CN115001005A - LCC-HVDC stability analysis method and device considering frequency coupling - Google Patents
LCC-HVDC stability analysis method and device considering frequency coupling Download PDFInfo
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Abstract
The invention discloses a method and a device for analyzing the stability of LCC-HVDC (low-voltage capacitor-high-voltage direct current) considering frequency coupling, wherein the method comprises the steps of modeling a LCC-HVDC control structure to obtain a switching function of the LCC-HVDC; modeling an LCC-HVDC main circuit to obtain a frequency coupling characteristic impedance model of the LCC-HVDC under a phase sequence domain, connecting a switching function of the LCC-HVDC in parallel, solving to obtain a solved frequency coupling characteristic impedance model of the LCC-HVDC, and obtaining a frequency coupling characteristic matrix; under the condition of considering frequency coupling, calculating to obtain a power grid impedance matrix; and judging the stability of the LCC-HVDC transmitting end power grid by adopting an equivalent SISO impedance stability analysis method according to the power grid impedance matrix and the frequency coupling characteristic matrix. The invention avoids errors caused by neglecting frequency coupling, and can accurately analyze the stability of the LCC-HVDC and weak power grid interconnection system under complex conditions.
Description
Technical Field
The invention relates to the technical field of high-voltage direct-current power transmission, in particular to a method and a device for analyzing the stability of LCC-HVDC (liquid crystal display-high voltage direct current) in consideration of frequency coupling.
Background
With the continuous development of social economy, in order to meet the demand of rapid load increase, the scale of a power grid is gradually enlarged, and high-voltage direct-current transmission is widely applied to a power system in China. The current high-voltage direct-current transmission technology comprises power grid commutation converter type high-voltage direct-current transmission (LCC-HVDC), voltage source converter type high-voltage direct-current transmission and modular multi-level converter type high-voltage direct-current transmission, wherein the LCC-HVDC technology is mature, has the characteristics of large transmission capacity, low converter station loss and the like, occupies a dominant position in the market, and still occupies a large share of the market in a period of time in the future. The local grid providing reactive support for LCC-HVDC operation has the feature of a "weak link grid" due to its distance from the HVDC rectifier stations, so that the weak grid and the LCC-HVDC interconnected system are at risk of subsynchronous/supersynchronous oscillations.
The stability analysis method based on the impedance model is a simple and effective system stability analysis method, which obtains the port impedance characteristics of the power electronic device and the power grid respectively and judges the stability of the interconnected system according to the impedance ratio between the port impedance characteristics and the impedance ratio.
In a traditional LCC-HVDC transmit-end grid stability analysis, it is generally considered that LCC-HVDC can be decomposed into a positive sequence subsystem and a negative sequence subsystem which are decoupled from each other, and each subsystem has a single-in and single-out characteristic in a frequency domain in a small-signal sense. Therefore, the transmission-end power grid can stably operate if and only if the LCC-HVDC positive sequence subsystem and the negative sequence subsystem both meet the single-in and single-out Nyquist stability criterion.
However, if the following is present in the LCC-HVDC control: (1) the bandwidth of the phase-locked loop controller is large; (2) the inductance of the direct current line is small; (3) the dc current controller has a large bandwidth, and when a voltage disturbance of a specific frequency is applied to a Point of Common Coupling (PCC), a current response component of a different frequency is generated in addition to a current response component of the same frequency, which is called a frequency coupling characteristic of LCC-HVDC. Because the frequency coupling phenomenon has the characteristic of single input and multiple output in a frequency domain, the positive sequence impedance and the negative sequence impedance of the system are not decoupled any more, and the original single input and single output stability criterion is not applicable any more.
In recent years, some researchers have conducted some studies on the stability of the LCC-HVDC transmission-side grid. LIU Hanchao et al, in a document titled Small-signal stability analysis of offset wire with LCC HVDC (2013IEEE Grenobel reference. Grenobel: IEEE, 2013: 1-8), set up an impedance model of an LCC-HVDC rectification station by performing Small-signal linearization on a phase-locked loop and a phase-controlled link, neglect a frequency coupling phenomenon, and have only positive sequence impedance and negative sequence impedance, and perform Small-signal stability analysis by using the positive sequence impedance. Liu and the like consider the influence of LCC-HVDC frequency coupling terms in a document which is titled as a direct-drive wind farm and analyzed by LCC-HVDC outgoing system impedance modeling and oscillation mechanism (Chinese Motor engineering report, 2021, 41 (10): 3492 and 3504), study the oscillation risk and mechanism which may exist in the direct-drive wind farm and the LCC-HVDC interconnection system, but only consider the frequency coupling characteristic of positive sequence impedance during analysis.
In summary, the current research on the stability of the LCC-HVDC transmission-end power grid does not adopt a unified 2 × 2 LCC-HVDC impedance analysis model which can accurately describe the coexistence of multiple frequency coupling reasons such as phase-locked loop control asymmetry and modulation module input signal asymmetry, and the stability problem of the LCC-HVDC and weak power grid interconnection system under the coexistence of multiple frequency coupling factors cannot be accurately analyzed; therefore, a more complete method for analyzing the stability of the LCC-HVDC system is urgently needed.
Disclosure of Invention
The technical problem to be solved by the invention is that a unified 2 x 2 LCC-HVDC impedance analysis model which can accurately describe the coexistence of multiple frequency coupling reasons such as phase-locked loop control asymmetry and modulation module input signal asymmetry is not adopted in the current research on the stability of an LCC-HVDC transmitting end power grid, and the stability problem of an LCC-HVDC and weak power grid interconnection system under the coexistence of multiple frequency coupling factors cannot be accurately analyzed.
The invention aims to provide an LCC-HVDC stability analysis method and device considering frequency coupling, wherein a corresponding LCC-HVDC impedance model can describe the frequency coupling characteristic under the condition that various frequency coupling factors coexist, and the corresponding criterion for analyzing and judging the stability is an equivalent SISO impedance stability analysis method; the stability problem of an LCC-HVDC and weak power grid interconnection system under the condition of coexistence of multiple frequency coupling factors can be accurately analyzed.
The invention is realized by the following technical scheme:
in a first aspect, the present invention provides a method for analyzing the stability of an LCC-HVDC system in consideration of frequency coupling characteristics, the method comprising:
modeling an LCC-HVDC control structure to obtain a switching function of the LCC-HVDC;
modeling an LCC-HVDC main circuit to obtain a frequency coupling characteristic impedance model of the LCC-HVDC under a phase sequence domain; the switching function of the LCC-HVDC and the frequency coupling characteristic impedance model of the LCC-HVDC are simultaneously established (namely, the switching function of the LCC-HVDC is substituted into the frequency coupling characteristic impedance model of the LCC-HVDC), the solved frequency coupling characteristic impedance model of the LCC-HVDC is obtained through solution, and a frequency coupling characteristic matrix Y is obtained LCC ；
Under the condition of considering frequency coupling, calculating to obtain a power grid impedance matrix Z g ；
According to the network impedance matrix Z g And the frequency coupling characteristic matrix Y LCC By usingAnd judging the stability of the LCC-HVDC transmitting end power grid based on an equivalent SISO impedance stability analysis method.
The working principle is as follows:
based on the LCC-HVDC stability analysis method in the prior art, LIU Hanchao and the like carry out Small signal linearization on a phase-locked loop and a phase-controlled link in a document with the title of Small-signal stability analysis of offset wire with frequency HVDC (2013IEEE Grenobel reference. Grenobel: IEEE, 2013: 1-8), thereby establishing an impedance model of the LCC-HVDC rectifying station, but neglecting the frequency coupling phenomenon, the established model only has positive sequence impedance and negative sequence impedance, and the positive sequence impedance is used for carrying out Small signal stability analysis. Liu and the like consider the influence of LCC-HVDC frequency coupling terms in a document which is titled as a direct-drive wind farm and analyzed by LCC-HVDC outgoing system impedance modeling and oscillation mechanism (Chinese Motor engineering report, 2021, 41 (10): 3492 and 3504), study the oscillation risk and mechanism which may exist in the direct-drive wind farm and the LCC-HVDC interconnection system, but only consider the frequency coupling characteristic of positive sequence impedance during analysis.
The invention considers that the positive sequence impedance and the negative sequence impedance of LCC-HVDC have frequency coupling phenomenon at the same time under the practical condition, and the characteristic presented to the outside is characterized by applying a 2 x 2 impedance matrix. The invention designs an LCC-HVDC system stability analysis method considering frequency coupling characteristics, and a frequency coupling characteristic matrix Y in a frequency coupling characteristic impedance model of the LCC-HVDC system solved by the method LCC Not only the presence of positive sequence impedance (Y) 11 Inverse of(s), negative sequence impedance (Y) 22 Inverse of(s), the frequency coupling characteristics of the positive sequence impedance and the frequency coupling characteristics of the negative sequence impedance (Y) are also taken into account 21 (s) is a positive sequence admittance coupling term, Y 12 (s) is a negative sequence admittance coupling term), and neither the positive sequence impedance coupling term nor the negative sequence impedance coupling term is zero; in practical situations, the frequency coupling degree of the LCC-HVDC is strong in the middle and low frequency bands, and the positive sequence impedance and the negative sequence impedance have frequency coupling characteristics. Therefore, the LCC-HVDC system stability analysis method provided by the invention is more suitable for actual conditions and is more perfect than the existing LCC-HVDC impedance stability analysis method, so that errors caused by neglecting frequency coupling are avoided, and the method can be used for accurately analyzing the stability of the LCC-HVDC systemAnd analyzing the stability of the LCC-HVDC and weak power grid interconnection system under a complex condition.
The LCC-HVDC system stability analysis method is not only suitable for complex conditions with various frequency coupling factors coexisting, but also suitable for simpler working conditions by correspondingly simplifying the LCC-HVDC model, so that the method has strong applicability.
Further, the frequency coupling characteristic impedance model of the LCC-HVDC system is:
in the formula: i is p [f p ]For LCC-HVDC at the point of common coupling at frequency f p Positive sequence current component of (I) n [f p -2f 1 ]For LCC-HVDC at the point of common coupling at a frequency f p -2f 1 Negative-sequence current component of (V) p [f p ]For LCC-HVDC at the point of common coupling at a frequency f p Positive sequence voltage component of, V p2 [f p -2f 1 ]For LCC-HVDC at the point of common coupling at a frequency f p -2f 1 Negative sequence voltage component of, Y LCC Frequency coupling characteristic matrix, Y, for LCC-HVDC 11 (s) is positive sequence admittance, Y 22 (s) is negative sequence admittance, Y 21 (s) is a positive sequence admittance coupling term, Y 12 (s) is a negative sequence admittance coupling term; f. of p For frequency of disturbance voltage on the AC side of LCC-HVDC, f 1 Is the fundamental frequency.
Wherein,
further, the step of modeling the LCC-HVDC main circuit comprises the following steps:
according to a frequency domain convolution theorem, convolving LCC-HVDC alternating voltage with a switching function of the LCC-HVDC to obtain direct-current voltage frequency domain components;
dividing the direct current voltage frequency domain component by the direct current line impedance to obtain a direct current frequency domain component;
convolving the direct current frequency domain component with the switching function of the LCC-HVDC to obtain an alternating current frequency domain component;
dividing the frequency domain component of the alternating current by the LCC-HVDC alternating voltage to obtain a frequency coupling characteristic matrix Y LCC 。
Further, the grid impedance matrix Z g The expression is as follows:
in the formula: z g As a network impedance matrix, Z 11 (s) is the positive sequence impedance of the grid in the complex frequency domain, Z 22 And(s) is the negative sequence impedance of the power grid in the complex frequency domain, and s is a Laplace operator.
Further, the method for judging the stability of the LCC-HVDC transmission end power grid by using the equivalent SISO-based impedance stability analysis method specifically includes:
adopting an equivalent SISO-based impedance stability analysis method to couple the frequency coupling characteristic matrix Y LCC The off-diagonal elements of the (admittance matrix of the converter system) and the grid impedance are transformed to the main diagonal, resulting in an equivalent SISO impedance Z SISO (ii) a The equivalent SISO impedance Z is plotted in Bode diagram SISO And the positive sequence impedance Z of the power grid 11 (s); making equivalent SISO impedance Z SISO And the positive sequence impedance Z of the power grid 11 (s) determining whether the phase difference at the intersection of the amplitudes of the two impedance curves exceeds 180 °; if yes, judging that the system is unstable; if not, the system is judged to be stable.
Further, the switching function expression of the LCC-HVDC comprises an expression of a frequency component and an expression of an amplitude component;
the expression for the frequency components is: f is mf 1 +n(f p -f 1 )；
The expression for the magnitude component is:
in the formula: s a1 [f]For the component of the LCC-HVDC A1 phase switching function at frequency f, m is 6k + -1, alpha 0 For the triggered delay angle steady state value of LCC-HVDC,
is the phase of the voltage at the fundamental frequency,
for modulating modules at frequency f p -f 1 The gain of the lower one of the two antennas,
for modulating modules at frequency f p -f 1 The conjugate of the gain of (d).
Further, said components
According to the LCC-HVDC control structure, small-signal modeling is performed on a direct current control link and a phase-locked loop control link step by step to obtain the LCC-HVDC control structure.
In a second aspect, the present invention further provides an LCC-HVDC system stability analysis apparatus considering frequency coupling characteristics, which supports the LCC-HVDC system stability analysis method considering frequency coupling characteristics; the device includes:
the LCC-HVDC control structure modeling unit is used for modeling the LCC-HVDC control structure to obtain a switching function of the LCC-HVDC;
the LCC-HVDC main circuit modeling unit is used for modeling the LCC-HVDC main circuit to obtain a frequency coupling characteristic impedance model of the LCC-HVDC in a phase sequence domain; the switching function of the LCC-HVDC and the frequency coupling characteristic impedance model of the LCC-HVDC are simultaneously established (namely, the switching function of the LCC-HVDC is substituted into the frequency coupling characteristic impedance model of the LCC-HVDC), the solved frequency coupling characteristic impedance model of the LCC-HVDC is obtained through solution, and a frequency coupling characteristic matrix Y is obtained LCC ；
A grid impedance matrix calculation unit for considering frequency couplingUnder the condition, a power grid impedance matrix Z is obtained through calculation g ；
A stability judgment unit for judging the stability of the grid impedance matrix Z g And the frequency coupling characteristic matrix Y LCC And judging the stability of the LCC-HVDC transmitting end power grid by adopting an equivalent SISO impedance stability analysis method.
In a third aspect, the present invention provides a computer device comprising a memory, a processor and a computer program stored in the memory and executable on the processor, wherein the processor implements the LCC-HVDC system stability analysis method taking the frequency coupling characteristic into account when executing the computer program.
In a fourth aspect, the present invention further provides a computer-readable storage medium storing a computer program, which when executed by a processor implements the LCC-HVDC system stability analysis method taking into account frequency coupling characteristics.
Compared with the prior art, the invention has the following advantages and beneficial effects:
1. the method can be used for analyzing the stability of the LCC-HVDC transmitting-end power grid under the frequency coupling characteristic; in an actual situation, the frequency coupling degree of the LCC-HVDC in the medium-low frequency band is high, and the positive sequence impedance and the negative sequence impedance have frequency coupling characteristics, so that the LCC-HVDC system stability analysis method considering the frequency coupling characteristics is more suitable for the actual situation and is more perfect than the existing LCC-HVDC impedance stability analysis method, errors caused by neglecting frequency coupling are avoided, and the stability of an LCC-HVDC and weak power grid interconnection system under a complex situation can be accurately analyzed;
2. the LCC-HVDC system stability analysis method and device considering the frequency coupling characteristic are not only suitable for complex situations with various frequency coupling factors coexisting, but also suitable for simpler working situations by correspondingly simplifying the LCC-HVDC model, so that the method and device have strong applicability.
Drawings
The accompanying drawings, which are included to provide a further understanding of the embodiments of the invention and are incorporated in and constitute a part of this application, illustrate embodiment(s) of the invention and together with the description serve to explain the principles of the invention. In the drawings:
FIG. 1 is a schematic flow chart of a method for analyzing the stability of an LCC-HVDC system in accordance with the present invention, taking frequency coupling characteristics into account;
FIG. 2 is a block diagram of the LCC-HVDC system architecture and control thereof in accordance with the present invention;
FIG. 3 is a schematic diagram of the results of an equivalent SISO impedance stability analysis method according to the present invention;
FIG. 4 is a schematic diagram of a simulation waveform of an LCC-HVDC system of the present invention;
FIG. 5 is a schematic diagram illustrating FFT analysis results of PCC voltages of the system of the present invention;
fig. 6 is a schematic structural diagram of an LCC-HVDC system stability analysis apparatus in accordance with the present invention, which takes frequency coupling characteristics into consideration.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail below with reference to examples and accompanying drawings, and the exemplary embodiments and descriptions thereof are only used for explaining the present invention and are not meant to limit the present invention.
Example 1
As shown in fig. 1, the present invention relates to a method for analyzing stability of an LCC-HVDC system in consideration of frequency coupling characteristics, the method including:
modeling an LCC-HVDC control structure to obtain a switching function of the LCC-HVDC;
modeling an LCC-HVDC main circuit to obtain a frequency coupling characteristic impedance model of the LCC-HVDC under a phase sequence domain; the switching function of the LCC-HVDC and the frequency coupling characteristic impedance model of the LCC-HVDC are simultaneously established (namely, the switching function of the LCC-HVDC is substituted into the frequency coupling characteristic impedance model of the LCC-HVDC), the solved frequency coupling characteristic impedance model of the LCC-HVDC is obtained through solution, and a frequency coupling characteristic matrix Y is obtained LCC ；
Under the condition of considering frequency coupling, calculating to obtain a power grid impedance matrix Z g ；
According to the network impedance matrix Z g And said frequencyCoupling characteristic matrix Y LCC And judging the stability of the LCC-HVDC transmission end power grid by adopting an equivalent SISO impedance stability analysis method.
The specific implementation is as follows:
(1) according to the LCC-HVDC system structure and the control block diagram (namely, the control structure and the main circuit), the LCC-HVDC control structure is modeled to obtain the relation between alternating and direct current voltages and currents of the LCC-HVDC, namely, the switching function of the LCC-HVDC, and then the relation is connected with the main circuit equation under the phase sequence domain, and the LCC-HVDC system structure and the control block diagram are shown in FIG. 2 by taking a 500MW twelve-pulse LCC-HVDC rectifier station system as an example.
In FIG. 2, the voltage at the PCC point is denoted v a 、v b 、v c LCC-HVDC AC input current is denoted as i a 、i b And i c The LCC-HVDC rectifier station adopts a constant direct current control mode, and the inverter station adopts a constant direct current voltage control mode, so that the inverter station can be approximately equivalent to a constant direct current source V dc0 . DC side inductor L d Representing the sum of the DC reactor and the DC line inductance, and the DC side resistance R d Representing the resistance of the DC line and the capacitance C on the DC side d Representing the dc line capacitance. The twelve-pulse LCC-HVDC generates trigger pulse by a phase control module, and the phase control module has two inputs including trigger angle alpha and equivalent grid voltage phase angle theta L 。I dc And I dc0 Respectively LCC-HVDC direct current and its reference value, H im (s) represents a DC current measurement stage comprising a constant gain and a first order low pass filter, H i (s) stands for direct current loop PI controller. H PLL (s) stands for phase-locked loop PI controller, [ theta ] L (0) Mod is the remainder operation for the phase lag of the lth switch.
Considering the frequency coupling, the frequency coupling characteristic impedance model of the LCC-HVDC is defined as follows:
in the formula: i is p [f p ]Is LCC-HVDCFrequency f at point of common coupling p Positive sequence current component of (I) n [f p -2f 1 ]For LCC-HVDC at the point of common coupling at a frequency f p -2f 1 Negative-sequence current component of, V p [f p ]For LCC-HVDC at the point of common coupling at a frequency f p Positive sequence voltage component of (V) p2 [f p -2f 1 ]For LCC-HVDC at the point of common coupling at a frequency f p -2f 1 Negative sequence voltage component of, Y LCC Frequency coupling characteristic matrix, f, for LCC-HVDC p For frequency of disturbance voltage on the AC side of LCC-HVDC, f 1 Is the fundamental frequency.
Frequency coupling characteristic matrix Y LCC Middle Y 11 (s) is positive sequence admittance, Y 22 (s) is negative sequence admittance, Y 21 (s) is a positive order admittance coupling term, Y 12 (s) is a negative sequence admittance coupling term; s is the laplace operator.
Wherein,
firstly, suppose that the A phase voltage of the AC power network is superimposed by a frequency f p The positive sequence admittance and the coupling term thereof are derived from the positive sequence small signal perturbation term.
LCC-HVDC alternating voltage: the time domain expression for a-phase voltages may be expressed as:
wherein, V 1 、f 1 、
Respectively, the amplitude, frequency, phase, V, of the fundamental voltage p 、f p 、
Respectively, the amplitude, frequency, phase, V, of the disturbance voltage p ＜＜V 1 。
LCC-HVDC ac voltage: the frequency domain expression for a-phase voltage may be expressed as:
according to the LCC-HVDC system block diagram shown in fig. 2, a switching function can be used to describe the relationship between the ac side and the dc side of the LCC-HVDC, with which the LCC-HVDC dc voltage can be expressed as:
wherein, V dc1 (t) is the DC voltage of the lower six-pulse bridge, V dc2 (t) is the DC voltage of the upper six-pulse bridge, S k1 (t)、S k2 (t) is the switching function of the phases k1, k2, respectively, v k1 (t)、v k2 And (t) are secondary side voltages of the k1 and k2 phases of the transformer respectively.
Similarly, the LCC-HVDC ac side current can be expressed as:
wherein, I dc (t) is LCC-HVDC direct current, i k1 (t)、i k2 And (t) secondary side currents of the k1 phases and the k2 phases respectively.
Assuming transformer leakage inductance is neglected, taking the switching function of phase a1 as an example, it is defined as:
and transforming the A1 phase switching function into a frequency domain by adopting 3-D Fourier transform, wherein the frequency components are as follows: mf (m) of 1 ±n(f p -f 1 ) The amplitude may be expressed as:
wherein S is a1 [f]For the component of LCC-HVDC A1 phase switching function under the frequency f, the switching functions of the other phases can be obtained only by carrying out phase shift of a certain angle on the basis of the A1 phase switching function, wherein m is 6k +/-1, and alpha is 0 For the triggered delay angle steady state value of LCC-HVDC,
for modulating modules at frequency f p -f 1 The following gain, expressed as:
where, P is input active power, Q is input reactive power, I ═ P + jQ dc Is the steady-state value of LCC-HVDC direct current,
Z dc (s) is the dc line impedance expressed as:
specifically, the step of modeling the LCC-HVDC main circuit includes:
according to a frequency domain convolution theorem, convolving LCC-HVDC alternating voltage with a frequency domain model of a switching function of the LCC-HVDC, and considering the influence of different wiring modes of a transformer winding on a voltage phase to obtain direct-current voltage frequency domain components; the direct-current voltage frequency domain component expression is as follows:
wherein, V dc [f]For the component of the LCC-HVDC direct voltage at frequency f, superscript " * "denotes the conjugation of a physical quantity.
Will direct the currentVoltage frequency domain component divided by dc line impedance Z dc (s) obtaining a direct current frequency domain component I dc (s)；
Similarly, according to the frequency domain convolution theorem, the direct current frequency domain component is convolved with the switching function of the LCC-HVDC, the influence of different wiring modes of a transformer winding on the current phase is considered, and the coupling relation between the switching function and the direct current side current is summarized as table 1 to obtain the alternating current frequency domain component;
dividing the frequency domain component of the alternating current by the LCC-HVDC alternating voltage to obtain a frequency coupling characteristic matrix Y LCC 。
As can be seen from table 1, there are two common ways of generating the LCC-HVDC frequency coupling component: 1) the frequency of the direct current is 12kf 1 The steady state harmonic component of (a) and the frequency of the switching function of (-12k-1) f 1 +(f p -f 1 ) The disturbance components of (a); 2) the frequency of the direct current is 12kf 1 +(f p -f 1 ) Has a frequency of (-12k-1) f in the disturbance component and the switching function 1 The steady state harmonic components of (a) interact.
TABLE 1 DC-CURRENT AND SWITCHING FUNCTION COUPLING RELATIONS TABLE
Considering that in practical engineering, the LCC rectifier station system is usually provided with an ac filter, including 11, 13 times of tuning filter and 24 times of high-pass damping filter, the expressions of the positive sequence admittance and the coupling term thereof of the LCC rectifier station system are:
since the conjugate of the positive sequence component of the three-phase alternating current physical quantity at a certain frequency f and the negative sequence component thereof at a negative frequency-f is equivalent, Y can be admitted by the positive sequence of LCC-HVDC and the coupling term thereof 11 (s) and Y 21 (s) carrying out a certain transformation to obtain negative sequence and its coupling term admittance Y 22 (s) andY 12 (s), the specific transformation process is as follows:
Y 22 (s)＝Y 11 [-(s-j2ω 1 )] *
Y 12 (s)＝Y 21 [-(s-j2ω 1 )] *
(2) under the condition of considering frequency coupling, calculating to obtain a power grid impedance matrix; the grid impedance matrix is as follows:
wherein: z g As a network impedance matrix, Z 11 (s) is the positive sequence impedance of the grid in the complex frequency domain, Z 22 And(s) is the negative sequence impedance of the power grid in the complex frequency domain, and s is a Laplace operator. In the examples, Z 11 (s) and Z 22 (s) are respectively:
Z 11 (s)＝sL g
Z 22 (s)＝(s-j4πf 1 )L g
s＝j2πf p
wherein: l is g Is the line inductance.
(3) According to the network impedance matrix Z g And the frequency coupling characteristic matrix Y LCC And judging the stability of the LCC-HVDC transmitting end power grid by adopting an equivalent SISO impedance stability analysis method. The method specifically comprises the following steps:
adopting an equivalent SISO-based impedance stability analysis method to couple the frequency coupling characteristic matrix Y LCC The off-diagonal elements and the grid impedance are converted to the main diagonal to obtain the equivalent SISO impedance Z SISO (ii) a The equivalent SISO impedance Z is plotted in Bode diagram SISO And the positive sequence impedance Z of the power grid 11 (s); making equivalent SISO impedance Z SISO And the positive sequence impedance Z of the power grid 11 (s) determining whether the phase difference at the intersection of the amplitudes of the two impedance curves exceeds 180 °; if yes, judging that the system is unstable; if not, the system is judged to be stable.
Equivalent SISO impedance model Z SISO The expression of (a) is:
the result of the equivalent SISO impedance stability analysis method based on the invention is shown in a schematic diagram as a figure 3.
A simulation model is built under a Simulink module of MATLAB software, system parameters of an LCC-HVDC rectifier station in the example are shown in a table 2, and the equivalent inductance of a power grid is L g 1.059H, corresponding to a short circuit ratio of 1.5.
TABLE 2 LCC-HVDC rectifier station system parameter table
In MATLAB/Simulink simulation, the DC current loop control bandwidth is changed at 2s so that k is ip ＝0.89、k ii The waveforms of the LCC-HVDC dc voltage and dc current, the PCC point ac voltage and the input LCC-HVDC ac current are shown in fig. 4, 88.2. In fig. 4, the abscissa indicates the time of the simulation operation, and the ordinate indicates the LCC-HVDC ac voltage, the LCC-HVDC ac current, the LCC-HVDC dc voltage, and the LCC-HVDC dc current, respectively, from top to bottom. As can be seen from fig. 4, the system has a significant oscillation phenomenon, which indicates that the sending-end power grid is unstable at this time.
The FFT analysis of the PCC point voltage shown in fig. 4 is performed, and the obtained FFT analysis result is shown in fig. 5. In fig. 5, the abscissa represents frequency and the ordinate represents amplitude. From fig. 5, it can be found that, the THD is 11.43%, the PCC point voltage has larger harmonic resonance of 24Hz and 124Hz, and the result is consistent with the prediction result based on the equivalent SISO impedance stability analysis method as shown in fig. 3, which proves the accuracy of the LCC-HVDC system stability analysis method considering the frequency coupling factor characteristic.
Aiming at an LCC-HVDC system, the method considers the coexistence of various frequency coupling factors, establishes an LCC-HVDC frequency coupling characteristic impedance model under a phase sequence coordinate system, and calculates to obtain a power grid impedance matrix under the condition of considering frequency coupling. The stability analysis method is based on an equivalent SISO impedance stability analysis method, the off-diagonal elements of the LCC-HVDC admittance matrix and the power grid impedance are converted to the main diagonal, the stability of the LCC-HVDC and weak power grid interconnection system is judged by judging the phase difference at the intersection point of the equivalent SISO impedance and the positive sequence impedance curve amplitude of the power grid, the stability analysis method can be used for considering the system stability analysis under the complex condition of frequency coupling in the actual engineering, and is more perfect compared with the existing stability analysis method based on the LCC-HVDC impedance, so that the analysis error caused by neglecting the frequency coupling is avoided, and the stability of the LCC-HVDC system under the complex condition can be more accurately analyzed.
Example 2
As shown in fig. 6, the present embodiment is different from embodiment 1 in that the present embodiment provides an LCC-HVDC system stability analysis apparatus that takes into account frequency coupling characteristics, which supports the LCC-HVDC system stability analysis method taking into account frequency coupling characteristics described in embodiment 1; the device includes:
the LCC-HVDC control structure modeling unit is used for modeling the LCC-HVDC control structure to obtain a switching function of the LCC-HVDC;
the LCC-HVDC main circuit modeling unit is used for modeling the LCC-HVDC main circuit to obtain a frequency coupling characteristic impedance model of the LCC-HVDC under a phase sequence domain; the switching function of the LCC-HVDC and the frequency coupling characteristic impedance model of the LCC-HVDC are simultaneously established (namely, the switching function of the LCC-HVDC is substituted into the frequency coupling characteristic impedance model of the LCC-HVDC), the solved frequency coupling characteristic impedance model of the LCC-HVDC is solved, and a frequency coupling characteristic matrix Y is obtained LCC ；
A grid impedance matrix calculation unit for calculating a grid impedance matrix Z under the condition of considering frequency coupling g ；
A stability judgment unit for judging the stability of the grid impedance matrix Z g And the frequency coupling characteristic matrix Y LCC To adoptAnd judging the stability of the LCC-HVDC transmission end power grid by using an equivalent SISO impedance stability analysis method.
The execution process of each unit is executed according to the flow steps of the LCC-HVDC system stability analysis method considering the frequency coupling characteristic described in embodiment 1, and details are not repeated in this embodiment.
The LCC-HVDC system stability analysis device provided by the invention is more suitable for actual conditions and is more perfect than the existing LCC-HVDC impedance stability analysis method, so that errors caused by neglecting frequency coupling are avoided, and the stability of an LCC-HVDC and weak power grid interconnection system under complex conditions can be accurately analyzed. The LCC-HVDC system stability analysis device is not only suitable for complex conditions with various frequency coupling factors, but also suitable for simpler working conditions by correspondingly simplifying the LCC-HVDC model, so the device has strong applicability.
Meanwhile, the invention also provides a computer device, which comprises a memory, a processor and a computer program stored in the memory and capable of running on the processor, wherein the processor realizes the LCC-HVDC system stability analysis method considering the frequency coupling characteristic when executing the computer program.
Meanwhile, the present invention also provides a computer-readable storage medium storing a computer program which, when executed by a processor, implements the LCC-HVDC system stability analysis method taking the frequency coupling characteristic into account.
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.
The above-mentioned embodiments are intended to illustrate the objects, technical solutions and advantages of the present invention in further detail, and it should be understood that the above-mentioned embodiments are merely exemplary embodiments of the present invention, and are not intended to limit the scope of the present invention, and any modifications, equivalent substitutions, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (10)
1. An LCC-HVDC system stability analysis method taking frequency coupling characteristics into account, the method comprising:
modeling an LCC-HVDC control structure to obtain a switching function of the LCC-HVDC;
modeling an LCC-HVDC main circuit to obtain a frequency coupling characteristic impedance model of the LCC-HVDC under a phase sequence domain; the switching function of the LCC-HVDC and the frequency coupling characteristic impedance model of the LCC-HVDC are connected, the solved frequency coupling characteristic impedance model of the LCC-HVDC is obtained through solving, and a frequency coupling characteristic matrix is obtained;
under the condition of considering frequency coupling, calculating to obtain a power grid impedance matrix;
and judging the stability of the LCC-HVDC transmitting end power grid by adopting an equivalent SISO impedance stability analysis method according to the power grid impedance matrix and the frequency coupling characteristic matrix.
2. The method of analyzing stability of an LCC-HVDC system in consideration of frequency coupling characteristics of claim 1, wherein the impedance model of frequency coupling characteristics of LCC-HVDC is:
in the formula: i is p [f p ]For LCC-HVDC at the point of common coupling at a frequency f p Positive sequence current component of (I) n [f p -2f 1 ]For LCC-HVDC at the point of common coupling at a frequency f p -2f 1 Negative-sequence current component of (V) p [f p ]For LCC-HVDC at the point of common coupling at a frequency f p Positive sequence voltage component of (V) p2 [f p -2f 1 ]For LCC-HVDC at the point of common coupling at a frequency f p -2f 1 Negative sequence voltage component of, Y LCC Frequency coupling characteristic matrix, Y, for LCC-HVDC 11 (s) is positive sequence admittance, Y 22 (s) is negative sequence admittance, Y 21 (s) is a positive order admittance coupling term, Y 12 (s) is a negative sequence admittance coupling term; f. of p For frequency of disturbance voltage on the AC side of LCC-HVDC, f 1 Is the fundamental frequency.
3. The method for analyzing stability of an LCC-HVDC system in consideration of frequency coupling characteristics according to claim 1 or 2, wherein the step of modeling the LCC-HVDC main circuit comprises:
according to a frequency domain convolution theorem, convolving LCC-HVDC alternating voltage with a switching function of the LCC-HVDC to obtain direct-current voltage frequency domain components;
dividing the direct current voltage frequency domain component by the direct current line impedance to obtain a direct current frequency domain component;
convolving the direct current frequency domain component with the switching function of the LCC-HVDC to obtain an alternating current frequency domain component;
and dividing the alternating current frequency domain component by the LCC-HVDC alternating voltage to obtain a frequency coupling characteristic matrix.
4. The LCC-HVDC system stability analysis method taking into account frequency coupling characteristics of claim 1, wherein the grid impedance matrix expression is:
in the formula: z g As a network impedance matrix, Z 11 (s) is the positive sequence impedance of the grid in the complex frequency domain, Z 22 And(s) is the negative sequence impedance of the power grid in a complex frequency domain, and s is a Laplace operator.
5. The method for analyzing stability of an LCC-HVDC system in consideration of frequency coupling characteristics according to claim 1, wherein said determining the stability of the LCC-HVDC transmit end grid using an equivalent SISO-based impedance stability analysis method specifically comprises:
converting off-diagonal elements of the frequency coupling characteristic matrix and the power grid impedance to a main diagonal by adopting an equivalent SISO impedance stability analysis method to obtain equivalent SISO impedance Z SISO (ii) a The equivalent SISO impedance Z is plotted in a Bode plot at the same time SISO And the positive sequence impedance Z of the power grid 11 (s); making equivalent SISO impedance Z SISO And the positive sequence impedance Z of the power grid 11 (s) determining whether the phase difference at the intersection of the amplitudes of the two impedance curves exceeds 180 °; if yes, judging that the system is unstable; if not, the system is judged to be stable.
6. The LCC-HVDC system stability analysis method in consideration of frequency coupling characteristics according to claim 1, wherein the expression of the switching function of the LCC-HVDC comprises an expression of a frequency component, an expression of an amplitude component;
the expression for the frequency components is: f is mf 1 +n(f p -f 1 )；
The expression for the magnitude component is:
in the formula: s a1 [f]For the component of the LCC-HVDC A1 phase switching function at frequency f, m is 6k + -1, alpha 0 For the triggered delay angle steady state value of LCC-HVDC,
for the phase of the voltage at the fundamental frequency,
for modulating modules at frequency f p -f 1 The gain of the lower gain is set to be,
for modulating modules at frequency f p -f 1 The conjugate of the gain of (d).
7. The LCC-HVDC system stability analysis method in consideration of frequency coupling characteristics of claim 6, wherein the component is
According to the LCC-HVDC control structure, small-signal modeling is performed on a direct current control link and a phase-locked loop control link step by step to obtain the LCC-HVDC control structure.
8. An LCC-HVDC system stability analysis apparatus taking into account frequency coupling characteristics, characterized in that the apparatus supports the LCC-HVDC system stability analysis method taking into account frequency coupling characteristics as recited in any one of claims 1 to 7; the device includes:
the LCC-HVDC control structure modeling unit is used for modeling the LCC-HVDC control structure to obtain a switching function of the LCC-HVDC;
the LCC-HVDC main circuit modeling unit is used for modeling the LCC-HVDC main circuit to obtain a frequency coupling characteristic impedance model of the LCC-HVDC under a phase sequence domain; the switching function of the LCC-HVDC and the frequency coupling characteristic impedance model of the LCC-HVDC are connected, the solved frequency coupling characteristic impedance model of the LCC-HVDC is obtained through solving, and a frequency coupling characteristic matrix is obtained;
the power grid impedance matrix calculation unit is used for calculating to obtain a power grid impedance matrix under the condition of considering frequency coupling;
and the stability judgment unit is used for judging the stability of the LCC-HVDC transmission end power grid by adopting an equivalent SISO impedance stability analysis method according to the power grid impedance matrix and the frequency coupling characteristic matrix.
9. A computer device comprising a memory, a processor and a computer program stored in the memory and executable on the processor, characterized in that the processor implements the LCC-HVDC system stability analysis method taking into account frequency coupling characteristics as claimed in any of claims 1 to 7 when executing the computer program.
10. A computer-readable storage medium storing a computer program, wherein the computer program, when executed by a processor, implements the LCC-HVDC system stability analysis method taking into account frequency coupling characteristics of any of claims 1-7.
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