simulation program ignores the electromagnetic transient process with higher frequency, and the simulation is not accurate enough; the electromagnetic transient simulation program has large node matrix scale and can only adopt small step length (-50 us) for simulation, which causes low efficiency of electromagnetic transient simulation and long simulation time consumption.
With the gradual access of new energy power generation and direct current transmission technologies to the power grid, the stability of the power grid operation is facing a serious challenge. Under the influence of the access of a direct current system, a traditional alternating current power grid may contain high-frequency harmonic components, and the transient process of the traditional alternating current power grid may affect a direct current converter device, so that cascading failure is caused. Time domain simulation is the most reliable way for safety evaluation of large-scale alternating current and direct current interconnected power grids. However, as the electromechanical transient program cannot simulate the electromagnetic transient process with higher frequency, the analysis of the high-frequency harmonic component of the alternating current power grid caused by the access of a direct current system is not facilitated; electromagnetic transient simulation is difficult to be applied to simulation of a large power grid due to the problems of efficiency and time consumption.
Many scholars at home and abroad have already searched for solutions to the problems of too small step length and low efficiency of the conventional electromagnetic transient program simulation, wherein important research results comprise two methods, namely frequency shift modeling (SFA) provided by professor J. The essence of both of these conventional frequency shift analysis methods is that instantaneous bilateral real signals in the conventional electromagnetic transient simulation are converted into unilateral complex analysis signals by using hilbert transform, and the frequency spectrum is shifted to the left by a fixed frequency (generally, power frequency) by frequency shift operation. Thus, the original alternating current periodic signal is converted into an analytic complex envelope signal with lower variation frequency. The key of frequency shift modeling is that the analytic signal shifts the whole frequency spectrum to the left by omega0The maximum frequency in the frequency spectrum is reduced, so that on the premise of ensuring the simulation precision, the integral step length which is larger than that of the traditional electromagnetic transient simulation is adopted, and accurate modeling and simulation of dynamic processes of different time scales in a wide frequency domain are realized by utilizing a unified physical model and changing the simulation step length.
However, when the SFA and FAST models proposed at present are used for simulation, the simulation result is not ideal when the simulation step length is large and the complex envelope fluctuation of the electrical signal is large. The reason is that the discretization method used in model building is a trapezoidal integration method, and the numerical integration method has larger truncation error when the simulation step length is larger, so that the accuracy is lost.
Disclosure of Invention
The application provides a frequency shift transient state simulation method, system, medium and equipment based on root matching method, through improving the SFA or FAST model of traditional symmetrical alternating current power grid, utilize the root matching method to carry out the discretization to the continuous model after the frequency shift, solved traditional frequency shift transient state model and simulated inaccurate problem when the electric quantity fluctuates greatly, improved transient state model's simulation accuracy. In addition, compared with the traditional frequency shift transient analysis model, the method has higher efficiency.
The embodiment of the application is realized by the following steps:
a frequency shift transient simulation method based on a root matching method comprises the following steps:
step 1: analyzing the topological structure of the electric system of the alternating current power grid, analyzing the admittance or admittance matrix G of all root matching frequency shift transient element models in the alternating current power grid, and forming a node admittance matrix Y of the whole network according to the topological structure and the admittance matrix Gn；
Step 2: calculating historical current terms of root matching frequency shift transient equations of all elements
Figure BDA0002276810500000021
IhIs a history current term in parallel with the element admittance or admittance matrix; and further matching the historical current item I of the frequency shift transient equation according to the roots of all the elementshAnd alternating currentA gas system topology structure for forming a network node injection current complex envelope vector In(ii) a Wherein n and m are positive integers; pn、QmAre constants or constant matrices within the root matched frequency-shifted transient model; i'hIs IhThe term in (1) that is not directly related to voltage and current history quantities; u (t-k Δ t) is the voltage complex envelope of the internal electrical quantity element at the time t-k Δ t; i (t-m delta t) is the complex envelope of the element current at the time of t-k delta t; i ishIs that the corresponding node injection current source is InA part of (a); i isnIs a node injection current source of the whole network; t is the current time value, and delta t is the time stepping value;
and step 3: based on steps 1 and 2, calculating a network node voltage equation
Figure BDA0002276810500000031
Calculating node voltage complex envelope Un；
And 4, step 4: based on steps 2 and 3, calculating the internal electrical element voltage complex envelope U (t) of the frequency shift transient equation matched with each element root and the internal electrical element current complex envelope I (t) GU (t) + I of the frequency shift transient equation matched with each element root at the time th；
And 5: t is t + delta t, if the current time t is larger than the ending time tendIf so, the simulation is ended, otherwise, the step 2 is skipped. Compared with the traditional frequency shift transient analysis model, the simulation result of the scheme improves the simulation step length and has higher precision and efficiency. Whether the node voltage complex envelope U can be obtainednAnd the voltage complex envelope U (t) of the internal electric element of each element root matching the frequency shift transient equation and the current complex envelope I (t) of the internal electric element of each element root matching the frequency shift transient equation are supplemented in terms of effect.
Preferably, the calculation process of u (t) in step 4 is: and (4) calculating the internal electrical quantity element voltage complex envelope U (t) of each element root matching frequency shift transient equation based on the node voltage complex envelope Un in the step (3) and according to the element topology.
Preferably, the current complex envelope I (t) gu (t) + IhThe calculation process is as follows: matching frequency-shifted transients according to the rootAn element model G, an internal electrical component voltage complex envelope u (t), and a current complex envelope equation I (t) gu (t) + IhAnd calculating to obtain a current complex envelope I (t). Has the advantages that: the model used for analysis in this patent is a root-matched frequency-shift transient model, rather than an electromagnetic transient model used in electromagnetic transient simulation, and thus G is different. G and Y in this patentnAre complex numbers and G in the electromagnetic transient simulation program is real number.
Preferably, the historical current term I of the root matching frequency shift transient equation of each element is calculatedhThe method is calculated according to an inductance-resistance series branch transient model, and the specific calculation process is as follows:
s101: the root matching frequency shift transient component model is an inductance-resistance series branch, and the formation process of the transient model of the inductance-resistance series branch comprises the following steps:
for the inductor-resistor series branch, the frequency shift transient differential equation can be written as:
Figure BDA0002276810500000041
the root matching frequency shift transient model is as follows:
I(t)＝GU(t)+Ih(t) (12)
wherein
Figure BDA0002276810500000042
S102: according to Q in the above formulam、PnU (t), I (t) calculating the historical current term Ih，
Figure BDA0002276810500000043
Figure BDA0002276810500000046
Is constant and can be represented by formula (15, 16); i'h(t) can be represented by the formula(17) To represent
Pn＝0,n＞0 (15)
Figure BDA0002276810500000045
I′h(t)＝0 (17)
L represents inductance, R represents resistance, omegasFor the frequency-shifted angular frequency, U and I represent complex envelope signals of the voltage and current signals after frequency shifting, respectively; i (t) represents a complex envelope signal of the current signal after frequency shift at the time t; i (t-delta t) represents a complex envelope signal of the current signal after frequency shift at the moment (t-delta t); i ishAnd (t) represents a historical current item at the time t. In the scheme, the root matching frequency shift transient analysis model is improved compared with the traditional frequency shift transient analysis model, the problem that the traditional frequency shift transient model is inaccurate in simulation when the electric quantity fluctuation is large is solved, and the simulation step length can be further increased.
Preferably, the historical current term I of the root matching frequency shift transient equation of each element is calculated in the step 2hThe calculation is carried out according to a capacitance-resistance series branch transient model; the specific calculation process is as follows:
s201: the root matching frequency shift transient component model is a capacitance-resistance series branch, and the transient model forming process of the capacitance-resistance series branch comprises the following steps:
the capacitance-resistance series branch frequency shift transient differential equation can be written as:
Figure BDA0002276810500000051
the root matching frequency shift transient model of the capacitor-resistor series branch circuit is as follows:
I(t)＝GU(t)+Ih(t) (19)
wherein
Figure BDA0002276810500000052
S202: according to Q in the above formulam、PnU (t), I (t) calculating the historical current term Ih，
Figure BDA0002276810500000053
Figure BDA0002276810500000054
Is constant and can be represented by the formula (21, 22); i'h(t) may be represented by formula (23);
Figure BDA0002276810500000055
Figure BDA0002276810500000056
I′h(t)＝0 (24)
c is a capacitance value, R is a resistance value, omegasFor the frequency-shifted angular frequency, U and I represent complex envelope signals of the voltage and current signals after frequency shifting, respectively; u (t-delta t) represents a complex envelope signal of the voltage signal after frequency shift at the time (t-delta t); i (t) represents a complex envelope signal of the current signal after frequency shift at the time t; i ishAnd (t) represents a historical current item at the time t. Compared with an electromagnetic transient simulation model using a root matching method, the root matching frequency shift transient model in the scheme solves the problem that partial models (including pure inductance, pure capacitance and the like) cannot be modeled, and the root matching frequency shift transient model is far more accurate in simulation of an alternating current system than the root matching electromagnetic transient model.
Preferably, the historical current term I of the root matching frequency shift transient equation of each element is calculatedhCalculated according to a single-phase transformer transient model; the specific calculation process is as follows:
s301: the root matching frequency shift transient component model is a single-phase transformer, and the transient model forming process of the single-phase transformer comprises the following steps:
the electromagnetic transient equation of a single-phase transformer can be written as:
Figure BDA0002276810500000061
the single-phase transformer root matching frequency shift transient discretization model comprises the following steps:
I(t)＝GU(t)+Ih(t) (26)
wherein:
Figure BDA0002276810500000062
s302: according to Q in the above formulam、PnU (t), I (t) calculating the historical current term Ih，
Figure BDA0002276810500000063
Figure BDA0002276810500000068
Is a constant matrix, and can be represented by equation (29, 30); i'h(t) may be represented by formula (31);
Figure BDA0002276810500000065
Figure BDA0002276810500000066
Figure BDA0002276810500000067
H[]is a Hilbert (Hilbert) transform; k is the transformation ratio of the single-phase transformer; r is1And R2The resistance values of the primary side and the secondary side of the transformer, LsIn order to have an inductance value reduced to the primary side,Rs＝R1+k2R2，Ls＝L1+k2L2，L1and L2Leakage inductances of the primary side and the secondary side of the transformer respectively; I.C. A1，I2Is a frequency-shifted complex envelope u of the primary and secondary side currents1，u2Is the instantaneous value of primary and secondary side voltages of a single-phase transformer i1，i2The instantaneous value of the primary side current and the secondary side current of the single-phase transformer.
Preferably, the historical current term I of the root matching frequency shift transient equation of each element is calculatedhCalculated from a single-phase voltage source transient model; the specific calculation process is as follows:
s401: the root matching frequency shift transient component model is a single-phase voltage source, and the forming process of the transient model of the single-phase voltage source is as follows:
for a single-phase voltage source, the current-voltage relationship can be written as:
u+Ri＝U0cos(ωt+φ) (32)
the single-phase voltage source root matching frequency shift transient discretization model comprises the following steps:
I(t)＝-GU(t)+Ih(t) (33)
wherein
Figure BDA0002276810500000071
S402: according to Q in the above formulam、PnU (t), I (t) calculating the historical current term Ih
Figure BDA0002276810500000072
Figure BDA0002276810500000073
Is constant and can be represented by the formula (36, 37); i'h(t) may be represented by formula (38);
Pn＝0,n＞0 (36)
Qm＝0,m＞0 (37)
Figure BDA0002276810500000074
U0the amplitude of the open circuit voltage of the voltage source is shown as omega, the frequency of the voltage source is shown as phi, the initial phase angle is shown as phi, i represents the instantaneous value of the current of the element branch, u represents the instantaneous value of the voltage of the element branch, and R represents the resistance value.
A frequency shift transient simulation system based on a root matching method comprises:
a node admittance matrix forming module: the method is used for analyzing the topological structure of the electric system of the alternating current power grid, analyzing the admittance or admittance matrix G of all root matching frequency shift transient element models in the alternating current power grid, and forming a node admittance matrix Y of the whole network according to the topological structure and the admittance matrix Gn；
A network node injection current complex envelope vector forming module for calculating the historical current item of the root matching frequency shift transient equation of each element
Figure BDA0002276810500000081
IhIs a history current term in parallel with the element admittance or admittance matrix; and further matching the historical current item I of the frequency shift transient equation according to the roots of all the elementshAnd an AC electrical system topology structure forming a network node injection current complex envelope vector In(ii) a Wherein n and m are positive integers; pn、QmAre constants or constant matrices within the root matched frequency-shifted transient model; i'hIs IhThe term in (1) that is not directly related to voltage and current history quantities; u (t-k Δ t) is the voltage complex envelope of the internal electrical quantity element at the time t-k Δ t; i (t-m delta t) is the complex envelope of the element current at the time of t-k delta t; I.C. AhIs that the corresponding node injection current source is InA part of (a); i isnIs a node injection current source of the whole network; t is the current time value, and delta t is the time stepping value;
a node voltage complex envelope forming module: node-based admittance matrix module andthe network node injection current complex envelope vector module calculates a network node voltage equation YnUn＝InCalculating the node voltage complex envelope Un；
A voltage-current complex envelope forming module: based on a node admittance matrix forming module and a network node injection current complex envelope vector module, calculating the time t, wherein the voltage complex envelope U (t) of the internal electric quantity element of each element root matched with the frequency shift transient equation, and the current complex envelope I (t) of the internal electric quantity element of each element root matched with the frequency shift transient equation GU (t) + Ih(ii) a When t is t + delta t, if the current time t is greater than the ending time tendIf not, the network node injection current complex envelope vector forming module calculates the network node injection current complex envelope vector.
A computer-readable storage medium stores a computer program. The computer-readable storage medium has stored thereon a computer program which, when being executed by a processor, implements the steps of the root matching method-based frequency shift transient simulation method according to any one of the above schemes 1 to 7.
A frequency shift transient simulation device based on a root matching method comprises: a memory for storing a computer program; a processor, configured to implement the steps of the root matching method-based frequency shift transient simulation method according to any one of the above schemes 1 to 7 when executing the computer program.
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In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings that are required to be used in the embodiments of the present application will be briefly described below, it should be understood that the following drawings only illustrate some embodiments of the present application and therefore should not be considered as limiting the scope, and that those skilled in the art can also obtain other related drawings based on the drawings without inventive efforts.
Fig. 1 is a flowchart of a frequency shift transient simulation method according to an embodiment of the present disclosure.
Detailed Description
The technical solution in the embodiments of the present application will be described below with reference to the drawings in the embodiments of the present application.
Description of related Art:
1. g and Y in step 1nThe matrix is a complex matrix (for example, G matrix in four root matching frequency shift transient models listed in the patent, which refers to an inductance-resistance series branch transient model, a capacitance-resistance series branch transient model, a single-phase transformer transient model, and a single-phase voltage source transient model), whereas in the prior art (electromagnetic transient simulation program), G matrix is a real matrix. This step is therefore different from the prior art. And Y is generated from GnThe method (2) is the existing technical scheme. In step 4, G is a complex matrix (e.g., G enumerating several models), and IhIs the I obtained in step 2h. And is therefore not an existing solution. Wherein, G in the electromagnetic transient simulation program is a real number.
2. "matching the historical current term I of the frequency-shifted transient equation according to the root of each elementhAnd an AC electrical system topology structure forming a network node injection current complex envelope vector In"is a process that can be implemented by the prior art.
The algorithm process of the invention, referring to fig. 1, includes:
step 1: analyzing the topological structure of the electric system of the alternating current power grid, analyzing the admittance or admittance matrix G of all root matching frequency shift transient element models in the alternating current power grid, and forming a node admittance matrix Y of the whole network according to the topological structure and the admittance matrix Gn；
Step 2: calculating historical current terms of root matching frequency shift transient equations of all elements
Figure BDA0002276810500000101
IhIs a history current term in parallel with the element admittance or admittance matrix; and further matching the historical current item I of the frequency shift transient equation according to the roots of all the elementshAnd an AC electrical system topology structure forming a network node injection current complex envelope vector In(ii) a Wherein n and m are positive integers; pn、QmAre all root matched frequency shift transient element modesA constant or matrix of constants within a type; i'hIs IhThe term in (1) that is not directly related to voltage and current history quantities; u (t-k Δ t) is the voltage complex envelope of the internal electrical quantity element at the time t-k Δ t; i (t-m delta t) is the complex envelope of the element current at the time of t-k delta t; i ishIs that the corresponding node injection current source is InA part of (a); i isnIs a node injection current source of the whole network; t is the current time value, and delta t is the time stepping value;
and step 3: based on steps 1 and 2, calculating a network node voltage equation
Figure BDA0002276810500000102
Solving node voltage complex envelope Un；
And 4, step 4: based on steps 2 and 3, calculating the internal electrical element voltage complex envelope U (t) of the frequency shift transient equation matched with each element root and the internal electrical element current complex envelope I (t) GU (t) + I of the frequency shift transient equation matched with each element root at the time th；
And 5: t is t + delta t, if the current time t is larger than the ending time tendIf so, the simulation is ended, otherwise, the step 2 is skipped.
In order to detail the frequency shift transient simulation method disclosed in the above embodiment, the calculation process of the internal electrical component voltage complex envelope u (t) is as follows: node voltage complex envelope U based on step 3nAnd calculating the voltage complex envelope U (t) of the internal electrical quantity element of each element root matching frequency shift transient equation according to the element topology.
In order to detail the frequency shift transient simulation method disclosed in the above embodiment, the current complex envelope i (t) ═ gu (t) + Ih calculation process is: according to the root matching frequency shift transient component model G, the internal electrical component voltage complex envelope U (t) and the current complex envelope equation I (t) GU (t) + IhAnd calculating to obtain a current complex envelope I (t).
In order to detail the frequency shift transient simulation method disclosed in the above embodiment, the G refers to G in the following four embodiments
The first embodiment is as follows: for a specific inductance resistance model, the frequency shift transient simulation method based on the tracking matching method specifically realizes the following steps:
step 1011: analyzing the topological structure of the electric system of the alternating current power grid, analyzing the admittance or admittance matrix G of all root matching frequency shift transient component models in the alternating current power grid, and forming a node admittance matrix Y of the whole network according to the topological structure and the admittance matrix Gn；
Step 1012: calculating historical current terms of root matching frequency shift transient equations of all elements
Figure BDA0002276810500000111
The specific calculation process is as follows:
step 10121: the root matching frequency shift transient component model is an inductance-resistance series branch, and the formation process of the transient model of the inductance-resistance series branch comprises the following steps:
for the inductor-resistor series branch, the frequency shift transient differential equation can be written as:
Figure BDA0002276810500000112
the root matching frequency shift transient model is as follows:
I(t)＝GU(t)+Ih(t) (12)
wherein
Figure BDA0002276810500000113
Step 10122: according to Q in the above formulam、PnU (t), I (t) calculating the historical current term Ih，
Figure BDA0002276810500000121
Figure BDA0002276810500000122
Is constant and can be represented by formula (15, 16); i'h(t) may be represented by formula (17)
Pn＝0,n＞0 (15)
Figure BDA0002276810500000123
I′h(t)＝0 (17)
L represents inductance, R represents resistance, omegasFor the frequency-shifted angular frequency, U and I represent complex envelope signals of the voltage and current signals after frequency shifting, respectively; i (t) represents a complex envelope signal of the current signal after frequency shift at the time t; i (t-delta t) represents a complex envelope signal of the current signal after frequency shift at the time (t-delta t); i ish(t) represents time t, historical current term;
step 1013: according to the historical current item I of the root matching frequency shift transient equation of each element of the inductance-resistance series branchhAnd an AC electrical system topology structure forming a network node injection current complex envelope vector In；
Step 1014: based on steps 1011, 1012 and 1013, the voltage equation of the network node of the inductor-resistor series branch is calculated
Figure BDA0002276810500000124
Calculating node voltage complex envelope Un；
Step 1015: based on steps 1012, 1013 and 1014, at time t, an internal electrical element voltage complex envelope u (t) of the inductor-resistor series branch whose element root matches the frequency shift transient equation, and an internal electrical element current complex envelope I (t) of the inductor-resistor series branch whose element root matches the frequency shift transient equation are calculatedh；
Step 1016: t is t + delta t, if the current time t is larger than the ending time tendThe simulation is ended, otherwise it jumps back to step 1012.
Example two: for a specific transient model of a capacitor-resistor series branch, the frequency shift transient simulation method based on the tracking matching method specifically realizes the following steps:
step 2011: analyzing the topology of the electrical system of the AC grid and analyzing the premises in the AC gridMatching the admittance or admittance matrix G of the frequency shift transient element model with the root, and forming a node admittance matrix Y of the whole network according to the topological structure and the admittance matrix Gn；
Step 2012: calculating historical current items of root matching frequency shift transient equations of each element of capacitor-resistor series branch
Figure BDA0002276810500000131
The specific calculation process is as follows:
step 20121: the root matching frequency shift transient component model is a capacitance-resistance series branch, and the transient model forming process of the capacitance-resistance series branch comprises the following steps:
the capacitance-resistance series branch frequency shift transient differential equation can be written as:
Figure BDA0002276810500000132
the root matching frequency shift transient model of the capacitor-resistor series branch circuit is as follows:
I(t)＝GU(t)+Ih(t) (19)
wherein
Figure BDA0002276810500000133
Step 20122: according to Q in the above formulam、PnU (t), I (t) calculating the historical current term Ih，
Figure BDA0002276810500000134
Figure BDA0002276810500000135
Is constant and can be represented by the formula (21, 22); i'h(t) may be represented by formula (23);
Figure BDA0002276810500000136
Figure BDA0002276810500000137
I′h(t)＝0 (24)
c is a capacitance value, R is a resistance value, omegasFor the angular frequency of the frequency shift, U and I represent the complex envelope signals of the voltage and current signals after the frequency shift, respectively; u (t-delta t) represents a complex envelope signal of the voltage signal after frequency shift at the moment (t-delta t); i (t) represents a complex envelope signal of the current signal after frequency shift at the time t; i ish(t) represents time t, historical current term;
step 2013: according to the historical current item I of the root matching frequency shift transient equation of each element of the capacitor-resistor series branchhAnd an AC electrical system topology structure forming a network node injection current complex envelope vector In；
Step 2014: calculating a capacitance-resistance series branch network node voltage equation based on the steps 2011, 2012 and 2013
Figure BDA0002276810500000141
Calculating node voltage complex envelope Un；
Step 2015: based on steps 2012, 2013 and 2014, calculating the internal electrical component voltage complex envelope u (t) of the capacitance-resistance series branch whose element root matches the frequency shift transient equation and the internal electrical component current complex envelope I (t) of the capacitance-resistance series branch whose element root matches the frequency shift transient equation at time th；
Step 2016: t is t + delta t, if the current time t is larger than the ending time tendThe simulation ends, otherwise it jumps back to step 2012.
Example three: for a specific single-phase transformer transient model, the frequency shift transient simulation method based on the tracking matching method specifically realizes the following steps:
step 3011: analyzing the topology of the electrical system of the AC grid and analyzing the topology of the AC gridAll the root matching frequency shift transient component models are subjected to admittance or admittance matrix G, and a node admittance matrix Y of the whole network is formed according to the topological structure and the admittance matrix Gn；
Step 3012: calculating historical current items of root matching frequency shift transient equations of each element of single-phase transformer
Figure BDA0002276810500000142
The specific calculation process is as follows:
s30121: the root matching frequency shift transient component model is a single-phase transformer, and the transient model forming process of the single-phase transformer comprises the following steps:
the electromagnetic transient equation of a single-phase transformer can be written as:
Figure BDA0002276810500000151
the single-phase transformer root matching frequency shift transient discretization model comprises the following steps:
I(t)＝GU(t)+Ih(t) (26)
wherein:
Figure BDA0002276810500000152
s30122: according to Q in the above formulam、PnU (t), I (t) calculating the historical current term Ih，
Figure BDA0002276810500000153
Figure BDA0002276810500000154
Is a constant matrix, and can be represented by equation (29, 30); i'h(t) may be represented by formula (31);
Figure BDA0002276810500000155
Figure BDA0002276810500000156
Figure BDA0002276810500000157
H[]is a Hilbert (Hilbert) transform; k is the transformation ratio of the single-phase transformer; r1And R2The resistance values of the primary and secondary sides of the transformer, respectively, Ls being the inductance value reduced to the primary side, Rs＝R1+k2R2，Ls＝L1+k2L2，L1And L2Leakage inductances of the primary side and the secondary side of the transformer respectively; i is1，I2Is a frequency-shifted complex envelope u of the primary and secondary side currents1，u2Is the instantaneous value of primary and secondary side voltages of a single-phase transformer i1，i2The instantaneous values of primary and secondary side currents of the single-phase transformer are obtained;
step 3013: matching historical current item I of frequency shift transient equation according to roots of each element of single-phase transformerhAnd an AC electrical system topology structure forming a network node injection current complex envelope vector In；
Step 3014: based on steps 3011, 3012, and 3013, a voltage equation of the network node of the single-phase transformer is calculated
Figure BDA0002276810500000161
Calculating node voltage complex envelope Un；
Step 3015: based on steps 3012, 3013 and 3014, at time t, the internal electrical component voltage complex envelope u (t) of the transient frequency-shift equation for each component root of the single-phase transformer and the internal electrical component current complex envelope I (t) ═ gu (t) + I of the transient frequency-shift equation for each component root of the single-phase transformer are calculatedh；
Step 3016: t is t + delta t, if the current time t is larger than the ending time tendIf yes, the simulation is ended, otherwiseJumping back to step 3012.
Example four: aiming at a specific single-phase voltage source transient model, the frequency shift transient simulation method based on the following matching method is specifically implemented by the following steps:
step 4011: analyzing the topological structure of the electric system of the alternating current power grid, analyzing the admittance or admittance matrix G of all root matching frequency shift transient component models in the alternating current power grid, and forming a node admittance matrix Y of the whole network according to the topological structure and the admittance matrix Gn；
Step 4012: calculating historical current items of root matching frequency shift transient equations of each element of single-phase voltage source
Figure BDA0002276810500000162
The specific calculation process is as follows:
step S40121: the root matching frequency shift transient component model is a single-phase voltage source, and the forming process of the transient model of the single-phase voltage source is as follows:
for a single-phase voltage source, the current-voltage relationship can be written as:
u+Ri＝U0cos(ωt+φ) (32)
the single-phase voltage source root matching frequency shift transient discretization model comprises the following steps:
I(t)＝-GU(t)+Ih(t) (33)
wherein
Figure BDA0002276810500000163
Step S40122: according to Q in the above formulam、PnU (t), I (t) calculating the historical current term Ih
Figure BDA0002276810500000171
Figure BDA0002276810500000172
Is constant and can be represented by the formula (36,37)Shown in the specification; i'h(t) may be represented by formula (38);
Pn＝0,n＞0 (36)
Qm＝0,m＞0 (37)
Figure BDA0002276810500000173
U0the method comprises the steps that the amplitude of a voltage source open circuit voltage is shown, omega is the frequency of the voltage source, phi is an initial phase angle, i represents an element branch current instantaneous value, u represents an element branch voltage instantaneous value, and R represents a resistance value;
step 4013: matching historical current item I of frequency shift transient equation according to roots of elements of single-phase voltage sourcehAnd an AC electrical system topology structure forming a network node injection current complex envelope vector In；
Step 4014: based on the steps 4011, 4012 and 4013, calculating a voltage equation of the single-phase voltage source network node
Figure BDA0002276810500000174
Calculating node voltage complex envelope Un；
Step 4015: based on steps 4012, 4013 and 4014, at time t, the internal electrical component voltage complex envelope u (t) of the frequency shift transient equation matched with each component root of the single-phase voltage source and the internal electrical component current complex envelope I (t) ═ gu (t) + I of the frequency shift transient equation matched with each component root of the single-phase voltage source are calculatedh；
Step 4016: t is t + delta t, if the current time t is larger than the ending time tendThe simulation is finished, otherwise, the process goes back to step 4012.
The above description is only an example of the present application and is not intended to limit the scope of the present application, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, improvement and the like made within the spirit and principle of the present application shall be included in the protection scope of the present application. It should be noted that: like reference numbers and letters refer to like items in the following figures, and thus, once an item is defined in one figure, it need not be further defined and explained in subsequent figures.
The above description is only for the specific embodiments of the present application, but the scope of the present application is not limited thereto, and any person skilled in the art can easily think of the changes or substitutions within the technical scope of the present application, and shall be covered by the scope of the present application. Therefore, the protection scope of the present application shall be subject to the protection scope of the claims.
It is noted that, herein, relational terms such as first and second, and the like may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other identical elements in a process, method, article, or apparatus that comprises the element.

Claims (10)

1. A frequency shift transient simulation method based on a root matching method is characterized in that:
step 1: analyzing the topological structure of the electric system of the alternating current power grid, analyzing the admittance or admittance matrix G of all root matching frequency shift transient element models in the alternating current power grid, and forming a node admittance matrix Y of the whole network according to the topological structure and the admittance matrix Gn；
Step 2: calculating historical current terms of root matching frequency shift transient equations of all elements
Figure FDA0003610656500000011
And according toHistorical current item I of root matching frequency shift transient equation of each elementh(t) and an AC electrical system topology structure, forming a network node injection current complex envelope vector I at time tn(t)；
And step 3: based on steps 1 and 2, calculating a network node voltage equation
Figure FDA0003610656500000012
Solving node voltage complex envelope Un(t)；
And 4, step 4: based on steps 2 and 3, calculating the internal electric quantity element voltage complex envelope U (t) of each element root matched with the frequency shift transient equation at the time t, and the internal electric quantity element current complex envelope I (t) GU (t) + I of each element root matched with the frequency shift transient equationh(t)；
And 5: t is t + delta t, if the current time t is larger than the ending time tendIf so, the simulation is ended, otherwise, the step 2 is skipped.
2. The simulation method according to claim 1, wherein the calculation process of u (t) in step 4 is: node voltage complex envelope U based on step 3nAnd (t) calculating the voltage complex envelope U (t) of the internal electrical element of each element root matching frequency shift transient equation according to the element topology.
3. Simulation method according to claim 1, characterized in that the current complex envelope I (t) gu (t) + Ih(t) the calculation procedure is: according to the admittance or admittance matrix G of the root matching frequency shift transient component model, the internal electrical component voltage complex envelope U (t) and the current complex envelope equation I (t) GU (t) + Ih(t), calculating to obtain a current complex envelope I (t).
4. Simulation method according to one of the claims 1 to 3, characterized in that the calculation of the historical current term I of the root matched frequency-shifted transient equation of each elementh(t) calculating according to the transient model of the inductance-resistance series branch, wherein the specific calculation process is as follows:
s101: the root matching frequency shift transient component model is an inductance-resistance series branch, and the transient model forming process of the inductance-resistance series branch comprises the following steps:
for the inductor-resistor series branch, the frequency shift transient differential equation can be written as:
Figure FDA0003610656500000021
the root matching frequency shift transient model is as follows:
I(t)＝GU(t)+Ih(t) (12)
wherein
Figure FDA0003610656500000022
S102: according to Q in the above formulam、PnU (t), I (t) calculating the historical current term Ih(t)，
Figure FDA0003610656500000023
Pn，QmIs constant and can be represented by formula (15, 16); i'h(t) can be represented by formula (17)
Figure FDA0003610656500000024
Figure FDA0003610656500000025
I′h(t)＝0 (17)
L represents inductance, R represents resistance, omegasFor the frequency-shifted angular frequency, u (t) and i (t) represent the complex envelope signals of the voltage and current signals after frequency shifting, respectively; i (t) represents the complex envelope of the current signal after frequency shift at time tA signal; i (t-delta t) represents a complex envelope signal of the current signal after frequency shift at the moment (t-delta t); i ishAnd (t) represents a historical current item at the time t.
5. Simulation method according to one of the claims 1 to 3, characterized in that in step 2 the historical current term I of the root matched frequency-shift transient equation of each element is calculatedh(t) calculated from the capacitance-resistance series branch transient model; the specific calculation process is as follows:
s201: the root matching frequency shift transient component model is a capacitance-resistance series branch, and the transient model forming process of the capacitance-resistance series branch comprises the following steps:
the capacitance-resistance series branch frequency shift transient differential equation can be written as:
Figure FDA0003610656500000031
the root matching frequency shift transient model of the capacitor-resistor series branch circuit is as follows:
I(t)＝GU(t)+Ih(t) (19)
wherein
Figure FDA0003610656500000032
S202: according to Q in the above formulam、PnU (t), I (t) calculating the historical current term Ih(t)，
Figure FDA0003610656500000033
Pn，QmIs constant and can be represented by the formula (21, 22); i'h(t) may be represented by formula (23);
Figure FDA0003610656500000034
Figure FDA0003610656500000041
I′h(t)＝0 (24)
c is a capacitance value, R is a resistance value, omegasFor the frequency-shifted angular frequency, u (t) and i (t) represent the complex envelope signals of the voltage and current signals after frequency shifting, respectively; u (t-delta t) represents a complex envelope signal of the voltage signal after frequency shift at the time (t-delta t); i (t) represents a complex envelope signal of the current signal after frequency shift at the time t; i ishAnd (t) represents a historical current item at the time t.
6. Simulation method according to one of the claims 1 to 3, characterized in that the calculation of the historical current term I of the root matched frequency-shifted transient equation of each elementh(t) calculated from a single-phase transformer transient model; the specific calculation process is as follows:
s301: the root matching frequency shift transient component model is a single-phase transformer, and the transient model forming process of the single-phase transformer comprises the following steps:
the electromagnetic transient equation of a single-phase transformer can be written as:
Figure FDA0003610656500000042
the single-phase transformer root matching frequency shift transient discretization model comprises the following steps:
I(t)＝GU(t)+Ih(t) (26)
wherein:
Figure FDA0003610656500000043
s302: according to Q in the above formulam、PnU (t), I (t) calculating the historical current term Ih，
Figure FDA0003610656500000044
Pn，QmIs a constant matrix, and can be represented by equation (29, 30); i'h(t) may be represented by formula (31);
Figure FDA0003610656500000051
Figure FDA0003610656500000052
Figure FDA0003610656500000053
H[]is a Hilbert (Hilbert) transform; k is the transformation ratio of the single-phase transformer; r1And R2The resistance values of the primary side and the secondary side of the transformer, LsTo a value of inductance, R, reduced to the primary sides＝R1+k2R2，Ls＝L1+k2L2，L1And L2Leakage inductances of the primary side and the secondary side of the transformer respectively; u. of1，u2Is the instantaneous value of primary and secondary side voltages of a single-phase transformer i1(t)，i2And (t) is the instantaneous value of the primary side current and the secondary side current of the single-phase transformer.
7. Simulation method according to one of the claims 1 to 3, characterized in that the calculation of the historical current term I of the root matched frequency-shifted transient equation of each elementh(t) calculated from a single-phase voltage source transient model; the specific calculation process is as follows:
s401: the root matching frequency shift transient component model is a single-phase voltage source, and the forming process of the transient model of the single-phase voltage source is as follows:
for a single-phase voltage source, the current-voltage relationship can be written as:
u(t)+Ri(t)＝U0coS(ωt+φ) (32)
the single-phase voltage source root matching frequency shift transient discretization model comprises the following steps:
I(t)＝-GU(t)+Ih(t) (33)
wherein
Figure FDA0003610656500000054
S402: according to Q in the above formulam、PnU (t), I (t) calculating the historical current term Ih(t)，
Figure FDA0003610656500000061
Pn，QmIs constant and can be represented by the formula (36, 37); i'h(t) may be represented by formula (38);
Figure FDA0003610656500000062
Figure FDA0003610656500000063
Figure FDA0003610656500000064
U0the amplitude of the open circuit voltage of the voltage source is shown, omega is the frequency of the voltage source, phi is the initial phase angle, i (t) represents the instantaneous value of the current of the component branch, u (t) represents the instantaneous value of the voltage of the component branch, and R represents the resistance value.
8. A frequency shift transient simulation system based on a root matching method is characterized in that:
a node admittance matrix forming module: the method is used for analyzing the topological structure of the electric system of the alternating current power grid, analyzing the admittance or admittance matrix G of all root matching frequency shift transient element models in the alternating current power grid, and forming a node admittance matrix Y of the whole network according to the topological structure and the admittance matrix Gn；
A network node injection current complex envelope vector forming module for calculating the historical current item of the root matching frequency shift transient equation of each element
Figure FDA0003610656500000065
Ih(t) is a history current term in parallel with the element admittance or admittance matrix; and further matching the historical current item I of the frequency shift transient equation according to the roots of all the elementsh(t) and an AC electrical system topology forming a network node injection current complex envelope vector In(t); wherein n and m are positive integers; pn、QmAre constants or constant matrices in the root matched frequency shift transient model; i'h(t) is Ih(t) entries not directly related to voltage, current history; u (t-n Δ t) is the voltage complex envelope of the internal electrical quantity element at the time of t-n Δ t; i (t-m delta t) is the complex envelope of the element current at the time of t-m delta t; i ish(t) is that the corresponding node injection current source is InA portion of (t); i isn(t) is the node injection current source of the entire network; t is the current time value, and delta t is the time stepping value;
a node voltage complex envelope forming module: calculating a network node voltage equation Y based on a node admittance matrix module and a network node injection current complex envelope vector modulenUn(t)＝In(t) obtaining a node voltage complex envelope Un(t)；
A voltage-current complex envelope forming module: based on a node admittance matrix forming module and a network node injection current complex envelope vector module, calculating the time t, wherein the voltage complex envelope U (t) of the internal electric quantity element of each element root matched with the frequency shift transient equation, and the current complex envelope I (t) of the internal electric quantity element of each element root matched with the frequency shift transient equation GU (t) + Ih(t); when t is t + delta t, if the current time t is greater than the ending time tendIf not, the network node injection current complex envelope vector forming module calculates the network node injection current complex envelope vector.
9. A computer-readable storage medium, characterized in that a computer program is stored on the computer-readable storage medium, which computer program, when being executed by a processor, carries out the steps of the root matching method-based frequency shift transient simulation method according to any one of claims 1 to 7.
10. A frequency shift transient simulation device based on a root matching method is characterized by comprising: a memory for storing a computer program; a processor for implementing the steps of the root matching method based frequency shift transient simulation method according to any of claims 1 to 7 when executing the computer program.
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