CN110362937B - Electromagnetic transient simulation method and system for modular multilevel converter - Google Patents
Electromagnetic transient simulation method and system for modular multilevel converter Download PDFInfo
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Abstract
The invention discloses an electromagnetic transient simulation method and system for a modular multilevel converter, and relates to the field of power systems. The method comprises the following steps: acquiring an electrical signal; obtaining a sub-band dynamic vector of the electrical complex signal through the electrical signal; obtaining a coefficient of a switching function model of the modular multilevel converter through a topological structure of the modular multilevel converter; obtaining a multi-band dynamic phasor model according to the switching function model and the sub-band dynamic vector; and obtaining the real voltage and current through a multi-band dynamic phasor model. According to the electromagnetic transient simulation method and system for the modular multilevel converter, a switching function model is obtained through calculation by a multi-band dynamic phasor method and is used for electromagnetic transient simulation; meanwhile, as the dynamic phasor of the sub-frequency band is a signal with a bandwidth meeting a narrow-band condition, the simulation speed can be improved by adopting large-step simulation, so that the electromagnetic transient simulation method and system of the modular multilevel converter can effectively give consideration to both simulation efficiency and precision.
Description
Technical Field
The invention relates to the field of power systems, in particular to an electromagnetic transient simulation method and system for a modular multilevel converter.
Background
For the power system, electromagnetic transient is the most important system analysis means, but as power electronic equipment is applied in the power system, electromagnetic transient simulation faces contradiction between simulation speed and simulation precision, so people continuously improve electromagnetic transient models and simulation algorithms of each element of the power system. Modular Multilevel Converters (MMC) have become the most promising power electronic technology and equipment today due to the advantages of small distortion, low switching loss, flexible control, and the like. In the existing electromagnetic transient simulation, an MMC adopts a detailed model, the precise change of a high-frequency switch can be captured only through small-step simulation, and a system admittance matrix needs to be updated when each switch acts. Along with the increase of the number of MMC sub-modules and the expansion of simulation scale, the MMC detailed model brings great simulation burden, and the simulation speed is rapidly reduced. Aiming at the problems of large calculation scale and slow simulation speed of the MMC detailed model, a plurality of improved models are proposed at present: (1) MMC Thevenin equivalent model: the Thevenin equivalent principle is introduced into the MMC bridge arm modeling process to realize the order reduction of the system admittance matrix, and the nested fast synchronous solving algorithm is adopted to optimize the admittance matrix solving process, so that the aim of improving the simulation speed is fulfilled. Although the dynamic condition of the sub-module can be simulated based on the Davinan equivalent MMC model, the change moment of the high-frequency switch can be accurately captured only by a small step length, so that the simulation step length is sharply reduced and the simulation complexity and the simulation time are sharply increased along with the increase of the level number of the MMC. (2) MMC average value model: the method is mainly characterized in that modeling details of the sub-modules are omitted, dynamic average response of the converter and the controller is expressed by using a controlled source and a simplified control function, and external characteristics of the MMC system are further simulated. On the MMC external characteristic simulation, the simulation speed of the average value model is improved, but as the Thevenin equivalent model, the change moment of the high-frequency switch can be accurately captured only by small step length, so that the simulation step length is sharply reduced along with the increase of the level number of the MMC, and the simulation complexity and the simulation time are sharply increased. (3) MMC traditional dynamic phasor model: the change moment of the high-frequency switch is not accurately captured through small step length, but with the increase of considered harmonic frequency, the number of differential equation sets of the MMC dynamic phasor model is increased sharply, the simulation scale is increased sharply, and the calculation amount is reduced by adopting a harmonic truncation mode, so that the simulation precision is lower. (4) MMC frequency migration method model: signals are analyzed by utilizing a Hilbert transform structure, power frequency is used as a main frequency shift frequency, large-step simulation is adopted after the signal frequency is reduced, but the bandwidth of the signals is limited to be close to the fundamental wave of the power frequency by the model, and the simulation precision is low. The improved models cannot effectively give consideration to both the precision and the efficiency of simulation, so that the problem that the precision and the efficiency of simulation cannot be given consideration to the existing MMC detailed model improved model exists.
Disclosure of Invention
The invention aims to provide an electromagnetic transient simulation method and system for a modular multilevel converter, and solves the problem that the simulation precision and efficiency cannot be considered at the same time.
In order to achieve the purpose, the invention provides the following scheme:
an electromagnetic transient simulation method for a modular multilevel converter comprises the following steps:
acquiring an electric signal input by the modular multilevel converter;
carrying out Fourier decomposition on the electrical signal to obtain an electrical complex signal;
dividing the electrical complex signal into a plurality of sub-bands according to signal frequency;
recombining and shifting the frequency of the electrical complex signal of each sub-frequency band to obtain a sub-frequency band dynamic vector of the electrical complex signal of the sub-frequency band;
obtaining a submodule of the modular multilevel converter through a topological structure of the modular multilevel converter;
acquiring a switching function model of the sub-module;
obtaining a switching function model of the modular multilevel converter through kirchhoff current and voltage law according to the switching function model of the sub-module and the topological structure;
acquiring an output waveform of the modular multilevel converter;
adjusting the output waveform according to a recent level modulation strategy to obtain a coefficient of a switching function model of the modular multilevel converter;
obtaining a multi-band dynamic phasor model of the modular multi-level converter according to the switching function model of the modular multi-level converter and the sub-band dynamic vector through a multi-band dynamic phasor principle;
performing electromagnetic transient simulation according to the multi-band dynamic phasor model to obtain simulation voltage and simulation current;
and sequentially carrying out reverse frequency shift, addition and real obtaining parts on the simulation voltage and the simulation current to obtain a real voltage and a real current.
Optionally, the performing fourier decomposition on the electrical signal to obtain an electrical complex signal specifically includes: fourier decomposition is carried out on the electrical signal through the following formula to obtain an electrical complex signal;
wherein X (t) represents the electrical complex signal; h represents the order of the Fourier coefficient; xh(t) denotes h-th order fourier coefficients; j represents an imaginary unit; omegasRepresenting the fundamental angular frequency, ωs＝2π/T0Where π denotes the circumference ratio, T0Represents a fundamental period of the electrical signal; t represents time.
Optionally, the recombining and frequency shifting the electrical complex signal of each sub-band to obtain a sub-band dynamic vector of the electrical complex signal of the sub-band specifically includes:
the electrical complex signals are sectionally recombined according to the following formula from small to large in frequency to obtain recombined sub-frequency band signals;
in the above formula, N represents the total number of the recombined sub-bands, N represents the serial number of the sub-band, and N is in the range of-N, N]；HnRepresenting all frequency components, H, in the first n sub-bandsn-1Representing all frequency components in the first n-1 sub-bands; omegahRepresenting the angular frequency, ω, of the h-th harmonich＝hωs；Bn(t) represents the recombined sub-band signal of the nth sub-band, i.e. the sub-band signal;
respectively carrying out frequency shift on each sub-frequency band signal according to the following formula to obtain the dynamic vector of the sub-frequency band;
in the above formula, the first and second carbon atoms are,
the dynamic vector of the electric sub-frequency band is expressed by
ωrnRepresenting the frequency shift angular frequency of the nth sub-band;
representing the upper frequency limit of the nth sub-band;
represents the lower frequency limit of the nth sub-band; b isnRepresenting the nth sub-band; f. ofhRepresenting the frequency of said sub-band signal in the nth sub-band,
optionally, the adjusting the output waveform according to the latest level modulation strategy to obtain a coefficient of a switching function model of the modular multilevel converter specifically includes:
obtaining the modulation ratio of the latest level modulation strategy;
solving the initial angle of the ith level of the output waveform according to a nearest level approximation principle and the modulation ratio;
performing Fourier decomposition on the nearest level control wave of the output waveform to obtain the sum of an upper bridge arm switching function and a lower bridge arm switching function of the modular multilevel converter;
performing Fourier decomposition on the nearest level control wave of the output waveform to obtain the difference between the upper bridge arm switching function and the lower bridge arm switching function; the difference between the sum of the upper bridge arm switching function and the lower bridge arm switching function and the upper bridge arm switching function and the lower bridge arm switching function is the coefficient of the switching function model;
and solving a kth order Fourier decomposition coefficient of the difference between the upper bridge arm switching function and the lower bridge arm switching function through the initial angle.
A modular multilevel converter electromagnetic transient simulation system comprises:
the electric signal module is used for acquiring an electric signal input by the modular multilevel converter;
the electrical complex signal module is used for carrying out Fourier decomposition on the electrical signal to obtain an electrical complex signal;
the sub-frequency band module is used for dividing the electrical complex signal into a plurality of sub-frequency bands according to signal frequency;
the frequency shift module is used for recombining and shifting the electric complex signal of each sub-frequency band to obtain a sub-frequency band dynamic vector of the electric complex signal of the sub-frequency band;
the submodule module is used for obtaining a submodule of the modular multilevel converter through a topological structure of the modular multilevel converter;
the sub-module switch function model module is used for acquiring a switch function model of the sub-module;
the switching function model module is used for obtaining a switching function model of the modular multilevel converter through kirchhoff current and voltage law according to the switching function model of the sub-module and the topological structure;
the output waveform module is used for acquiring the output waveform of the modular multilevel converter;
the switching function model coefficient module is used for adjusting the output waveform according to a recent level modulation strategy to obtain the coefficient of the switching function model of the modular multilevel converter;
the multi-band dynamic phasor model module is used for obtaining a multi-band dynamic phasor model of the modular multi-level converter according to the switching function model of the modular multi-level converter and the sub-band dynamic vectors through a multi-band dynamic phasor principle;
the simulation module is used for performing electromagnetic transient simulation according to the multi-band dynamic phasor model to obtain simulation voltage and simulation current;
and the real module is used for sequentially carrying out reverse frequency shift, addition and real obtaining parts on the simulation voltage and the simulation current to obtain the real voltage and the real current.
Optionally, the electrical complex signal module specifically includes:
an electrical complex signal unit for performing fourier decomposition on the electrical signal by the following formula to obtain an electrical complex signal;
wherein X (t) represents the electrical complex signal; h represents the order of the Fourier coefficient; xh(t) denotes h-th order fourier coefficients; j represents an imaginary unit; omegasRepresenting the fundamental angular frequency, ωs＝2π/T0Where π denotes the circumference ratio, T0Represents a fundamental period of the electrical signal; t represents time.
Optionally, the frequency shift module specifically includes:
the sub-frequency band signal unit is used for carrying out sectional recombination on the electrical complex signal according to the following formula from small to large to obtain a recombined sub-frequency band signal;
in the above formula, N represents the total number of the recombined sub-bands, N represents the serial number of the sub-band, and N is in the range of-N, N]；HnRepresenting all frequency components, H, in the first n sub-bandsn-1Representing all frequency components in the first n-1 sub-bands; omegahRepresenting the angular frequency, ω, of the h-th harmonich＝hωs；Bn(t) represents the recombined sub-frequency of the nth sub-bandSegment signals, i.e. the sub-band signals;
the electric sub-band dynamic vector unit is used for respectively shifting the frequency of each sub-band signal according to the following formula to obtain the sub-band dynamic vector;
in the above formula, the first and second carbon atoms are,
the dynamic vector of the electric sub-frequency band is expressed by
ωrnRepresenting the frequency shift angular frequency of the nth sub-band;
representing the upper frequency limit of the nth sub-band;
represents the lower frequency limit of the nth sub-band; b isnRepresenting the nth sub-band; f. ofhRepresenting the frequency of said sub-band signal in the nth sub-band,
optionally, the switching function model coefficient module specifically includes:
a modulation ratio unit for obtaining a modulation ratio of the recent level modulation strategy;
the starting angle unit is used for solving a starting angle of the ith level of the output waveform according to a nearest level approximation principle and the modulation ratio;
and the unit is used for carrying out Fourier decomposition on the nearest level control wave of the output waveform to obtain the sum of the upper bridge arm switching function and the lower bridge arm switching function of the modular multilevel converter;
a difference unit, configured to perform fourier decomposition on a latest level control wave of the output waveform to obtain a difference between the upper arm switching function and the lower arm switching function; the difference between the sum of the upper bridge arm switching function and the lower bridge arm switching function and the upper bridge arm switching function and the lower bridge arm switching function is the coefficient of the switching function model;
and solving a kth order Fourier decomposition coefficient of the difference between the upper bridge arm switching function and the lower bridge arm switching function through the initial angle.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
the invention provides an electromagnetic transient simulation method and system for a modular multilevel converter, wherein the method comprises the following steps: acquiring an electric signal input by the modular multilevel converter; carrying out Fourier decomposition on the electrical signal to obtain an electrical complex signal; dividing the electrical complex signal into a plurality of sub-bands according to the signal frequency; recombining and shifting the frequency of the electrical complex signal of each sub-band to obtain a sub-band dynamic vector of the electrical complex signal of the sub-band; obtaining a submodule of the modular multilevel converter through a topological structure of the modular multilevel converter; acquiring a switch function model of the sub-module; obtaining a switching function model of the modular multilevel converter through kirchhoff current and voltage law according to the switching function model and the topological structure of the sub-module; acquiring an output waveform of the modular multilevel converter; adjusting the output waveform according to the latest level modulation strategy to obtain the coefficient of a switching function model of the modular multilevel converter; obtaining a multi-frequency-band dynamic phasor model of the modular multi-level converter according to a switching function model and a sub-frequency-band dynamic vector of the modular multi-level converter through a multi-frequency-band dynamic phasor principle; performing electromagnetic transient simulation according to the multi-band dynamic phasor model to obtain simulation voltage and simulation current; and sequentially carrying out reverse frequency shift, addition and real obtaining parts on the simulation voltage and the simulation current to obtain a real voltage and a real current. According to the electromagnetic transient simulation method and system for the modular multilevel converter, a switching function model of the modular multilevel converter is obtained through calculation by applying a multi-band dynamic phasor method and is used for electromagnetic transient simulation; meanwhile, because the sub-band dynamic phasor is a signal with a bandwidth which meets a narrow-band condition, the simulation speed can be improved by adopting large-step simulation, and meanwhile, the very high signal frequency upper limit can be considered, so that the simulation precision is very high, and the electromagnetic transient simulation method and the system of the modular multilevel converter can effectively give consideration to both the simulation efficiency and the simulation precision.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed 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 to obtain other drawings without inventive exercise.
Fig. 1 is a flowchart of an electromagnetic transient simulation method for a modular multilevel converter according to embodiment 1 of the present invention;
fig. 2 is a schematic diagram of a frequency band segmentation provided in embodiment 1 of the present invention;
FIG. 3 is a flow chart of the multi-band dynamic phasor method according to embodiment 1 of the present invention;
fig. 4 is a structural diagram of an electromagnetic transient simulation model of a modular multilevel converter according to embodiment 1 of the present invention;
fig. 5 is a schematic diagram of an MMC topology provided in embodiment 1 of the present invention;
FIG. 6 is a diagram of a nearest level approximation modulation waveform provided in embodiment 1 of the present invention;
fig. 7 is a structural diagram of an electromagnetic transient simulation system of a modular multilevel converter according to embodiment 2 of the present invention.
Wherein, 1, an electrical signal; 2. time scale decomposition; 3. recombining; 4. time scale transformation; 5. a low frequency signal; 6. performing parallel large-step simulation; 7. a modular multilevel converter; 8. an alternating current system; 9. modulating a wave; 10. NLM wave; 11. a sub-module; 12. a bridge arm.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
Example 1
The embodiment provides an electromagnetic transient simulation method of a modular multilevel converter. The electromagnetic transient simulation method of the modular multilevel converter of the embodiment calculates a multi-band dynamic phasor model by a multi-band dynamic phasor method, and the principle of the multi-band dynamic phasor method comprises the following steps:
(1) the frequency of the electrical signal is decomposed and recombined:
voltage, current, etc. in an electrical power system can be seen as periodically varying electrical signals. For a fundamental wave period of T0In any period tau e (T-T) of the electrical signal x (tau) of (c)0,t]And t represents any time of the period tau, the fourier decomposition of the complex form of the electrical signal is:
in formula (1), x (t) is a complex form of the electrical signal x (τ), and is defined as an electrical complex signal; h represents the harmonic number of the Fourier series; xh(t) is the h-th order Fourier coefficient, i.e. the h-order "dynamic phasor", i.e. the h-th order Fourier coefficient of the harmonic wave; j represents an imaginary unit; omegasRepresenting the fundamental angular frequency, ωs＝2π/T0。
H in the formula (1) is theoretically infinite, but in electromagnetic transient simulation, the frequency corresponding to the simulation step length is generally 10 times of the signal frequency according to the requirements of precision and sampling theorem. Therefore, in electromagnetic transient simulation, the harmonic number h is generally finite, and the maximum value of h can be determined according to the simulation step size, for example: the maximum harmonic order h corresponding to a 50 mus simulation step is 40.
At this time, equation (1) can be expressed as:
m in the formula (2) represents the number of harmonic waves; omegahRepresenting the angular frequency, ω, of the h-th harmonich＝hωs。
The mathematical meaning of the fourier transform is: any periodic signal satisfying the dirichlet condition can be represented as a group to
Is a linear combination of orthogonal bases. Fig. 2 is a schematic diagram of a frequency band segmentation provided in embodiment 1 of the present invention, where f in fig. 2 represents a frequency; hNRepresenting the total number of frequency components, H, in the N sub-bandsN-1Representing the total number of frequency components in the N-1 th sub-band. The frequency of the electrical complex signal is divided into N sub-bands according to fig. 2, and the formula (2) is grouped and recombined according to the sub-bands according to the combination law of linear combination, and the electrical complex signals before and after combination are equal and represent the same complex signal x (t).
The result of each subband recombination is: recombining a plurality of sub-signals with different frequencies obtained by Fourier decomposition in each sub-band into 1 sub-band signal, wherein X (t) can be regarded as the sum of complex signals of each sub-band, that is:
in the formula (3), N represents the total number of the recombined sub-bands, N represents the serial number of the sub-bands, and N belongs to [ -N, N [ ]]；HnRepresenting all frequency components, H, in the first n sub-bandsn-1Representing all frequency components in the first n-1 sub-bands; omegahRepresenting the angular frequency, ω, of the h-th harmonich＝hωs；Bn(t) isAnd (4) the nth frequency sub-band recombined frequency sub-band signal.
Comparing the terms on the right of the formula (2) and the formula (3), it can be found that the term of the formula (2) is reduced, that is, the harmonic number is reduced from 2M to 2N.
(2) Sub-band dynamic phasor
The formula (3) carries out sectional recombination on the electrical complex signal X (t) according to the frequency from small to large. For each sub-band signal Bn(t), any frequency in the sub-frequency band can be selected to shift frequency respectively, namely:
in the formula (4), the first and second groups,
indicating the shifted signals of the sub-bands, abbreviated as
ωrnRepresenting the frequency shift angular frequency of the nth sub-band;
represents the lower frequency limit of the nth sub-band;
representing the upper frequency limit of the nth sub-band; b isnRepresenting the nth sub-band, wherein the sub-band can be selected from 0 to 200 hertz (Hz); f. ofhRepresents the frequency of the frequency shift signal in the nth sub-band and satisfies
The frequency shift frequency may select the center frequency of each sub-band.
(3) Multi-band dynamic phasor method
When the electromagnetic transient simulation is performed by the traditional dynamic phasor method, a signal is decomposed into dynamic phasors of each order according to a formula (2), and then the dynamic phasors of each order are placed in different CPU cores for parallel simulation by utilizing the characteristic of a Central Processing Unit (CPU) with multiple cores. However, because the number of cores of the CPU is limited, the conventional dynamic phasor method can only take a few orders of dynamic phasors to form an equation set and perform simulation. Therefore, the total bandwidth of the signals simulated by the traditional dynamic phasor method is far smaller than the actual bandwidth of the signals, so that the harmonic truncation error is large and the simulation precision is low. Fig. 3 is a simulation flowchart of a multi-band dynamic phasor method according to embodiment 1 of the present invention, and referring to fig. 3, different from the conventional dynamic phasor method, the electromagnetic transient simulation method of the modular multilevel converter according to the present embodiment performs time scale decomposition 2 and recombination 3 on an electrical signal 1 according to formula (3) to obtain a sub-band dynamic phasor, performs frequency shift on the sub-band dynamic phasor, performs time scale conversion 4 to obtain a low-frequency signal 5, and places the low-frequency signal 5 in a Graphics Processing Unit (GPU) multi-core CPU to perform parallel large-step simulation 6 calculation, that is, parallel calculation. Because the sub-frequency band signal has a certain bandwidth, under the condition that the number of equation sets is the same as that of a traditional dynamic phasor method, the bandwidth of a simulatable signal of the electromagnetic transient simulation method of the modular multilevel converter is far larger than that of the traditional dynamic phasor method, and a harmonic truncation error is far smaller than that of the traditional dynamic phasor method, so that the simulation precision is extremely high.
Fig. 1 is a flowchart of an electromagnetic transient simulation method for a modular multilevel converter according to embodiment 1 of the present invention, and fig. 4 is a topological structure diagram of an MMC according to embodiment 1 of the present invention. Referring to fig. 1 and 4, in embodiment 1, a Modular Multilevel Converter (MMC) 7 is connected to an ac system 8, where R denotes a resistor and L denotes a reactor in fig. 4. An electromagnetic transient simulation model is established for the MMC according to a modularized multi-level converter electromagnetic transient simulation method, and voltage signals and current signals of all positions between the MMC and an alternating current system 8 can be obtained through simulation.
An electromagnetic transient simulation method for a modular multilevel converter comprises the following steps:
and 101, acquiring an electric signal input by the modular multilevel converter.
And 102, carrying out Fourier decomposition on the electrical signal to obtain an electrical complex signal.
Step 102 comprises:
carrying out Fourier decomposition on the electrical signal through a formula (1) to obtain an electrical complex signal;
in formula (1), x (t) represents an electrical complex signal; h represents the order of the Fourier coefficient; xh(t) denotes h-th order fourier coefficients; j represents an imaginary unit; omegasRepresenting the fundamental angular frequency, ωs＝2π/T0Where π denotes the circumference ratio, T0Represents the fundamental period of the electrical signal; t represents time.
H in equation (1) is theoretically infinite, but is generally a finite value in engineering applications. In the Electro-Magnetic Transient Program (EMTP), the simulation step size is typically 10 times the signal frequency, depending on the accuracy and sampling theorem requirements. Thus, the upper frequency limit of the signal for accurate simulation can be determined in terms of simulation step size, for example: the signal frequency for 50 mus is 2 kHz.
At this time, equation (1) can be expressed as:
m in the formula (2) represents the number of harmonic waves; omegahRepresenting the angular frequency, ω, of the h-th harmonich＝hωs。
Dividing the 2M electrical complex signals in the formula (2) into N groups according to the frequency from small to large to obtain N sub-frequency bands.
And 104, recombining and shifting the frequency of the electric complex signal of each sub-band to obtain a sub-band dynamic vector of the electric complex signal of the sub-band.
Step 104 comprises:
superposing the electrical complex signal of each sub-frequency band into an electrical sub-signal, so that the electrical complex signal U (x, t) becomes a signal with reduced frequency components, and the U (x, t) can be regarded as the sum of the signals of the electrical sub-frequency bands, namely, the electrical complex signal is sectionally recombined according to a formula (3) from small to large according to the frequency to obtain a recombined sub-frequency band signal;
in the formula (3), N represents the total number of the recombined sub-bands, N represents the serial number of the sub-bands, and N belongs to [ -N, N [ ]]；HnRepresenting all frequency components, H, in the first n sub-bandsn-1Representing all frequency components in the first n-1 sub-bands; omegahRepresenting the angular frequency, ω, of the h-th harmonich＝hωs；BnAnd (t) represents the recombined sub-band signal of the nth sub-band, namely the sub-band signal.
Acquiring a frequency shift frequency; the method specifically comprises the following steps: selecting any frequency in each sub-frequency band as frequency shift frequency frnFrequency shift frequency frnThe center frequency of each sub-band may be selected.
Respectively carrying out frequency shift on the recombined electrical signals according to the frequency shift frequency to obtain sub-frequency band dynamic vectors of the electrical complex signals, which specifically comprises the following steps:
respectively carrying out frequency shift on each sub-frequency band signal according to a formula (4) to obtain an electric sub-frequency band dynamic vector;
in the formula (4), the first and second groups,
represents the dynamic vector of the electric sub-frequency band, which is abbreviated as
ωrnRepresenting the frequency shift angular frequency of the nth sub-band;
representing the upper frequency limit of the nth sub-band;
represents the lower frequency limit of the nth sub-band; b isnRepresenting the nth sub-band; f. ofhRepresenting the frequency of the sub-band signal in the nth sub-band,
And 105, obtaining a submodule of the modular multilevel converter through the topological structure of the modular multilevel converter.
Step 105 specifically includes: fig. 5 is a topological structure diagram of MMCs provided in embodiment 1 of the present invention, and referring to fig. 5, each MMC includes: the phase-a unit, the phase-b unit and the phase-c unit are three phase units, each phase is divided into an upper bridge arm and a lower bridge arm, and each bridge arm 12 is formed by connecting Num Sub-modules 11 (Sub-modules, SM), 1 resistor R and 1 reactor L in series. In FIG. 5
Representing the sum of the voltages of the bridge arm submodules on the phase a;
representing the sum of the voltages of the sub-modules of the a-phase lower bridge arm; i.e. icirShowing current circulation between the bridge arms; num represents the number of bridge arm submodules; raThe equivalent resistance of an upper bridge arm and the equivalent resistance of a lower bridge arm of the phase-a unit are represented, and the equivalent resistances of the upper bridge arm and the lower bridge arm of the phase-a unit of the MMC are the same; rbRepresenting equivalent resistance of upper arm and lower arm of b-phase unitThe equivalent resistance of an upper bridge arm and a lower bridge arm of a b-phase unit of the MMC is the same; rcThe equivalent resistance of an upper bridge arm and the equivalent resistance of a lower bridge arm of the c-phase unit are represented, and the equivalent resistances of the upper bridge arm and the lower bridge arm of the c-phase unit of the MMC are the same; l isaThe equivalent reactance of an upper bridge arm and the equivalent reactance of a lower bridge arm of the phase-a unit are represented, and the equivalent reactances of the upper bridge arm and the lower bridge arm of the phase-a unit of the MMC are the same; l isbThe equivalent reactance of an upper bridge arm and the equivalent reactance of a lower bridge arm of the b-phase unit are represented, and the equivalent reactances of the upper bridge arm and the lower bridge arm of the b-phase unit of the MMC are the same; l iscThe equivalent reactance of an upper bridge arm and the equivalent reactance of a lower bridge arm of the c-phase unit are represented, and the equivalent reactances of the upper bridge arm and the lower bridge arm of the c-phase unit of the MMC are the same; capacitor C of each submodule of upper bridge arm and lower bridge arm of MMC topological structuresmThe sizes are the same;
representing the current of the upper bridge arm of the phase a unit;
representing the current of the lower bridge arm of the phase a unit;
representing the current of the upper bridge arm of the b-phase unit;
representing the current of the lower bridge arm of the b-phase unit;
representing the current of the upper bridge arm of the c-phase unit;
representing the current of the lower bridge arm of the c-phase unit; u. ofaRepresenting the AC port voltage of the a-phase cell in the MMC; u. ofbRepresenting the alternating current port voltage of a b-phase cell in the MMC; u. ofcRepresenting the ac port voltage of a c-phase cell in an MMC; i.e. iaRepresenting the injection current of an a-phase cell in the MMC; i.e. ibTo represent MMThe injection current of the b-phase unit in C; i.e. icRepresenting the injection current of a c-phase cell in the MMC; i isdcRepresenting the direct-current side current of the MMC; u shapedcRepresenting the MMC dc side voltage.
And 106, acquiring a switching function model of the submodule.
The switching function model of the sub-module is:
in the formula (5), s k-y1 represents that the kth sub-module is coupled to a bridge arm and participates in the operation of the bridge arm; sk-y0 means that the kth sub-module is bypassed and does not participate in bridge arm operation; k represents the sub-module number, k is equal to 0, Num](ii) a y represents any one of a-phase unit, a b-phase unit and a c-phase unit.
Step 106 further comprises: according to the characteristics of the MMC current converter, an upper bridge arm switching function and a lower bridge arm switching function can be obtained through a sub-module switching function:
in the formula (6), the first and second groups,
representing an upper bridge arm switching function;
representing a lower bridge arm switching function; when in use
When the temperature of the water is higher than the set temperature,
representing the kth submodule coupled to the upper leg; when in use
When the temperature of the water is higher than the set temperature,
the kth sub-module is bypassed and does not participate in the operation of an upper bridge arm; when in use
When the temperature of the water is higher than the set temperature,
representing the kth submodule coupled to the lower leg; when in use
When the temperature of the water is higher than the set temperature,
indicating that the kth sub-module is bypassed and does not participate in the lower leg operation.
Defining the sum of the upper bridge arm switching function and the lower bridge arm switching function as:
in the formula (7a), the first and second groups,
representing the sum of the upper and lower leg switching functions of any phase cell,
representing the upper arm switching function of any phase cell,
representing the lower arm switching function of any phase cell.
Defining the difference between the upper bridge arm switching function and the lower bridge arm switching function as:
in the formula (7b), the first and second groups,
the difference between the upper and lower leg switching functions of any phase cell is represented.
Defining the sum of the currents of the upper bridge arm and the lower bridge arm as follows:
in the formula (8a), the first and second groups,
representing the sum of the currents of the upper and lower legs of any phase unit,
representing the current of the upper arm of any phase cell,
representing the current of the lower arm of any phase cell.
Defining the difference between the currents of the upper bridge arm and the lower bridge arm as:
in the formula (8b), the first and second groups,
the difference between the currents of the upper arm and the lower arm of any phase unit is shown.
Defining the sum of the voltage sum of the upper bridge arm submodule and the voltage sum of the lower bridge arm submodule as follows:
in the formula (9a), the first and second groups,
represents the sum of the voltage sum of the upper arm submodule and the voltage sum of the lower arm submodule of any phase unit,
representing the sum of the voltages of the upper arm sub-modules of any phase cell,
the sum of the voltages of the lower arm submodules of any phase cell is shown.
Defining the difference between the voltage sum of the upper bridge arm submodule and the voltage sum of the lower bridge arm submodule as follows:
in the formula (9b), the first and second groups,
the difference between the voltage sum of the upper arm submodule and the voltage sum of the lower arm submodule of any phase unit is shown.
And 107, obtaining a switching function model of the modular multilevel converter through kirchhoff current and voltage law according to the switching function model and the topological structure of the sub-module.
Step 107 specifically includes: according to the switching function model, topology of the sub-modules and defined in step 106
And
obtaining a switching function model of the modular multilevel converter through kirchhoff current and voltage laws:
in the formula (10a), the formula (10b), the formula (10c), and the formula (10d), when y is a, Ly＝La，uy＝ua，Ry＝Ra(ii) a When y is b, Ly＝Lb，uy＝ub，Ry＝Rb(ii) a When y is equal to c, Ly＝Lc，uy＝uc，Ry＝Rc。
Can be calculated by formula (10a), formula (10b), formula (10c) and formula (10d)
And
and step 108, acquiring an output waveform of the modular multilevel converter.
And step 109, adjusting the output waveform according to the latest level modulation strategy to obtain the coefficient of the switching function model of the modular multilevel converter. Fig. 6 is a recent Level approximation modulation waveform diagram provided in embodiment 1 of the present invention, where an NLM (recent Level modulation) wave in fig. 6 represents a waveform of an upper bridge arm or a lower bridge arm of an MMC; the vertical axis represents voltage in units of voltage: kilovolts (kV); the horizontal axis represents time in seconds(s). Referring to fig. 6, a modulated wave 9 is generated by the control system, and the waveform of the MMC output is ideally the modulated wave 9, but due to the characteristics of the MMC, an NLM wave 10 is actually output.
Step 109 specifically includes:
and acquiring the modulation ratio of the latest level modulation strategy. The modulation ratio is:
u in formula (11)mRepresenting the amplitude, U, of the modulated wavedcRepresenting the MMC dc side voltage.
And solving the starting angle of the ith level of the output waveform according to the nearest level approximation principle and the modulation ratio. The starting angle of the ith level is:
in the formula (12), i represents a level number, and m represents a modulation ratio.
Performing Fourier decomposition on the nearest level control wave of the output waveform to obtain the sum of an upper bridge arm switching function and a lower bridge arm switching function of the modular multilevel converter; performing Fourier decomposition on the nearest level control wave of the output waveform to obtain the difference between an upper bridge arm switching function and a lower bridge arm switching function; the difference between the sum of the upper bridge arm switching function and the lower bridge arm switching function and the upper bridge arm switching function and the lower bridge arm switching function is a coefficient of the switching function model, and the coefficient is specifically as follows:
in the formula (13)
Fourier decomposition coefficients representing the h-th order; omegasRepresents the fundamental angular frequency; delta represents the initial phase of the modulation wave; when y is a, phiyIndicating the phase of the a-phase cell, i.e. + -.)y＝φ a0; when y is b, phiyRepresenting the phase of the b-phase cell, i.e. + -.)y＝φb120; when y is equal to c, phiyIndicating the phase of the c-phase cell, i.e. phiy＝φc＝-120。
Solving the kth order Fourier decomposition coefficient of the difference between the upper bridge arm switching function and the lower bridge arm switching function through the initial angle, which specifically comprises the following steps:
the formula (10a), the formula (10b), the formula (10c), the formula (10d) and the formula (13) form a switching function model when the MMC adopts the recent level approximation modulation strategy.
And step 110, obtaining a multi-band dynamic phasor model of the modular multi-level converter according to the switching function model and the sub-band dynamic vector of the modular multi-level converter through a multi-band dynamic phasor principle.
Step 110 specifically includes:
applying the multi-band dynamic phasor principle to the voltage, current and switching functions of formula (10a), formula (10b), formula (10c) and formula (10d) to obtain the multi-band dynamic phasor model of the MMC, namely:
ω in formula (15a), formula (15b), formula (15c) and formula (15d)nRepresenting the frequency of the nth sub-band shift.
And step 111, performing electromagnetic transient simulation according to the multi-band dynamic phasor model to obtain simulation voltage and simulation current.
Step 111 specifically includes: the formula (15a), the formula (15b), the formula (15c) and the formula (15d) are applied to carry out large-step electromagnetic transient simulation to obtain upper bridge arm current and signals of each sub-frequency band
Lower bridge arm current difference signal
Upper bridge arm voltage sum signal
And lower leg voltage sum signal
fhRepresenting the frequency of the sub-band signal in the nth sub-band.
And 112, sequentially carrying out reverse frequency shift, addition and real obtaining parts on the simulation voltage and the simulation current to obtain a real voltage and a real current.
Step 112 specifically includes: calculating the simulation voltage and the simulation current according to a formula (16a), a formula (16b), a formula (16c) and a formula (16d) to obtain a real voltage and a real current:
among formula (16a), formula (16b), formula (16c) and formula (16d),
representing a reverse frequency shift; omegarnRepresenting the frequency shift angular frequency of the nth sub-band;
representing the sum of real currents of an upper bridge arm and a lower bridge arm of any phase unit;
representing the sum of the real voltage sum of the upper bridge arm submodule and the real voltage sum of the lower bridge arm submodule;
representing the difference between the real currents of the upper bridge arm and the lower bridge arm of any phase unit;
representing the difference between the real voltage sum of the upper bridge arm submodule of any phase unit and the real voltage sum of the lower bridge arm submodule; re represents the real part.
Example 2
The embodiment provides an electromagnetic transient simulation system of a modular multilevel converter. Fig. 7 is a structural diagram of an electromagnetic transient simulation system of a modular multilevel converter according to an embodiment of the present invention. Referring to fig. 7, a modular multilevel converter electromagnetic transient simulation system includes:
and the electrical signal module 201 is used for acquiring an electrical signal input by the modular multilevel converter.
The electrical complex signal module 202 is configured to perform fourier decomposition on the electrical signal to obtain an electrical complex signal.
The electrical complex signal module 202 specifically includes:
the electrical complex signal unit is used for carrying out Fourier decomposition on the electrical signal through a formula (1) to obtain an electrical complex signal;
in formula (1), x (t) represents an electrical complex signal; h represents the order of the Fourier coefficient; xh(t) denotes h-th order fourier coefficients; j represents an imaginary unit; omegasRepresenting the fundamental angular frequency, ωs＝2π/T0Where π denotes the circumference ratio, T0Represents the fundamental period of the electrical signal; t represents time.
H in equation (1) is theoretically infinite, but is generally a finite value in engineering applications. In the Electro-Magnetic transient program (EMTP), the simulation step size is typically 10 times the signal frequency, depending on the accuracy and sampling theorem requirements. Thus, the upper frequency limit of the signal for accurate simulation can be determined in terms of simulation step size, for example: the signal frequency for 50 mus is 2 kHz.
At this time, equation (1) can be expressed as:
m in the formula (2) represents the number of harmonic waves; omegahRepresenting the angular frequency, ω, of the h-th harmonich＝hωs。
The sub-band module 203 is configured to divide the electrical complex signal into a plurality of sub-bands according to the signal frequency.
The sub-band module 203 includes: and the setting unit is used for acquiring the simulation step length and the number of the CPU cores and setting the number of the sub-frequency bands according to the simulation step length and the number of the CPU cores.
And the sub-frequency band unit is used for dividing the 2M electrical complex signals in the formula (2) into N groups according to the frequency from small to large to obtain N sub-frequency bands.
And the frequency shift module 204 is configured to recombine and shift the electrical complex signal of each sub-band to obtain a sub-band dynamic vector of the electrical complex signal of the sub-band.
The frequency shift module 204 includes:
the sub-frequency band signal unit is used for carrying out sectional recombination on the electrical complex signal according to the formula (3) from small to large according to the frequency to obtain a recombined sub-frequency band signal;
in the formula (3), N represents the total number of the recombined sub-bands, N represents the serial number of the sub-bands, and N belongs to [ -N, N [ ]]；HnRepresenting all frequency components, H, in the first n sub-bandsn-1Representing all of the first n-1 sub-bandsA frequency component; omegahRepresenting the angular frequency, ω, of the h-th harmonich＝hωs；BnAnd (t) represents the recombined sub-band signal of the nth sub-band, namely the sub-band signal.
The frequency shift frequency unit is used for acquiring a frequency shift frequency; the method specifically comprises the following steps: selecting any frequency in each sub-frequency band as frequency shift frequency frnFrequency shift frequency frnThe center frequency of each sub-band may be selected.
The electric sub-band dynamic vector unit is used for respectively shifting the frequency of each sub-band signal according to a formula (4) to obtain an electric sub-band dynamic vector;
in the formula (4), the first and second groups,
represents the dynamic vector of the electric sub-frequency band, which is abbreviated as
ωrnRepresenting the frequency shift angular frequency of the nth sub-band;
representing the upper frequency limit of the nth sub-band;
represents the lower frequency limit of the nth sub-band; b isnRepresenting the nth sub-band; f. ofhRepresenting the frequency of the sub-band signal in the nth sub-band,
the sub-module 205 is configured to obtain a sub-module of the modular multilevel converter according to a topological structure of the modular multilevel converter.
A sub-module switch function model module 206, configured to obtain a switch function model of the sub-module. The sub-module switch function model module 206 includes: the submodule switch function model unit is used for obtaining a submodule switch function model, and the submodule switch function model is as follows:
in the formula (5), s k-y1 represents that the kth sub-module is coupled to a bridge arm and participates in the operation of the bridge arm; sk-y0 means that the kth sub-module is bypassed and does not participate in bridge arm operation; k represents the sub-module number, k is equal to 0, Num](ii) a y represents any one of a-phase unit, a b-phase unit and a c-phase unit.
And the definition unit is used for obtaining an upper bridge arm switching function and a lower bridge arm switching function according to the characteristics of the MMC current converter by the sub-module switching function:
in the formula (6), the first and second groups,
representing an upper bridge arm switching function;
representing a lower bridge arm switching function; when in use
When the temperature of the water is higher than the set temperature,
representing the kth submodule coupled to the upper leg; when in use
When the temperature of the water is higher than the set temperature,
the kth sub-module is bypassed and does not participate in the operation of an upper bridge arm; when in use
When the temperature of the water is higher than the set temperature,
representing the kth submodule coupled to the lower leg; when in use
When the temperature of the water is higher than the set temperature,
indicating that the kth sub-module is bypassed and does not participate in the lower leg operation.
Defining the sum of the upper bridge arm switching function and the lower bridge arm switching function as:
in the formula (7a), the first and second groups,
representing the sum of the upper and lower leg switching functions of any phase cell,
representing the upper arm switching function of any phase cell,
representing the lower arm switching function of any phase cell.
Defining the difference between the upper bridge arm switching function and the lower bridge arm switching function as:
in the formula (7b), the first and second groups,
the difference between the upper and lower leg switching functions of any phase cell is represented.
Defining the sum of the currents of the upper bridge arm and the lower bridge arm as follows:
in the formula (8a), the first and second groups,
representing the sum of the currents of the upper and lower legs of any phase unit,
representing the current of the upper arm of any phase cell,
representing the current of the lower arm of any phase cell.
Defining the difference between the currents of the upper bridge arm and the lower bridge arm as:
in the formula (8b), the first and second groups,
the difference between the currents of the upper arm and the lower arm of any phase unit is shown.
Defining the sum of the voltage sum of the upper bridge arm submodule and the voltage sum of the lower bridge arm submodule as follows:
in the formula (9a), the first and second groups,
represents the sum of the voltage sum of the upper arm submodule and the voltage sum of the lower arm submodule of any phase unit,
voltage sum of upper arm submodules representing any phase unit，
The sum of the voltages of the lower arm submodules of any phase cell is shown.
Defining the difference between the voltage sum of the upper bridge arm submodule and the voltage sum of the lower bridge arm submodule as follows:
in the formula (9b), the first and second groups,
the difference between the voltage sum of the upper arm submodule and the voltage sum of the lower arm submodule of any phase unit is shown.
And the switching function model module 207 is used for obtaining a switching function model of the modular multilevel converter through kirchhoff current and voltage law according to the switching function model and the topological structure of the sub-module.
The switching function model module 207 specifically includes: a switching function model unit for modeling the switching function according to the sub-modules, the topology and the switching function defined in step 106
And
obtaining a switching function model of the modular multilevel converter through kirchhoff current and voltage laws:
in the formula (10a), the formula (10b), the formula (10c), and the formula (10d), when y is a, Ly＝La，uy＝ua，Ry＝Ra(ii) a When y is b, Ly＝Lb，uy＝ub，Ry＝Rb(ii) a When y is equal to c, Ly＝Lc，uy＝uc，Ry＝Rc。
Can be calculated by formula (10a), formula (10b), formula (10c) and formula (10d)
And
and an output waveform module 208, configured to obtain an output waveform of the modular multilevel converter.
And a switching function model coefficient module 209, configured to adjust the output waveform according to the latest level modulation strategy to obtain a coefficient of a switching function model of the modular multilevel converter.
The switching function model coefficients module 209 includes:
a modulation ratio unit for obtaining a modulation ratio of the latest level modulation strategy; the modulation ratio is:
u in formula (11)mRepresenting the amplitude, U, of the modulated wavedcRepresenting the MMC dc side voltage.
The starting angle unit is used for solving the starting angle of the ith level of the output waveform according to the nearest level approximation principle and the modulation ratio; the starting angle of the ith level is:
in the formula (12), i represents a level number, and m represents a modulation ratio.
The unit is used for carrying out Fourier decomposition on the nearest level control wave of the output waveform to obtain the sum of the upper bridge arm switching function and the lower bridge arm switching function of the modular multilevel converter;
the difference unit is used for carrying out Fourier decomposition on the nearest level control wave of the output waveform to obtain the difference between the upper bridge arm switching function and the lower bridge arm switching function; the difference between the sum of the upper bridge arm switching function and the lower bridge arm switching function and the upper bridge arm switching function and the lower bridge arm switching function is the coefficient of the switching function model;
the sum and difference units are specifically:
in the formula (13)
Fourier decomposition coefficients representing the h-th order; omegasRepresents the fundamental angular frequency; delta represents the initial phase of the modulation wave; when y is a, phiyIndicating the phase of the a-phase cell, i.e. + -.)y＝φ a0; when y is b, phiyRepresenting the phase of the b-phase cell, i.e. + -.)y＝φb120; when y is equal to c, phiyIndicating the phase of the c-phase cell, i.e. phiy＝φc＝-120。
Solving the kth order Fourier decomposition coefficient of the difference between the upper bridge arm switching function and the lower bridge arm switching function through the initial angle, which specifically comprises the following steps:
the formula (10a), the formula (10b), the formula (10c), the formula (10d) and the formula (13) form a switching function model when the MMC adopts the recent level approximation modulation strategy.
And the multi-band dynamic phasor model module 210 is used for obtaining a multi-band dynamic phasor model of the modular multi-level converter according to the switching function model and the sub-band dynamic vectors of the modular multi-level converter through a multi-band dynamic phasor principle.
The simulation module 211 is configured to perform electromagnetic transient simulation according to the multi-band dynamic phasor model to obtain a simulation voltage and a simulation current.
The simulation module 211 specifically includes:
a simulation unit, configured to apply the multi-band dynamic phasor principle to the voltage, current, and switching functions of equation (10a), equation (10b), equation (10c), and equation (10d) to obtain a multi-band dynamic phasor model of the MMC, that is:
ω in formula (15a), formula (15b), formula (15c) and formula (15d)nRepresenting the frequency of the nth sub-band shift.
And a real module 212, configured to perform inverse frequency shift, addition, and real extraction on the simulation voltage and the simulation current in sequence to obtain a real voltage and a real current.
The real module 212 specifically includes: the real unit is used for calculating the simulation voltage and the simulation current according to a formula (16a), a formula (16b), a formula (16c) and a formula (16d) to obtain the real voltage and the real current:
among formula (16a), formula (16b), formula (16c) and formula (16d),
representing a reverse frequency shift; omegarnRepresenting the frequency shift angular frequency of the nth sub-band;
representing the sum of real currents of an upper bridge arm and a lower bridge arm of any phase unit;
representing the sum of the real voltage sum of the upper bridge arm submodule and the real voltage sum of the lower bridge arm submodule;
representing the difference between the real currents of the upper bridge arm and the lower bridge arm of any phase unit;
representing the difference between the real voltage sum of the upper bridge arm submodule of any phase unit and the real voltage sum of the lower bridge arm submodule; re represents the real part.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. For the system disclosed by the embodiment, the description is relatively simple because the system corresponds to the method disclosed by the embodiment, and the relevant points can be referred to the method part for description.
The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.
Claims (6)
1. An electromagnetic transient simulation method for a modular multilevel converter is characterized by comprising the following steps:
acquiring an electric signal input by the modular multilevel converter;
carrying out Fourier decomposition on the electrical signal to obtain an electrical complex signal;
dividing the electrical complex signal into a plurality of sub-bands according to signal frequency;
recombining and shifting the frequency of the electrical complex signal of each sub-frequency band to obtain a sub-frequency band dynamic vector of the electrical complex signal of the sub-frequency band;
obtaining a submodule of the modular multilevel converter through a topological structure of the modular multilevel converter;
acquiring a switching function model of the sub-module;
obtaining a switching function model of the modular multilevel converter through kirchhoff current and voltage law according to the switching function model of the sub-module and the topological structure;
acquiring an output waveform of the modular multilevel converter;
adjusting the output waveform according to a recent level modulation strategy to obtain a coefficient of a switching function model of the modular multilevel converter;
obtaining a multi-band dynamic phasor model of the modular multi-level converter according to the switching function model of the modular multi-level converter and the sub-band dynamic vector through a multi-band dynamic phasor principle;
performing electromagnetic transient simulation according to the multi-band dynamic phasor model to obtain simulation voltage and simulation current;
sequentially carrying out reverse frequency shift, addition and real obtaining parts on the simulation voltage and the simulation current to obtain a real voltage and a real current;
the recombining and frequency shifting the electrical complex signal of each sub-band to obtain the sub-band dynamic vector of the electrical complex signal of the sub-band specifically includes:
the electrical complex signals are sectionally recombined according to the following formula from small to large in frequency to obtain recombined sub-frequency band signals;
in the above formula, N represents the total number of the recombined sub-bands, N represents the serial number of the sub-band, and N is in the range of-N, N]；HnRepresenting all frequency components, H, in the first n sub-bandsn-1Representing all frequency components in the first n-1 sub-bands; xh(t) denotes h-th order fourier coefficients; omegahRepresenting the angular frequency, ω, of the h-th harmonich＝hωs，ωsRepresents the fundamental angular frequency; b isn(t) represents the recombined sub-band signal of the nth sub-band, i.e. the sub-band signal;
respectively carrying out frequency shift on each sub-frequency band signal according to the following formula to obtain the dynamic vector of the sub-frequency band;
in the above formula, the first and second carbon atoms are,
the dynamic vector of the electric sub-frequency band is expressed by
ωrnRepresenting the frequency shift angular frequency of the nth sub-band;
representing the upper frequency limit of the nth sub-band;
represents the lower frequency limit of the nth sub-band; b isnRepresenting the nth sub-band; f. ofhRepresenting the frequency of said sub-band signal in the nth sub-band,
2. the method according to claim 1, wherein the fourier decomposition of the electrical signal to obtain an electrical complex signal comprises: fourier decomposition is carried out on the electrical signal through the following formula to obtain an electrical complex signal;
wherein X (t) represents the electrical complex signal; h represents the order of the Fourier coefficient; xh(t) denotes h-th order fourier coefficients; j represents an imaginary unit; omegasRepresenting the fundamental angular frequency, ωs＝2π/T0Where π denotes the circumference ratio, T0Represents a fundamental period of the electrical signal; t represents time.
3. The method according to claim 1, wherein the adjusting the output waveform according to the recent level modulation strategy to obtain the coefficients of the switching function model of the modular multilevel converter comprises:
obtaining the modulation ratio of the latest level modulation strategy;
solving the initial angle of the ith level of the output waveform according to a nearest level approximation principle and the modulation ratio;
performing Fourier decomposition on the nearest level control wave of the output waveform to obtain the sum of an upper bridge arm switching function and a lower bridge arm switching function of the modular multilevel converter;
performing Fourier decomposition on the nearest level control wave of the output waveform to obtain the difference between the upper bridge arm switching function and the lower bridge arm switching function; the difference between the sum of the upper bridge arm switching function and the lower bridge arm switching function and the upper bridge arm switching function and the lower bridge arm switching function is the coefficient of the switching function model;
and solving a kth order Fourier decomposition coefficient of the difference between the upper bridge arm switching function and the lower bridge arm switching function through the initial angle.
4. A modular multilevel converter electromagnetic transient simulation system is characterized by comprising:
the electric signal module is used for acquiring an electric signal input by the modular multilevel converter;
the electrical complex signal module is used for carrying out Fourier decomposition on the electrical signal to obtain an electrical complex signal;
the sub-frequency band module is used for dividing the electrical complex signal into a plurality of sub-frequency bands according to signal frequency;
the frequency shift module is used for recombining and shifting the electric complex signal of each sub-frequency band to obtain a sub-frequency band dynamic vector of the electric complex signal of the sub-frequency band;
the submodule module is used for obtaining a submodule of the modular multilevel converter through a topological structure of the modular multilevel converter;
the sub-module switch function model module is used for acquiring a switch function model of the sub-module;
the switching function model module is used for obtaining a switching function model of the modular multilevel converter through kirchhoff current and voltage law according to the switching function model of the sub-module and the topological structure;
the output waveform module is used for acquiring the output waveform of the modular multilevel converter;
the switching function model coefficient module is used for adjusting the output waveform according to a recent level modulation strategy to obtain the coefficient of the switching function model of the modular multilevel converter;
the multi-band dynamic phasor model module is used for obtaining a multi-band dynamic phasor model of the modular multi-level converter according to the switching function model of the modular multi-level converter and the sub-band dynamic vectors through a multi-band dynamic phasor principle;
the simulation module is used for performing electromagnetic transient simulation according to the multi-band dynamic phasor model to obtain simulation voltage and simulation current;
the real module is used for sequentially carrying out reverse frequency shift, addition and real obtaining parts on the simulation voltage and the simulation current to obtain a real voltage and a real current;
the frequency shift module specifically comprises:
the sub-frequency band signal unit is used for carrying out sectional recombination on the electrical complex signal according to the following formula from small to large to obtain a recombined sub-frequency band signal;
in the above formula, N represents the total number of the recombined sub-bands, N represents the serial number of the sub-band, and N is in the range of-N, N]；HnRepresenting all frequency components, H, in the first n sub-bandsn-1Representing all frequency components in the first n-1 sub-bands; xh(t) denotes h-th order fourier coefficients; omegahRepresenting the angular frequency, ω, of the h-th harmonich＝hωs，ωsRepresents the fundamental angular frequency; b isn(t) represents the recombined sub-band signal of the nth sub-band, i.e. the sub-band signal;
the electric sub-band dynamic vector unit is used for respectively shifting the frequency of each sub-band signal according to the following formula to obtain the sub-band dynamic vector;
in the above formula, the first and second carbon atoms are,
the dynamic vector of the electric sub-frequency band is expressed by
ωrnRepresenting the frequency shift angular frequency of the nth sub-band;
representing the upper frequency limit of the nth sub-band;
represents the lower frequency limit of the nth sub-band; b isnRepresenting the nth sub-band; f. ofhRepresenting the frequency of said sub-band signal in the nth sub-band,
5. the modular multilevel converter electromagnetic transient simulation system of claim 4, wherein the electrical complex signal module specifically comprises:
an electrical complex signal unit for performing fourier decomposition on the electrical signal by the following formula to obtain an electrical complex signal;
wherein X (t) represents the electrical complex signal; h represents the order of the Fourier coefficient; xh(t) denotes h-th order fourier coefficients; j represents an imaginary unit; omegasRepresenting the fundamental angular frequency, ωs＝2π/T0Where π denotes the circumference ratio, T0Representing the fundamental period of the electrical signal(ii) a t represents time.
6. The electromagnetic transient simulation system of a modular multilevel converter according to claim 4, wherein the switching function model coefficient module specifically comprises:
a modulation ratio unit for obtaining a modulation ratio of the recent level modulation strategy;
the starting angle unit is used for solving a starting angle of the ith level of the output waveform according to a nearest level approximation principle and the modulation ratio;
and the unit is used for carrying out Fourier decomposition on the nearest level control wave of the output waveform to obtain the sum of the upper bridge arm switching function and the lower bridge arm switching function of the modular multilevel converter;
a difference unit, configured to perform fourier decomposition on a latest level control wave of the output waveform to obtain a difference between the upper arm switching function and the lower arm switching function; the difference between the sum of the upper bridge arm switching function and the lower bridge arm switching function and the upper bridge arm switching function and the lower bridge arm switching function is the coefficient of the switching function model;
and solving a kth order Fourier decomposition coefficient of the difference between the upper bridge arm switching function and the lower bridge arm switching function through the initial angle.
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| CN111310325B (en) * | 2020-02-10 | 2022-01-11 | 华北电力大学 | Dynamic simulation method and system of modular multilevel converter |
| CN111708398B (en) * | 2020-07-10 | 2022-07-05 | 中国南方电网有限责任公司超高压输电公司天生桥局 | Circuit electromagnetic analysis method and device |
| CN111969639B (en) * | 2020-08-17 | 2022-03-11 | 中国科学院电工研究所 | Multi-time scale transient modeling method for power electronic power grid cascade type converter |
| CN112100860B (en) * | 2020-09-18 | 2024-09-17 | 中国南方电网有限责任公司超高压输电公司检修试验中心 | MMC model building method and electromagnetic transient simulation method of multi-terminal direct current transmission system |
| CN113094887B (en) * | 2021-03-31 | 2024-05-03 | 清华大学 | Optimization method and device for frequency-shifting electromagnetic transient simulation and electronic equipment |
| CN113139321B (en) * | 2021-05-14 | 2024-05-31 | 华北电力大学 | Calculation method and system for internal magnetic field distribution of direct-current transmission converter valve tower |
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