CN111654052B - Flexible direct current converter modeling device and method based on dynamic phasor method - Google Patents

Flexible direct current converter modeling device and method based on dynamic phasor method Download PDF

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CN111654052B
CN111654052B CN202010457363.3A CN202010457363A CN111654052B CN 111654052 B CN111654052 B CN 111654052B CN 202010457363 A CN202010457363 A CN 202010457363A CN 111654052 B CN111654052 B CN 111654052B
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fourier
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CN111654052A (en
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胡畔
钱一民
陈乔
李伟
丁凯
王易
叶畅
陈堃
柳丹
吴文斌
方定
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State Grid Corp of China SGCC
State Grid Hubei Electric Power Co Ltd
Electric Power Research Institute of State Grid Hubei Electric Power Co Ltd
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State Grid Corp of China SGCC
State Grid Hubei Electric Power Co Ltd
Electric Power Research Institute of State Grid Hubei Electric Power Co Ltd
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/36—Arrangements for transfer of electric power between ac networks via a high-tension dc link
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/36—Arrangements for transfer of electric power between ac networks via a high-tension dc link
    • H02J2003/365—Reducing harmonics or oscillations in HVDC
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E60/00—Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation
    • Y02E60/60—Arrangements for transfer of electric power between AC networks or generators via a high voltage DC link [HVCD]

Abstract

The invention provides a flexible direct current converter modeling device and method based on a dynamic phasor method, wherein the method comprises the following steps of firstly, determining each time of Fourier components required to be selected by a system, wherein each time of Fourier components comprises an alternating current side current component and a direct current side voltage component of an MMC; calculating each time of Fourier dynamic component, and rewriting each time of dynamic component into a dq axis lower time-frequency form; and step three, combining the Fourier dynamic components rewritten into the dq-axis lower time frequency form, establishing a flexible direct current converter time frequency model, and establishing an oscillation analysis model or an impedance analysis model according to an application object. The modeling method of the soft direct current converter is provided in the time domain state space based on DP, the accuracy problem of the soft direct current converter model caused by quasi-steady-state assumption is improved on the premise of ensuring the calculation rate, and the modeling method can adapt to the analysis of the stability of the broadband and has high engineering application value.

Description

Flexible direct current converter modeling device and method based on dynamic phasor method
Technical Field
The invention relates to the technical field of modeling of a flexible direct current converter, in particular to a flexible direct current converter modeling device and method based on a dynamic phasor method.
Background
Modular Multilevel Converters (MMC) are widely used in the field of High Voltage Direct Current (HVDC) transmission and the like. The field engineering experience shows that the MMC also brings stability problems of low frequency, high frequency resonance, subsynchronous resonance and the like to a power grid when in operation.
When the flexible-direct power transmission system establishes the oscillation stability analysis model, because the mathematical model established by adopting the quasi-steady state assumption is adopted, the switching frequency is high, the continuous rapid dynamic change in the power system is difficult to characterize, and a corresponding calculation error can be generated. If electromagnetic transient simulation is adopted, the step length is very small, and the occupied memory is large; when a detailed time domain model is adopted to simulate the switching process of power electronics, the operation speed is greatly reduced, and the method cannot be applied to the stability analysis of an actual power system. Therefore, it is difficult to reduce the error caused by the assumption of "quasi-steady state" due to neglecting high switching frequency, while ensuring the operation speed.
Disclosure of Invention
The invention provides a flexible direct current converter modeling device and method based on a dynamic phasor method, aiming at the problem of limitation of the existing quasi-steady-state assumed analysis model, and simultaneously considering the characteristics of higher harmonics in an MMC and the change process of internal power electronic switch state quantity.
A flexible direct current converter modeling device and method based on a dynamic phasor method comprises the following steps:
determining each Fourier component required to be selected by a system, wherein each Fourier component comprises an alternating current side current component and a direct current side voltage component of an MMC (modular multilevel converter), the alternating current side current comprises a Fourier dynamic component for +/-1 time or +/-2 times, and the direct current side voltage comprises a Fourier alternating current dynamic component and a direct current component for +/-1 time or +/-2 times or +/-3 times;
calculating each time of Fourier dynamic component, and rewriting each time of dynamic component into a dq axis lower time-frequency form;
and step three, combining the Fourier dynamic components rewritten into the dq-axis lower time frequency form, establishing a flexible direct current converter time frequency model, and establishing an oscillation analysis model or an impedance analysis model according to an application object.
Furthermore, in the step one, the negative sequence part of each alternating current component is considered, and according to the principle of a dynamic phasor method, the alternating current i of the MMCx(t) and a DC voltage ud(t) is represented as:
Figure GDA0002580077060000021
Figure GDA0002580077060000022
in the formula u1,u2,u3,i1,i2Respectively are primary, secondary and tertiary alternating voltage and current components,<>in its dynamic phasor form, the subscripts negative represent the conjugate form and Re represents the real part of the variable.
Further, an oscillation analysis model or an impedance analysis model is established by adopting a transfer function or a transfer function matrix method according to the application object.
Further, the second step specifically includes:
for the fundamental frequency component of the MMC, an external steady-state mathematical model of the ith (i ═ 1,2, …, N) converter valve and ac measurement in a dq coordinate system of a certain flexible interconnection device is expressed as:
Figure GDA0002580077060000023
in the formula, LiAnd RiEquivalent resistance and inductive reactance, C, from valve side to AC sideeqThe equivalent capacitive reactance is VSC-HVDC; u shapesdi、UsqiD-axis and q-axis components of the alternating current measurement equivalent bus voltage are respectively measured; u shapecdi、UcqiThe voltages of d and q axis buses at the alternating current side are respectively; i.e. id、UdiRespectively representing the current and the voltage of the direct current side;
for the high-frequency component of the current, the secondary circulating current satisfies the following conditions:
Figure GDA0002580077060000031
wherein i2dAnd i2qIs the dq-axis component of the secondary circulating current, L0And R0The subscript x is a, b and c; subscripts p, n represent upper and lower bridge arms, respectively;
the voltage components on the capacitor are as follows:
Figure GDA0002580077060000032
Figure GDA0002580077060000033
Figure GDA0002580077060000034
wherein (M)1d,M1q) And (M)2d,M2q) Respectively corresponding to (omega) in dq coordinate system0And 2 omega0) And subscripts d, q represent d, q axis components.
Further, the third step specifically comprises:
3.1 constructing a flexible-straight state time domain oscillation analysis model
Firstly, constructing a controller structure model and a converter valve characteristic time domain model, and then combining high-frequency components according to formulas (23) - (25) and a time-frequency model formula (34) so as to construct a flexible and straight state time domain oscillation analysis model;
Figure GDA0002580077060000041
in the formula, A represents a state matrix, B represents an input matrix, n corresponds to the number of times of dynamic phasors, and < > is the form of the dynamic phasors;
and 3.2, performing time-domain frequency-domain conversion according to the oscillation analysis model constructed in the step 3.1 to obtain an impedance analysis model.
A flexible direct current converter modeling device based on a dynamic phasor method comprises the following steps:
the Fourier component determination module is used for determining each time of Fourier components required to be selected by the system, wherein each time of Fourier components comprises an alternating current side current component and a direct current side voltage component of the MMC, the alternating current side current comprises +/-1 time of Fourier dynamic components and +/-2 times of Fourier dynamic components, and the direct current side voltage comprises +/-1 time of Fourier alternating current dynamic components and +/-2 times of Fourier dynamic components and +/-3 times of Fourier alternating current dynamic components and direct current components;
the Fourier dynamic component calculation module is used for calculating each time of Fourier dynamic components and rewriting each time of dynamic phasor into a dq axis lower time-frequency form;
and the model construction module is used for rewriting the Fourier dynamic component calculation module into each time of Fourier dynamic component combination in a dq-axis lower time-frequency form, establishing a flexible direct current converter time-frequency model, and establishing an oscillation analysis model or an impedance analysis model according to an application object.
Further, the model construction module establishes an oscillation analysis model or an impedance analysis model by adopting a transfer function or a transfer function matrix method according to the application object.
Further, the flexible direct current converter modeling apparatus based on the dynamic phasor method according to claim 6, wherein: the Fourier component determination module considers negatives of the alternating current components at each timeSequence part, according to the principle of dynamic phasor method, AC current i of MMCx(t) and a DC voltage ud(t) is represented as:
Figure GDA0002580077060000042
Figure GDA0002580077060000051
in the formula u1,u2,u3,i1,i2Respectively are primary, secondary and tertiary alternating voltage and current components,<>in its dynamic phasor form, the subscripts negative represent the conjugate form and Re represents the real part of the variable.
Further, for the MMC fundamental frequency component, an external steady-state mathematical model of the ith (i ═ 1,2, …, N) converter valve and the ac measurement in a dq coordinate system of a certain flexible interconnection device is expressed as:
Figure GDA0002580077060000052
in the formula, LiAnd RiEquivalent resistance and inductive reactance, C, from valve side to AC sideeqThe equivalent capacitive reactance is VSC-HVDC; u shapesdi、UsqiD-axis and q-axis components of the alternating current measurement equivalent bus voltage are respectively measured; u shapecdi、UcqiThe voltages of d and q axis buses at the alternating current side are respectively; i.e. id、UdiRespectively representing the current and the voltage of the direct current side;
for the high-frequency component of the current, the secondary circulating current satisfies the following conditions:
Figure GDA0002580077060000053
wherein i2dAnd i2qIs the dq-axis component of the secondary circulating current, L0And R0Equivalent inductive reactance for secondary circulating bridge armResistance, subscript x ═ a, b, c; subscripts p, n represent upper and lower bridge arms, respectively;
the voltage components on the capacitor are as follows:
Figure GDA0002580077060000054
Figure GDA0002580077060000061
Figure GDA0002580077060000062
wherein (M)1d,M1q) And (M)2d,M2q) Respectively corresponding to (omega) in dq coordinate system0And 2 omega0) And subscripts d, q represent d, q axis components.
Further, the model construction module comprises a time domain oscillation analysis model construction module and a time domain frequency domain conversion module, wherein
The time domain oscillation analysis model construction module is used for constructing a controller structure model and a converter valve characteristic time domain model, and then combining high-frequency components according to formulas (23) - (25) and a time-frequency model formula (34) so as to construct a flexible and straight state time domain oscillation analysis model;
Figure GDA0002580077060000063
in the formula, A represents a state matrix, B represents an input matrix, n corresponds to the number of times of dynamic phasors, and < > is the form of the dynamic phasors;
and the time domain and frequency domain conversion module is used for carrying out time domain and frequency domain conversion according to the oscillation analysis model constructed by the time domain oscillation analysis model construction module to obtain an impedance analysis model.
On the premise of ensuring the calculation rate, the method improves the problem of the accuracy of the flexible-direct current converter model caused by the assumption of quasi-steady state; in addition, because the high-order harmonic component in the converter valve is considered, an oscillation component model meeting different wide-frequency band analysis is obtained by utilizing a dynamic phasor method.
Drawings
FIG. 1(a) is a block diagram of a DC-DC converter and its sub-modules; FIG. 1(b) is an equivalent model diagram of a soft-direct current converter;
FIG. 2 is a schematic diagram of VSC steady-state control;
FIG. 3 is a block diagram of a control architecture for direct current control;
FIG. 4 is a schematic diagram of the nearest level approximation (NLM);
FIG. 5 is an equivalent circuit diagram of the converter valve and the external AC side of the flexible interconnection apparatus;
FIG. 6 is a diagram of an oscillation analysis model according to the present invention;
FIG. 7 shows the results of the impedance spectrum characteristics of the present invention;
FIG. 8 is a four-terminal MMC-HVDC example system;
fig. 9(a) is the d-axis component of ac current in the MMC1 circulator response, fig. 9(b) is the q-axis component of ac current in the MMC1 circulator response, fig. 9(c) is the dc voltage in the MMC1 circulator response, and fig. 9(d) is the dc current in the MMC1 circulator response;
fig. 10(a) is the d-axis component of ac current in the MMC2 circulator response, fig. 10(b) is the q-axis component of ac current in the MMC1 circulator response, fig. 10(c) is the dc voltage in the MMC1 circulator response, and fig. 10(d) is the dc current in the MMC1 circulator response;
fig. 11(a) is the d-axis component of ac current in the MMC2 circulator response, fig. 11(b) is the q-axis component of ac current in the MMC1 circulator response, fig. 11(c) is the dc voltage in the MMC1 circulator response, and fig. 11(d) is the dc current in the MMC1 circulator response;
fig. 12(a) shows the d-axis component of the ac current in the MMC2 circulator response, fig. 12(b) shows the q-axis component of the ac current in the MMC1 circulator response, fig. 12(c) shows the dc voltage in the MMC1 circulator response, and fig. 12(d) shows the dc current in the MMC1 circulator response.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, 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 some, but not all, embodiments of the present invention. All other embodiments, which can be obtained by a person skilled in the art without any inventive step based on the embodiments of the present invention, are within the scope of the present invention.
The following technical terms are explained first:
definition 1: dynamic phasor method
The dynamic phasor is proposed based on a time-varying fourier decomposition for a non-sinusoidal time variable, the definition of the dynamic phasor being given first from a mathematical point of view.
For a waveform represented in the time domain as x (τ), in any interval τ e (T-T, T), it can be represented by a time-varying Fourier series as:
Figure GDA0002580077060000081
wherein, ω iss＝2π/T，Xk(t) is the k-th time-varying Fourier coefficient, Xk(t) is a function of time. From the fourier decomposition, the k-th order coefficient can be written in the form of:
Figure GDA0002580077060000082
definition of<x>k(t) (or X)k(t)) is the "dynamic phasor" of the kth order, with the fourier coefficients of different orders being defined as the dynamic phasors of different orders. The dynamic phasor is a fourier series that it decomposes within a "sliding window" on the time axis. When a "sliding window" of width T is shifted along the time axis over x (τ), the phasor<x>k(t) changes with time and is therefore also referred to as a "dynamic" phasor, also known as a time-varying phasor.
As can be seen from the above concept of dynamic phasors, dynamic phasors can be interpreted from two perspectives, time domain and frequency domain, respectively. From the time domain, after the window width of a sliding window is selected, real-time Fourier decomposition is carried out on the original time domain signal in the window, each order of dynamic phasor corresponds to each order of time-varying Fourier series, and the original signal can be restored through the Fourier series; from the frequency domain, when the original signal contains different frequency components, the dynamic phasor can decompose the original signal into a form of different frequency signal combinations, namely a fundamental frequency signal and a higher harmonic signal, and each dynamic phasor corresponds to the complex envelope of each frequency signal.
The main ideas of the dynamic phasor modeling are as follows: the time-varying Fourier decomposition of the variables in the system simplifies the original system by ignoring those unimportant terms in the series, while preserving the main series terms (depending on the research needs) that may reflect the properties of the model itself.
Definition 2: flexible direct current converter
1) MMC topological structure and basic mathematical model
The basic principle of MMC is shown in FIG. 1. Fig. 1(a) shows the structure of the MMC circulator submodule, and fig. 1(b) is an equivalent model thereof. The MMC is different from a traditional two-level converter and a clamp type multi-level converter, and a bridge arm of the MMC is not formed by directly connecting a plurality of switching devices in series, but adopts a Sub-Module (SM) cascading mode. The submodule of the MMC generally adopts a half-bridge structure, wherein VT1 and VT2 respectively represent an upper IGBT and a lower IGBT, VD1 and VD2 respectively represent anti-parallel freewheeling diodes corresponding to the upper IGBT and the lower IGBT, and C is a submodule capacitor. u. ofcIs the capacitor voltage usmIs the voltage across the submodule, ismIs the current flowing into the submodule.
For the modular multilevel converter, the submodules of each bridge arm can be independently controlled, so that each bridge arm can be equivalent to a controllable voltage source.
In FIG. 1(a), ixpI represents an upper arm current (x ═ a, b, and c, which represent A, B, C phases, respectively, the same applies hereinafter), and ixnIs the lower arm current uxpIs the upper bridge arm voltage uxnFor the lower bridge arm voltage, p and n represent the upper and lower bridge arms respectively(the same applies below); the o point is a neutral point on the direct current side, and the ground potential is uo；udIs a direct voltage idIs direct current; r0And L0Respectively a bridge arm equivalent loss resistance and a bridge arm reactor, RsAnd LsRespectively an equivalent loss resistance and an equivalent connection reactance at the AC side of the MMC; u. ofsxFor AC system voltage, ixIs an alternating current.
From fig. 1(b), in the equivalent model, each submodule of the MMC is not explicitly given, and in fact, for the MMC, the submodule of each bridge arm can be independently controlled, so that each bridge arm can be equivalent to a controllable voltage source, and the phase voltage and the phase current of the bridge arm can be represented as:
Figure GDA0002580077060000091
Figure GDA0002580077060000092
in the formula (I), the compound is shown in the specification,
Figure GDA0002580077060000101
and
Figure GDA0002580077060000102
respectively corresponding upper and lower bridge arm phase voltages; i.e. ixp、ixnRespectively corresponding upper and lower bridge arm phase currents. The internal virtual electromotive force of the MMC is defined as:
Figure GDA0002580077060000103
the MMC voltage and current modulation ratio can be expressed as
Figure GDA0002580077060000104
Is easy to know, K is more than or equal to 0U,KI≤1，ixIs an ac side line current. Assuming that each phase voltage and current has no negative sequence current and each submodule secondary circulation is zero, each phase voltage and current of the upper bridge arm and each phase current of the lower bridge arm can be respectively expressed as:
Figure GDA0002580077060000105
definition 3: steady-state control strategy for soft-direct current converter
(1) And (3) station level control strategy formulation: the active control mainly comprises active power control, direct current voltage control and frequency control, and the reactive control mainly comprises reactive power control and alternating current voltage control. Because each station cannot simultaneously select two active or reactive control quantities, only one of the two control quantities can be selected. In addition, in different applications, such as two-end active station system, one-end active station/one-end passive station system, and multi-end (three-end and above) system, an instruction for changing the active control strategy and the reactive control strategy can be properly issued according to the needs of the control system in the operation process, as shown in fig. 2.
And the station level control obtains a modulation ratio M and a phase shift angle delta according to the active class instruction reference value and the reactive class instruction reference value given by the system level control, and provides the modulation ratio M and the phase shift angle delta for a trigger pulse generation link of the valve level control. Since the variation of δ mainly affects the transmission of active power and the variation of M mainly affects the transmission of reactive power, the active power can be controlled by changing the phase angle δ and the reactive power can be controlled by changing the modulation ratio M.
Because of having good dynamic response characteristic and being insensitive to system parameter, the current high-power current converter mainly adopts direct current control mode extensively. The direct current control adopts a double-loop control strategy of outer loop voltage control and inner loop current control, and the structure is shown in fig. 3. The outer loop controller generates a suitable reference signal according to an instruction sent by the system level controller and transmits the reference signal to the inner loop current controller. And the inner loop current controller obtains an alternating current voltage reference value expected to be output by the alternating current side of the converter through logic operation according to the instruction signal of the outer loop voltage controller, and sends the alternating current voltage reference value to the valve level control layer.
(2) Optimum level approximation
The recent level approximation modulation strategy (NLM) is to enable the MMC alternating current output voltage to approximate a modulation wave by inputting and cutting out sub-modules. By us(t) instantaneous value, U, of the modulated waveCRepresents the average value of the sub-module capacitor voltage. Each bridge arm comprises the number n of submodules, and only n submodules in each phase unit are put into use at any moment. The upper and lower bridge arms are shared by n submodules in average, and the output voltage of the phase unit is 0 at the moment. As shown in fig. 4, as the instantaneous value of the modulation wave increases from 0, the submodules of the lower arm in the on state of the phase unit gradually increase, the submodules of the upper arm in the on state correspondingly decrease, so that the ac output voltage of the phase unit increases accordingly, and the difference between the two is controlled to be ± UCWithin/2.
The number n of submodules needing to be input into the lower bridge arm and the upper bridge arm at any timedownAnd nupCan be respectively expressed as:
Figure GDA0002580077060000111
in the formula: round (x) denotes taking the nearest integer to x. N is more than or equal to 0 and limited by the number of sub-modulesdown，nup≤n。
After the number of input of the bridge arm sub-modules is determined, the specific input sub-modules need to be further determined by combining the charge and discharge control of the sub-modules. N submodules of each bridge arm are sorted according to the capacitance voltage, and the number of the submodules to be put into is assumed to be NaSelecting N with lowest capacitor voltage when bridge arm current direction is the same as capacitor voltage of submoduleaThe sub-module is used for outputting direct current voltage and charging the direct current voltage at the same time; selecting N with the highest capacitor voltage when the current direction is opposite to the capacitor voltageaAnd the sub-modules are put into operation, discharge the direct-current voltage while outputting the direct-current voltage, and finally realize the balance control of the capacitor voltage. Considering the secondary circulation component, the switching functions of the upper and lower bridge arms meet the following requirements:
Figure GDA0002580077060000121
Figure GDA0002580077060000122
for the phase of the fundamental component of voltage and current, UcirAnd
Figure GDA0002580077060000123
the voltage amplitude and phase of the secondary circulating current component. The modulation ratio of the fundamental and secondary circulating current components can be expressed as:
Figure GDA0002580077060000124
wherein (M)1d,M1q) And (M)2d,M2q) Respectively corresponding to (omega) in dq coordinate system0And 2 omega0) The dq axis component of (a).
The embodiment of the invention provides a flexible direct current converter modeling method based on a dynamic phasor method, which comprises the following steps:
step 1: determining each Fourier component to be selected by the system
Unlike conventional VSCs, the MMC contains a large number of switching processes of power electronic devices inside, and harmonic circulation often occurs between the arms of the bridge. Therefore, if secondary circulation is considered and bridge arm impedance and voltage drop are ignored, the upper and lower bridge arm currents of each phase satisfy:
Figure GDA0002580077060000125
due to the large number of SMs in the submodules of MMC-HVDC, the switching function SpAnd SnThe waveform of (c) can be considered continuous, with an average electromagnetic transient model that satisfies:
Figure GDA0002580077060000126
wherein, C0If C/N is the equivalent capacitance reactance of the bridge arm reactor, the direct-current component and the high-frequency alternating-current component as shown in the formula (13) exist in the direct-current capacitor of each submodule of the MMC-HVDC:
Figure GDA0002580077060000131
in the formula u1,δ1,u2,δ2,u3And delta3The amplitude and the phase of the primary, secondary and tertiary alternating current components are respectively. As can be seen from equation (13):
1) the alternating side current should contain + -1 time and + -2 times Fourier dynamic components;
2) the DC-side voltage should contain the AC-dynamic Fourier components plus or minus 1, plus or minus 2, and plus or minus 3 times, as well as the DC component.
If the negative sequence part of each AC component is considered, the AC current i of MMC is calculated according to the principle of dynamic phasor methodx(t) and a DC voltage ud(t) may be expressed as:
Figure GDA0002580077060000132
Figure GDA0002580077060000133
in the formula u1,u2,u3,i1,i2Respectively are primary, secondary and tertiary alternating voltage and current components,<>in its dynamic phasor form, the subscripts negative represent the conjugate form and Re represents the real part of the variable.
The respective dynamic phasors can be incorporated into the fundamental component by equation (14). It should be noted that the conventional dynamic phasor method often causes the system characteristic root to move (-jn ω) on the virtual axis, which brings calculation errors to the system oscillation analysis. However, since the negative sequence part of each alternating current component is considered in the formula (14), the oscillation analysis model proposed by the present invention can cancel the (-jn ω) -containing part and only take into account the influence of the real part of the dynamic component on the system stability. Therefore, the model provided by the invention is more suitable for the stability analysis of the power system, and the calculation methods of each dynamic component are respectively given below.
Step 2: and calculating the dynamic component of each Fourier, and rewriting the dynamic phasor of each time into a time-frequency form under the dq axis. And fusing the fundamental frequency component and other high-order dynamic components to obtain an integral dynamic phasor model.
(1) MMC fundamental frequency component
The existing VSC and MMC models are more, but mainly aim at parameter design and dynamic optimization control of an internal circulator, and the number of models suitable for oscillation stability analysis of a power system is less.
In order to establish an oscillation analysis model for system stability analysis, the internal dynamic processes of the VSC and the MCC need to be equivalent to the alternating current side. As shown in fig. 5, for a certain flexible interconnection device, the external steady-state mathematical model of the i (i ═ 1,2, …, N) th converter valve and the ac measurement in the dq coordinate system can be expressed as:
Figure GDA0002580077060000141
in the formula (16), LiAnd RiEquivalent resistance and inductive reactance, C, from valve side to AC sideeqThe equivalent capacitive reactance is VSC-HVDC; u shapesdi、UsqiD-axis and q-axis components of the alternating current measurement equivalent bus voltage are respectively measured; u shapecdi、UcqiThe voltages of d and q axis buses at the alternating current side are respectively; i.e. id、UdiRepresenting the dc side current and voltage, respectively.
(2) MMC high-frequency component model
For the current high-frequency component, the secondary loop current satisfies the following formula (12) according to KVL:
Figure GDA0002580077060000142
wherein i2dAnd i2qIs the dq-axis component of the secondary circulating current，L0And R0The subscript x is a, b and c; subscripts p, n denote upper and lower arms, respectively. Assuming that the voltages of the submodules are equal and are kept constant, the bridge arm voltages meet the following conditions:
Figure GDA0002580077060000143
Figure GDA0002580077060000144
submodule voltage uc(i.e., u)cpOr ucq) Equation (13) is satisfied. Substituting equations (18) and (12) into equation (17) while ignoring the third and fourth high frequency components, there are:
Figure GDA0002580077060000145
for ± 1st, + 2nd, + 3rd high frequency voltage phasors, the current flowing through the sub-modules according to KCL satisfies:
Figure GDA0002580077060000151
equation (20) is equivalent to
Figure GDA0002580077060000152
Assuming that the secondary circulating current portion has no fundamental frequency component,
Figure GDA0002580077060000153
substituting the equations (12) and (21) into (22) and converting the equations into dq0 mode, and combining the same terms, the voltage components of each time on the capacitor can be obtained:
Figure GDA0002580077060000154
Figure GDA0002580077060000155
Figure GDA0002580077060000156
and step 3: and combining the Fourier dynamic components rewritten into the dq-axis lower time-frequency form, establishing a flexible direct current converter time-frequency model, and establishing an oscillation analysis model or an impedance analysis model by adopting a transfer function or transfer function matrix method according to an application object.
3.1 constructing a flexible-straight state time domain oscillation analysis model
1. Structure model of construction controller
The main controller is double-ring decoupling control, the outer ring control is constant direct current voltage control, the inner ring control is alternating current control, and the definition is as follows: gcc1，Gcc2And GdccAnd the dynamic states of the current loop PI, the current loop decoupling term and the direct current voltage loop PI are respectively expressed.
Figure GDA0002580077060000161
Figure GDA0002580077060000162
Gdcc＝[kpdcc+kidcc/s 0]T (28)
Figure GDA0002580077060000163
Wherein k ispccAnd kiccIs the coefficient of the current loop PI; k is a radical ofpdccAnd kidccIs a direct current voltage loop PIThe coefficient of (a); zbaseIs a reference value for the impedance, where the superscript "c" represents a variable in the control coordinate system, θ is the angle of the PLL output, fPLL＝kppll+kipllS is a transfer function representing the PI-link dynamics of the PLL, UdAnd UbaseRepresenting the system d-axis terminal voltage and the reference voltage. In addition, voltage feed-forward control is introduced to improve controller performance. In conjunction with equations (26) - (29), a frequency domain representation of the master controller dynamics can be obtained:
Gm1i+Gm2idiff0+Gm3m＝Gmuvuv (30)
wherein:
Figure GDA0002580077060000164
Figure GDA0002580077060000165
Figure GDA0002580077060000166
for CCSC, m2Is the output signal of CCSC for suppressing idiff2，Gccsc1And Gccsc2PI dynamics and decoupling terms used to represent CCSC, respectively:
Figure GDA0002580077060000171
Figure GDA0002580077060000172
wherein k ispccscAnd kiccscIs the coefficient of PI, the frequency domain of the CCSC dynamics is represented as:
Gm21idiff2+Gm22m2＝Gm2uvuv (33)
wherein:
Figure GDA0002580077060000173
Figure GDA0002580077060000174
fig. 6 shows a structural block diagram of an oscillation stability analysis model construction of the soft-direct current converter. The figure shows the converter stations as network pivot points, and synchronous generators or wind farms/photovoltaic plants are connected to the stations by using kirchhoff's law.
2. Constructing a converter valve characteristic time domain model
And obtaining a converter valve characteristic time domain model according to the formulas (3) to (7).
3. Combining high frequency components
The high frequency components are combined according to equations (23) - (25), equation (34) and fig. 6 to establish a system differential dynamic equation, where n is the dynamic component of each time.
From the state space models (16) - (33) and the respective dynamic components, the time-frequency model can be expressed as:
Figure GDA0002580077060000175
in the formula, A represents a state matrix, B represents an input matrix, n corresponds to the number of times of dynamic phasors, and < > is the form of the dynamic phasors.
And 3.2, performing time-domain frequency-domain conversion according to the oscillation analysis model constructed in the step 3.1 to obtain an impedance analysis model.
The time domain state space model of a linear time invariant system can be represented as:
Figure GDA0002580077060000181
wherein x is a state variable; z is an algebraA variable; u and y are input and output, respectively; a. the1，A2，B，C1，C2And D and E are coefficient matrices, respectively. Converting (2) to the frequency domain by a laplacian transform, the state space model can be represented in the s-plane as:
Figure GDA0002580077060000182
where I and 0 represent the identity matrix and the zero matrix of the corresponding dimension. The TFM from input to output can be written as:
Figure GDA0002580077060000183
if the input u is defined as the MMC AC side voltage uvd,uvq]TDefining the output y as MMC AC [ i ]d,iq]TObtaining a theoretical AC admittance model of the MMC according to the step (37); if the input and output are reversed, an alternating current impedance model, i.e. an impedance analysis model, can be obtained.
The embodiment of the invention also provides a modeling device of a soft direct current converter based on a dynamic phasor method, which comprises the following steps:
the Fourier component determination module is used for determining each time of Fourier components required to be selected by the system, wherein each time of Fourier components comprises an alternating current side current component and a direct current side voltage component of the MMC, the alternating current side current comprises +/-1 time of Fourier dynamic components and +/-2 times of Fourier dynamic components, and the direct current side voltage comprises +/-1 time of Fourier alternating current dynamic components and +/-2 times of Fourier dynamic components and +/-3 times of Fourier alternating current dynamic components and direct current components;
the Fourier dynamic component calculation module is used for calculating each time of Fourier dynamic components and rewriting each time of dynamic phasor into a dq axis lower time-frequency form;
and the model construction module is used for rewriting the Fourier dynamic component calculation module into each time of Fourier dynamic component combination in a dq-axis lower time-frequency form, establishing a flexible direct current converter time-frequency model, and establishing an oscillation analysis model or an impedance analysis model according to an application object.
The model construction module establishes an oscillation analysis model or an impedance analysis model by adopting a transfer function or transfer function matrix method according to an application object.
The Fourier component determination module considers the negative sequence part of each alternating current component and the alternating current i of the MMC according to the principle of a dynamic phasor methodx(t) and a DC voltage ud(t) is represented as:
Figure GDA0002580077060000191
Figure GDA0002580077060000192
in the formula u1,u2,u3,i1,i2Respectively are primary, secondary and tertiary alternating voltage and current components,<>in its dynamic phasor form, the subscripts negative represent the conjugate form and Re represents the real part of the variable.
For the MMC fundamental frequency component, an external steady-state mathematical model of the ith (i ═ 1,2, …, N) converter valve and the alternating current measurement in a dq coordinate system of a certain flexible interconnection device is expressed as:
Figure GDA0002580077060000193
in the formula, LiAnd RiEquivalent resistance and inductive reactance, C, from valve side to AC sideeqThe equivalent capacitive reactance is VSC-HVDC; u shapesdi、UsqiD-axis and q-axis components of the alternating current measurement equivalent bus voltage are respectively measured; u shapecdi、UcqiThe voltages of d and q axis buses at the alternating current side are respectively; i.e. id、UdiRespectively representing the current and the voltage of the direct current side;
for the high-frequency component of the current, the secondary circulating current satisfies the following conditions:
Figure GDA0002580077060000194
wherein i2dAnd i2qIs the dq-axis component of the secondary circulating current, L0And R0The subscript x is a, b and c; subscripts p, n represent upper and lower bridge arms, respectively;
the voltage components on the capacitor are as follows:
Figure GDA0002580077060000201
Figure GDA0002580077060000202
Figure GDA0002580077060000203
wherein (M)1d,M1q) And (M)2d,M2q) Respectively corresponding to (omega) in dq coordinate system0And 2 omega0) And subscripts d, q represent d, q axis components.
Wherein the model construction module comprises a time domain oscillation analysis model construction module and a time domain frequency domain conversion module, wherein
The time domain oscillation analysis model construction module is used for constructing a controller structure model and a converter valve characteristic time domain model, and then combining high-frequency components according to formulas (23) - (25) and a time-frequency model formula (34) so as to construct a flexible and straight state time domain oscillation analysis model;
Figure GDA0002580077060000204
in the formula, A represents a state matrix, B represents an input matrix, n corresponds to the number of times of dynamic phasors, and < > is the form of the dynamic phasors;
and the time domain and frequency domain conversion module is used for carrying out time domain and frequency domain conversion according to the oscillation analysis model constructed by the time domain oscillation analysis model construction module to obtain an impedance analysis model.
Frequency domain impedance analysis results of the soft direct current converter:
in order to verify the effectiveness of the proposed method, under the condition that the system generates small disturbance, the proposed improved low-frequency oscillation stability model, the electromagnetic transient model and the traditional low-frequency oscillation stability model are compared and analyzed, and a four-terminal MM-HVDC system with the voltage level of +/-320 kV is built (as shown in FIG. 8). The system consists of a three-terminal alternating current system and a one-terminal wind power plant, wherein the alternating current system 1 is a weak alternating current system (the short circuit ratio is 1.18), the wind power plant adopts a double-fed asynchronous wind driven generator, and the transmission distance of direct current network lines is 100 km. Table 1 gives the converter station operating parameters and control modes,
table 2 shows dc network control parameters and PI controller parameters, respectively. The total order of the low-frequency oscillation stability equation of the multi-end MMC-HVDC system is 60 multiplied by 60.
In order to verify the accuracy of the model provided by the invention when the system generates small disturbance (the disturbance amplitude is 10-20%), the following two operation scenes are specially set:
1) the system oscillation (MMC4 active power decreased from 1.0p.u to 0.8p.u) was set at two seconds for 0.1 s. Pairs of simulated waveforms for each converter station are for example fig. 9 to 12.
TABLE 1 AC network simulation parameters
Figure GDA0002580077060000211
TABLE 2 DC network and control parameters
Figure GDA0002580077060000221
Although the traditional low-frequency oscillation stability model can finally converge to a correct steady-state response value, the method cannot reflect the process of system oscillation in electromagnetic transient simulation. Since the conventional model uses quasi-steady-state assumptions, it cannot reflect the rapidly changing component in the system dynamic response. In contrast, an improved low-frequency oscillation stabilization model based on the dynamic phasor method can successfully reflect the system high-frequency dynamic characteristics, since the dynamic characteristics of higher frequencies of the electronic device are taken into account. As can be seen from fig. 9 to 12, the oscillation process of the system at any time can be successfully predicted by using the low-frequency oscillation stability analysis method provided by the present invention.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solutions of the present invention and not for limiting the same, and although the present invention is described in detail with reference to the above embodiments, those of ordinary skill in the art should understand that: modifications and equivalents may be made to the embodiments of the invention without departing from the spirit and scope of the invention, which is to be covered by the claims.

Claims (8)

1. A flexible direct current converter modeling method based on a dynamic phasor method is characterized by comprising the following steps: the method comprises the following steps:
determining each Fourier component required to be selected by a system, wherein each Fourier component comprises an alternating current side current component and a direct current side voltage component of an MMC (modular multilevel converter), the alternating current side current comprises a Fourier dynamic component for +/-1 time or +/-2 times, and the direct current side voltage comprises a Fourier alternating current dynamic component and a direct current component for +/-1 time or +/-2 times or +/-3 times;
calculating each time of Fourier dynamic component, and rewriting each time of dynamic component into a dq axis lower time-frequency form;
combining the dynamic components of each Fourier rewritten into a dq-axis lower time-frequency form, establishing a flexible direct current converter time-frequency model, and establishing an oscillation analysis model or an impedance analysis model according to an application object;
the second step specifically comprises:
for MMC fundamental frequency components, an external steady-state mathematical model of an ith converter valve and alternating current measurement in a dq coordinate system of certain flexible interconnection equipment is expressed as follows:
Figure FDA0003476801570000011
wherein i is 1,2, …, N, LiAnd RiEquivalent resistance and inductive reactance, C, from valve side to AC sideeqThe equivalent capacitive reactance is VSC-HVDC; u shapesdi、UsqiD-axis and q-axis components of the alternating current measurement equivalent bus voltage are respectively measured; u shapecdi、UcqiThe voltages of d and q axis buses at the alternating current side are respectively; i.e. id、UdiRespectively representing the current and the voltage of the direct current side;
for the high-frequency component of the current, the secondary circulating current satisfies the following conditions:
Figure FDA0003476801570000012
wherein i2dAnd i2qIs the dq-axis component of the secondary circulating current, L0And R0The subscript x is a, b and c; subscripts p, n represent upper and lower bridge arms, respectively;
the voltage components on the capacitor are as follows:
Figure FDA0003476801570000021
Figure FDA0003476801570000022
Figure FDA0003476801570000023
wherein M is1d,M1qAnd M2d,M2qThe dq axis components corresponding to the first and second orders in the dq coordinate system are shown, and the subscripts d and q represent the d and q axis components.
2. A flexible dc converter modeling method based on dynamic phasor method according to claim 1, characterized by: in the first step, the negative sequence part of each alternating current component is considered, and according to the principle of a dynamic phasor method, the alternating current i of the MMCx(t) and a DC voltage ud(t) is represented as:
Figure FDA0003476801570000024
Figure FDA0003476801570000025
in the formula u1,u2,u3,i1,i2Respectively are primary, secondary and tertiary alternating voltage and current components,<>in its dynamic phasor form, the subscripts negative represent the conjugate form and Re represents the real part of the variable.
3. A flexible dc converter modeling method based on dynamic phasor method according to claim 1, characterized by: and establishing an oscillation analysis model or an impedance analysis model by adopting a transfer function or a transfer function matrix method according to the application object.
4. A flexible dc converter modeling method based on dynamic phasor method according to claim 1, characterized by: the third step specifically comprises:
3.1 constructing a flexible-straight state time domain oscillation analysis model
Firstly, constructing a controller structure model and a converter valve characteristic time domain model, and then combining high-frequency components according to formulas (23) - (25) and a time-frequency model formula (34) so as to construct a flexible and straight state time domain oscillation analysis model;
Figure FDA0003476801570000031
in the formula, A represents a state matrix, B represents an input matrix, n corresponds to the number of times of dynamic phasors, and < > is the form of the dynamic phasors;
and 3.2, performing time-domain frequency-domain conversion according to the oscillation analysis model constructed in the step 3.1 to obtain an impedance analysis model.
5. The utility model provides a gentle direct current converter modeling device based on dynamic phasor method which characterized in that includes:
the Fourier component determination module is used for determining each time of Fourier components required to be selected by the system, wherein each time of Fourier components comprises an alternating current side current component and a direct current side voltage component of the MMC, the alternating current side current comprises +/-1 time of Fourier dynamic components and +/-2 times of Fourier dynamic components, and the direct current side voltage comprises +/-1 time of Fourier alternating current dynamic components and +/-2 times of Fourier dynamic components and +/-3 times of Fourier alternating current dynamic components and direct current components;
the Fourier dynamic component calculation module is used for calculating each time of Fourier dynamic components and rewriting each time of dynamic phasor into a dq axis lower time-frequency form;
the model construction module is used for rewriting the Fourier dynamic component calculation module into each time of Fourier dynamic component combination in a dq-axis lower time-frequency form, establishing a flexible direct current converter time-frequency model, and establishing an oscillation analysis model or an impedance analysis model according to an application object;
for MMC fundamental frequency components, an external steady state mathematical model of an ith converter valve and alternating current measurement in a dq coordinate system of certain flexible interconnection equipment is expressed as follows:
Figure FDA0003476801570000041
wherein i is 1,2, …, N, LiAnd RiEquivalent resistance and inductive reactance, C, from valve side to AC sideeqThe equivalent capacitive reactance is VSC-HVDC; u shapesdi、UsqiD-axis and q-axis components of the alternating current measurement equivalent bus voltage are respectively measured; u shapecdi、UcqiThe voltages of d and q axis buses at the alternating current side are respectively; i.e. id、UdiRespectively representing the current and the voltage of the direct current side;
for the high-frequency component of the current, the secondary circulating current satisfies the following conditions:
Figure FDA0003476801570000042
wherein i2dAnd i2qIs the dq-axis component of the secondary circulating current, L0And R0The subscript x is a, b and c; subscripts p, n represent upper and lower bridge arms, respectively;
the voltage components on the capacitor are as follows:
Figure FDA0003476801570000043
Figure FDA0003476801570000044
Figure FDA0003476801570000051
wherein M is1d,M1qAnd M2d,M2qThe dq axis components corresponding to the first and second orders in the dq coordinate system are shown, and the subscripts d and q represent the d and q axis components.
6. A flexible DC/DC converter modeling apparatus based on dynamic phasor method according to claim 5, characterized in that: and the model construction module establishes an oscillation analysis model or an impedance analysis model by adopting a transfer function or transfer function matrix method according to the application object.
7. A flexible DC/DC converter modeling apparatus based on dynamic phasor method according to claim 5, characterized in that: the Fourier component determination module considers the negative sequence part of each alternating current component and according to the principle of a dynamic phasor method, the alternating current i of the MMCx(t) and a DC voltage ud(t) is represented as:
Figure FDA0003476801570000052
Figure FDA0003476801570000053
in the formula u1,u2,u3,i1,i2Respectively are primary, secondary and tertiary alternating voltage and current components,<>in its dynamic phasor form, the subscripts negative represent the conjugate form and Re represents the real part of the variable.
8. A flexible DC/DC converter modeling apparatus based on dynamic phasor method according to claim 5, characterized in that: the model construction module comprises a time domain oscillation analysis model construction module and a time domain and frequency domain conversion module, wherein
The time domain oscillation analysis model construction module is used for constructing a controller structure model and a converter valve characteristic time domain model, and then combining high-frequency components according to formulas (23) - (25) and a time-frequency model formula (34) so as to construct a flexible and straight state time domain oscillation analysis model;
Figure FDA0003476801570000054
in the formula, A represents a state matrix, B represents an input matrix, n corresponds to the number of times of dynamic phasors, and < > is the form of the dynamic phasors;
and the time domain and frequency domain conversion module is used for carrying out time domain and frequency domain conversion according to the oscillation analysis model constructed by the time domain oscillation analysis model construction module to obtain an impedance analysis model.
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