CN113964821A - Small signal model modular modeling method and device suitable for LCC-HVDC system - Google Patents

Small signal model modular modeling method and device suitable for LCC-HVDC system Download PDF

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CN113964821A
CN113964821A CN202111205926.0A CN202111205926A CN113964821A CN 113964821 A CN113964821 A CN 113964821A CN 202111205926 A CN202111205926 A CN 202111205926A CN 113964821 A CN113964821 A CN 113964821A
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lcc
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hvdc
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CN113964821B (en
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江克证
柳丹
曹侃
叶畅
肖繁
胡畔
熊平
康逸群
谭道军
罗恒
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State Grid Corp of China SGCC
Electric Power Research Institute of State Grid Hubei Electric Power Co Ltd
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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
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • 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
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2113/00—Details relating to the application field
    • G06F2113/04—Power grid distribution networks
    • 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]
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    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
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Abstract

The invention discloses a small signal model modular modeling method and a small signal model modular modeling device suitable for a power grid commutation converter high-voltage direct current transmission (LCC-HVDC) system, wherein the method comprises the following steps: respectively processing modules of a rectifier station converter, a rectifier station controller, an inverter station converter, an inverter station controller, a direct current network, an alternating current side main loop and a filter to obtain an LCC-HVDC original nonlinear period time-varying modular mathematical model; carrying out track linearization on the modular mathematical model to obtain a linear period time-varying small signal model of the LCC-HVDC system; and applying Fourier series and harmonic balance principles to the LCC-HVDC system linear period time-varying small signal model to obtain the LCC-HVDC system modularized harmonic state space small signal model. The invention can effectively solve the problems of low portability, high complexity and difficult expansion of the existing modeling technology, and can better reflect the dynamic stability characteristics of the system.

Description

Small signal model modular modeling method and device suitable for LCC-HVDC system
Technical Field
The invention relates to the technical field of power system modeling, in particular to a small signal model modular modeling method and device suitable for an LCC-HVDC system.
Background
High Voltage Direct Current (HVDC) technology based on a power grid commutation Converter (LCC) is widely applied to modern power systems by virtue of a plurality of advantages, dynamic characteristics of the modern power systems are changed greatly along with application of power electronic equipment in the modern power systems, new systematic stability problems are generated continuously, LCC-HVDC equipment is used as an important component of the modern power systems, dynamic characteristics of the LCC-HVDC equipment change dynamic behaviors of the modern power systems, and modeling research of the LCC-HVDC equipment is a problem which needs to be paid attention to by researchers.
Trigonometric function operation in LCC-HVDC control system coordinate transformation and periodic on/off process of converter switching device make it present nonlinear periodic time-varying characteristic, traditional modeling mode of transforming it to linear steady system will face huge challenge due to nonlinearity and periodicity of LCC-HVDC, and complexity increases sharply with increasing considered orders. Therefore, it is needed to provide a modeling method capable of reducing complexity and having higher scalability for LCC-HVDC nonlinear periodic time-varying characteristics.
Disclosure of Invention
Aiming at the problems, the invention provides a small-signal model modular modeling method and a small-signal model modular modeling device which are suitable for an LCC-HVDC system, and can effectively solve the problems of low portability, high complexity and difficult expansion of the existing modeling technology.
In order to achieve the above object, an embodiment of the present invention provides a small signal model modular modeling method suitable for an LCC-HVDC system, including the following steps:
s1, adopting an CIGRE HVDC Benchmark standard model topological structure to respectively process modules of a converter of a rectification station, a controller of the rectification station, a converter of an inversion station, a controller of the inversion station, a direct current network, a main circuit at an alternating current side and a filter, establishing original mathematical models of the modules, and integrating to obtain an LCC-HVDC original nonlinear period time-varying modular mathematical model.
And S2, linearization is carried out on the steady-state track of the modular mathematical model with time varying original nonlinear period of the LCC-HVDC system to obtain a linear period time varying small signal model of each module of the LCC-HVDC system.
And S3, applying Fourier series and harmonic balance methods to the LCC-HVDC system linear period time-varying small signal model to obtain a linear steady system, namely the LCC-HVDC system modularized harmonic state space small signal model.
Meanwhile, correspondingly, the embodiment of the invention provides a small signal model modular modeling device suitable for an LCC-HVDC system, which comprises the following steps:
a first processing module: the method is used for processing each module of a rectifier station converter, a rectifier station controller, an inverter station converter, an inverter station controller, a direct current network, an alternating current side main loop and a filter to obtain an original mathematical model of each module.
A second processing module: the method is used for linearizing the original mathematical models of the modules to obtain linear periodic time-varying small signal models of the modules of the LCC-HVDC system.
A third processing module: the method is used for obtaining the modularized harmonic state space small signal model of the LCC-HVDC system by applying Fourier series and a harmonic balancing method to the linear period time-varying small signal model of each module.
Compared with the prior modeling technology, the small-signal model modular modeling method and the small-signal model modular modeling device suitable for the LCC-HVDC system provided by the embodiment of the invention have the following beneficial effects:
the modeling method can establish a modular small signal model for LCC-HVDC, effectively solves the huge challenge of nonlinear period time variation caused by the periodic on-off characteristics of a switching device and controller trigonometric function operation in an LCC-HVDC system, wherein HSS modeling can consider all order frequency components, modular processing can well understand and know the interface relationship among modules of the LCC-HVDC system, and meanwhile for a complex LCC-HVDC system, the modular processing can effectively solve the problems of low portability, high complexity and difficult expansion of the existing modeling technology.
Drawings
Fig. 1 is a schematic flow chart of a small-signal modular modeling method suitable for an LCC-HVDC system according to an embodiment of the present invention;
FIG. 2 is a structural diagram of an LCC-HVDC original nonlinear periodic time-varying modular mathematical model according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of an LCC-HVDC system topology;
FIG. 4 is a time domain response result graph of detailed nonlinear time domain models and modular HSS small signal model commutation station firing angles;
FIG. 5 is a time domain response result graph of DC current on the DC side of a rectifier station of a detailed nonlinear time domain model and a modular HSS small signal model;
FIG. 6 is a time domain response result graph of a detailed nonlinear time domain model and modular HSS small signal model inversion station firing angles;
FIG. 7 is a graph of time domain response results of DC current on DC side of inversion station of detailed nonlinear time domain model and modular HSS small signal model.
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 the accompanying drawings and embodiments, and it is to be understood that the embodiments described herein are merely illustrative and not restrictive. Moreover, all other embodiments without innovative work product are within the scope of the invention
Example one
The flow chart of the small signal model modularization modeling method suitable for the LCC-HVDC system provided by the invention is shown in fig. 1, and comprises the following steps:
s1, adopting an CIGRE HVDC Benchmark standard model topological structure to respectively process modules of a converter of a rectification station, a controller of the rectification station, a converter of an inversion station, a controller of the inversion station, a direct current network, a main circuit at an alternating current side and a filter, establishing original mathematical models of the modules, and integrating to obtain an LCC-HVDC original nonlinear period time-varying modular mathematical model.
And S2, linearization is carried out on the steady-state track of the modular mathematical model with time varying original nonlinear period of the LCC-HVDC system to obtain a linear period time varying small signal model of each module of the LCC-HVDC system.
And S3, applying Fourier series and harmonic balance methods to the LCC-HVDC system linear period time-varying small signal model to obtain a linear steady system, namely the LCC-HVDC system modularized harmonic state space small signal model.
Further, for step S1, obtaining a time-varying modular mathematical model of the LCC-HVDC original nonlinear period is shown in fig. 2, and the specific method obtained by the original mathematical model of each module is as follows:
original mathematical model of the current converter of the rectification station:
Figure BDA0003306836980000041
wherein: srva、srvb、srvcA phase voltage switching function s of the rectifier station converters a, b and cria、srib、sricThe phase current switching functions are respectively the current switching functions of the current converters a, b and c of the rectifying station.
The rectifier station controller comprises a current controller module and a phase-locked loop controller module, wherein the current controller has an original mathematical model:
Figure BDA0003306836980000051
wherein: t isrFor sampling the filter time constant, idrfFor sampling the output of the filter, idrefFor a direct current command value, alpha, in constant current controlrordAs the firing angle command value, krpccAnd kriccIs the current controller PI parameter.
Original mathematical model of the rectifier station phase-locked loop controller:
Figure BDA0003306836980000052
wherein: u. ofrαβIs an alternating-current bus voltage vector of a rectification station under a two-phase static coordinate system; u. ofrdqIs an AC bus voltage vector u of a rectification station under a rotating coordinate systemrqIs its q-axis component; k is a radical ofrppllAnd kripllIs a phase-locked loop controller PI parameter; t is constant amplitude Clark conversion; pθIs a Park rotation coordinate transformation, the input phase of which is dynamically determined by the phase lock, so the transformation is a nonlinear transformation; thetarpllThe phase is output for the phase locked loop.
An original mathematical model of a converter of an inverter station:
Figure BDA0003306836980000053
wherein: siva、sivb、sivcThe phase voltage switching functions of the inverter station converters a, b and c are respectively siia、siib、siicThe phase current switching functions are respectively phase current switching functions of an inverter station converter a, a phase current switching function b and a phase current switching function c.
The inverter controller comprises a voltage controller module and a phase-locked loop controller module, wherein the original mathematical model of the voltage controller is as follows:
Figure BDA0003306836980000061
wherein: t isiFor sampling the filter time constant, uidrfFor sampling the output of the filter, uidrefIs a DC voltage command value, beta, in constant voltage controliordIs the command value of arc-quenching angle, kipAnd kiiIs the constant voltage controller PI parameter.
An original mathematical model of an inverter station phase-locked loop controller:
Figure BDA0003306836980000062
wherein: u. ofiαβThe voltage vector of the alternating-current bus of the inversion station under the two-phase static coordinate system is obtained; u. ofrdqFor inverting the AC bus voltage vector u of the station under a rotating coordinate systemrqIs its q-axis component; k is a radical ofippllAnd kiipllIs a phase-locked loop controller PI parameter; thetaipllThe phase is output for the phase locked loop.
Original mathematical model of direct current network
Figure BDA0003306836980000063
The original mathematical model of the alternating current main loop and the filter of the rectifier station is as follows:
Figure BDA0003306836980000064
Figure BDA0003306836980000065
Figure BDA0003306836980000066
Figure BDA0003306836980000071
Figure BDA0003306836980000072
Figure BDA0003306836980000073
Figure BDA0003306836980000074
wherein Ki11～Ki78Are all constants. Due to the coefficient Ki18The term introduces a switching function, so that the LCC-HVDC original relation state equation contains periodic time variable, x is a, b and c three-phase, ucix,uc2ix,u3cix,u4cixRespectively corresponding to the voltage i of the capacitor in the filter of the inverter station1ix,i2ix,i3ixRespectively corresponding to the current u of the inductor in the filter and the main loop of the inverter stationsixThe voltage of the alternating current power grid of the inverter station is obtained.
The original mathematical model of the AC main loop and the filter of the inverter station is as follows:
Figure BDA0003306836980000075
Figure BDA0003306836980000076
Figure BDA0003306836980000077
Figure BDA0003306836980000078
Figure BDA0003306836980000079
Figure BDA00033068369800000710
Figure BDA00033068369800000711
Figure BDA00033068369800000712
further, for step S2, obtaining linear periodic time-varying small signal models of each module of the LCC-HVDC system by linearizing in a steady-state trajectory of the modular mathematical model whose original nonlinear period is time-varying, the specific method is as follows:
and (3) carrying out linearization calculation on the converter module of the rectification station:
Figure BDA0003306836980000081
where Δ represents the amount of disturbance around the periodic steady-state trajectory of the corresponding variable, and the subscript "0" represents the periodic steady-state trajectory of the variable.
And (3) carrying out linearization calculation on the current controller of the rectifying station:
Figure BDA0003306836980000082
and (3) linear calculation of a rectifier station phase-locked loop controller:
Figure BDA0003306836980000083
and (3) carrying out linearization calculation on the inverter station converter module:
Figure BDA0003306836980000091
and (3) linear calculation of the inverter station voltage controller module:
Figure BDA0003306836980000092
and (3) linear calculation of the inverter station phase-locked loop controller module:
Figure BDA0003306836980000093
and (3) linear calculation of the direct current network module:
Figure BDA0003306836980000094
and (3) carrying out linearization calculation on a main loop and a filter module on the alternating current side of the rectification station:
Figure BDA0003306836980000095
Figure BDA0003306836980000101
Figure BDA0003306836980000102
Figure BDA0003306836980000103
Figure BDA0003306836980000104
Figure BDA0003306836980000105
Figure BDA0003306836980000106
and (3) carrying out linearization calculation on a main loop and a filter module at the alternating current side of the inverter station:
Figure BDA0003306836980000107
Figure BDA0003306836980000108
Figure BDA0003306836980000109
Figure BDA00033068369800001010
Figure BDA00033068369800001011
Figure BDA00033068369800001012
Figure BDA00033068369800001013
Figure BDA00033068369800001014
further, for step S3, a fourier series and harmonic balancing method is applied to the linear period time-varying small signal model of the LCC-HVDC system to obtain a modular harmonic state space small signal model of the LCC-HVDC system, and the specific process is as follows:
harmonic state space small signal model of rectifier station transverter module:
Figure BDA0003306836980000111
where the symbol t represents the Toeplitz matrix and the subscript "0" represents the steady state value of the variable.
Harmonic state space small signal model of rectifier station controller module:
Figure BDA0003306836980000112
Figure BDA0003306836980000113
Figure BDA0003306836980000114
Figure BDA0003306836980000115
wherein I represents an identity matrix of order (2k +1) and Z represents a zero matrix of order (2k + 1); n is a diagonal matrix, and the specific form is as follows:
N＝diag[-jkω,...,-jω,0,jω,...,jkω] (50)
harmonic state space small signal model of inverter station transverter module:
Figure BDA0003306836980000121
harmonic state space small signal model of inverter controller module:
Figure BDA0003306836980000122
Figure BDA0003306836980000123
Figure BDA0003306836980000124
Figure BDA0003306836980000125
harmonic state space small signal model of the direct current network module:
Figure BDA0003306836980000126
the harmonic state space small signal model of the main loop at the alternating current side of the rectification station and the filter module is as follows:
Figure BDA0003306836980000127
(s+N)Δuc2rx＝Kr25Δi2rx (58)
(s+N)Δuc3rx＝Kr31Δucrx+Kr33Δuc3rx+Kr35Δi2rx (59)
(s+N)Δuc4rx＝Kr41Δucrx+Kr44Δuc4rx+Kr46Δi3rx (60)
(s+N)Δi2rx＝Kr51Δucrx+Kr52Δuc2rx+Kr53Δuc3rx+Kr55Δi2rx (61)
(s+N)Δi3rx＝Kr61Δucrx+Kr64Δuc4rx (62)
(s+N)Δi1rx＝Kr71Δucrx+Kr77Δi1rx+Kr78Δusrx (63)
the harmonic state space small signal model of the main loop at the alternating current side of the inverter station and the filter module is as follows:
Figure BDA0003306836980000131
(s+N)Δuc2ix＝Ki25Δi2ix (65)
(s+N)Δuc3ix＝Ki31Δucix+Ki33Δuc3ix+Ki35Δi2ix (66)
(s+N)Δuc4ix＝Ki41Δucix+Ki44Δuc4ix+Ki46Δi3ix (67)
(s+N)Δi2ix＝Ki51Δucix+Ki52Δuc2ix+Ki53Δuc3ix+Ki55Δi2ix (68)
(s+N)Δi3ix＝Ki61Δucix+Ki64Δuc4ix (69)
(s+N)Δis1ix＝Ki71Δucix+Ki77Δis1ix+Ki78Δusix+Ki79Δis2ix (70)
(s+N)Δis2ix＝Ki87Δis1ix+Ki89Δis2ix (71)
in a specific embodiment, a detailed nonlinear time domain model of the system shown in fig. 3 is built in PSCAD/EMTDC, and a modular HSS small signal model of the system shown in fig. 3 is built according to a small signal model modular modeling method suitable for an LCC-HVDC system provided by an embodiment of the present invention, and main parameters of the system refer to CIGRE HVDC Benchmark standard model.
Referring to fig. 4, which is a time domain response result diagram of the trigger angles of the detailed nonlinear time domain model and the modular HSS small signal model rectifying station, when the instruction reference value of the dc current controller of the LCC-HVDC transmitting end system falls from 1pu to 0.97pu at 0.02s, the time domain response results of the trigger angles of the detailed nonlinear time domain model and the modular HSS small signal model rectifying station are basically consistent.
Referring to fig. 5, a time domain response result diagram of the dc current at the dc side of the rectifying station with the detailed nonlinear time domain model and the modular HSS small signal model is shown, and it can be seen from the time domain response result that when the command reference value of the dc current controller of the sending end system changes, the time domain response results of the dc current at the dc side of the rectifying station with the detailed nonlinear time domain model and the modular HSS small signal model are basically consistent.
Referring to fig. 6, a time domain response result diagram of the trigger angle of the inversion station of the detailed nonlinear time domain model and the modular HSS small signal model is shown, and it can be seen from the time domain response result that when the instruction reference value of the dc current controller of the sending end system changes, the time domain response results of the trigger angle of the inversion station of the detailed nonlinear time domain model and the modular HSS small signal model are basically consistent.
Referring to fig. 7, a time domain response result diagram of the dc current at the dc side of the inverter station of the detailed nonlinear time domain model and the modular HSS small signal model is shown, and it can be seen from the time domain response result that when the command reference value of the dc current controller of the sending end system changes, the time domain response result of the dc current at the dc side of the inverter station of the detailed nonlinear time domain model and the modular HSS small signal model are basically consistent.
In summary, according to the comparison between the detailed nonlinear time domain model and the time domain response result of the modular HSS small signal model in the first embodiment of the present invention, the correctness of the small signal model modular modeling method applicable to the LCC-HVDC system provided by the present invention is verified.
Example two
A small signal model modular modeling device suitable for an LCC-HVDC system comprises the following components:
the first processing module is used for respectively processing modules of a rectifier station converter, a rectifier station controller, an inverter station converter, an inverter station controller, a direct current network, an alternating current side main loop and a filter by adopting an CIGRE HVDC Benchmark standard model topological structure, establishing an original mathematical model of each module, and integrating to obtain an LCC-HVDC original nonlinear cycle time-varying modular mathematical model;
the second processing module is used for carrying out track linearization on the LCC-HVDC original nonlinear period time-varying modular mathematical model to obtain a LCC-HVDC system linear period time-varying small signal model;
and the third processing module is used for applying Fourier series and harmonic balance methods to the LCC-HVDC system linear period time-varying small signal model to obtain a linear steady system, namely the LCC-HVDC system modularized harmonic state space small signal model.
Compared with the prior art, the small signal module modular modeling method and the small signal module modular modeling device suitable for the LCC-HVDC system provided by the embodiment of the invention have the following beneficial effects:
the modularized small-signal model can be established for LCC-HVDC, and the huge challenges of nonlinear periodic time variation caused by the periodic on-off characteristics of a switching device and controller trigonometric function operation in an LCC-HVDC system are effectively solved, wherein HSS modeling can consider all order frequency components. The modularized processing can well understand and know the interface relation among all modules of the LCC-HVDC system, and meanwhile, for the complex LCC-HVDC system, the modularized processing can effectively solve the problems of low portability, high complexity and difficult expansion of the existing modeling technology.
Finally, it is worth noting that: the embodiments described above are only for explaining the present invention, not limiting the present invention, and all other embodiments without innovative labor and modifications, substitutions and the like without departing from the principle of the present invention are within the protection scope of the present invention.

Claims (5)

1. A small signal model modularization modeling method suitable for an LCC-HVDC system is characterized by comprising the following steps:
s1, adopting a CIGRE HVDC Benchmark standard model topological structure, respectively processing modules of a converter station, a converter station controller, an inverter station converter, an inverter station controller, a direct current network, an alternating current side main loop and a filter, establishing an original mathematical model of each module, and integrating to obtain an LCC-HVDC original nonlinear period time-varying modular mathematical model;
s2, carrying out track linearization on the LCC-HVDC original nonlinear period time-varying modular mathematical model to obtain a LCC-HVDC system linear period time-varying small signal model;
and S3, applying Fourier series and harmonic balance methods to the LCC-HVDC system linear period time-varying small signal model to obtain a linear steady system, namely the LCC-HVDC system modularized harmonic state space small signal model.
2. The small-signal model modeling method suitable for the LCC-HVDC system in accordance with claim 1, wherein: in step S1, the original mathematical models processed by the modules of the rectifier station converter, the rectifier station controller, the inverter station converter, the inverter station controller, the dc network, the ac side main loop, and the filter are specifically:
original mathematical model of the current converter of the rectification station:
Figure FDA0003306836970000011
wherein: srva、srvb、srvcA phase voltage switching function s of the rectifier station converters a, b and cria、srib、sricA current switching function of the current converter a, b and c of the rectifier station, ucra、ucrb、ucrcAre respectively AC bus voltage ira、irb、ircRespectively, an AC side AC current u of a converter of the rectifier stationdcrFor the DC-side DC voltage, i, of the converter of the rectification stationdcrDirect current is the direct current on the direct current side of the converter of the rectification station;
the rectifier station controller comprises a current controller module and a phase-locked loop controller module, wherein an original mathematical model of the inverter station controller is as follows:
Figure FDA0003306836970000021
wherein: t isrFor sampling the filter time constant, idrfFor sampling the output of the filter, idrefFor a direct current command value, alpha, in constant current controlrordAs the firing angle command value, krpccAnd kriccIs a current controller PI parameter;
original mathematical model of phase-locked loop controller module of rectifier station controller:
Figure FDA0003306836970000022
wherein: u. ofcrThe vector is an alternating-current bus voltage vector of a rectifier station under a three-phase coordinate system; u. ofrαβIs an alternating-current bus voltage vector of a rectification station under a two-phase static coordinate system; u. ofrdqIs an AC bus voltage vector u of a rectification station under a rotating coordinate systemrqIs its q-axis component; k is a radical ofrppllAnd kripllIs a phase-locked loop controller PI parameter; t is constant amplitude Clark conversion; pθIs a Park rotation coordinate transformation, the input phase of which is dynamically determined by the phase lock, so the transformation is a nonlinear transformation; thetarpllOutputting the phase for the phase locked loop;
an original mathematical model of a converter of an inverter station:
Figure FDA0003306836970000023
wherein: siva、sivb、sivcThe phase voltage switching functions of the inverter station converters a, b and c are respectively siia、siib、siicThe current switching functions of the current converters a, b and c of the inverter station are ucia、ucib、ucicAre respectively AC bus voltage iia、iib、iicRespectively, an AC side AC current u of a converter of the rectifier stationdciFor the DC-side DC voltage, i, of the converter of the rectification stationdciFor the direct current side of the converter of the rectifier station
The inverter controller comprises a voltage controller module and a phase-locked loop controller module, wherein the voltage controller module adopts an original mathematical model:
Figure FDA0003306836970000031
wherein: t isiFor sampling the filter time constant, uidrfFor sampling the output of the filter, uidrefIs a DC voltage command value, beta, in constant voltage controliordIs the command value of arc-quenching angle, kipAnd kiiSetting the parameter as a PI parameter of a constant voltage controller;
the original mathematical model of the phase-locked loop controller module of the inverter controller is as follows:
Figure FDA0003306836970000032
wherein: u. ofciThe vector is an alternating-current bus voltage vector of the inverter station under a three-phase coordinate system; u. ofiαβThe voltage vector of the alternating-current bus of the inversion station under the two-phase static coordinate system is obtained; u. ofrdqFor inverting the AC bus voltage vector u of the station under a rotating coordinate systemiqIs its q-axis component; k is a radical ofippllAnd kiipllIs a phase-locked loop controller PI parameter; thetaipllOutputting the phase for the phase locked loop;
original mathematical model of the direct current network:
Figure FDA0003306836970000033
wherein: l isdcrAnd LdciIs a direct current side smoothing reactor, RdcrAnd RdciIs a DC T-type equivalent network resistance, CdcIs a T-type equivalent network capacitance, udcIs the capacitor voltage.
The method comprises the following steps of (1) performing an original mathematical model on a main loop and a filter on an alternating current side of a rectification station:
Figure FDA0003306836970000041
Figure FDA0003306836970000042
Figure FDA0003306836970000043
Figure FDA0003306836970000044
Figure FDA0003306836970000045
Figure FDA0003306836970000046
Figure FDA0003306836970000047
wherein Kr11～Kr78Are all constant due to the coefficient Kr18The term introduces a switching function, so that the LCC-HVDC original relation state equation contains periodic time variable, x is a, b and c three-phase, ucrx,uc2rx,u3crx,u4crxCorresponding respectively to the voltage, i, of the capacitors in the filter of the rectifier station1rx,i2rx,i3rxCorresponding to the currents, u, of the inductors in the filter and the main circuit, respectively, of the rectifier stationsrxIs the rectifier station ac grid voltage;
the method comprises the following steps of (1) carrying out an original mathematical model on a main loop and a filter on an alternating current side of an inversion station:
Figure FDA0003306836970000048
Figure FDA0003306836970000049
Figure FDA00033068369700000410
Figure FDA0003306836970000051
Figure FDA0003306836970000052
Figure FDA0003306836970000053
Figure FDA0003306836970000054
Figure FDA0003306836970000055
wherein Ki11～Ki89Are all constants. Due to the coefficient Ki18The term introduces a switching function, so that the LCC-HVDC original relation state equation contains periodic time variable, x is a, b and c three-phase, ucix,uc2ix,u3cix,u4cixRespectively corresponding to the voltage i of the capacitor in the filter of the inverter stations1ix,is2ix,i2ix,i3ixRespectively corresponding to the current u of the inductor in the filter and the main loop of the inverter stationsixThe voltage of the alternating current power grid of the inverter station is obtained.
3. The small-signal model modeling method suitable for the LCC-HVDC system in accordance with claim 2, wherein: in step S2, performing trajectory linearization on the LCC-HVDC original nonlinear period time-varying modular mathematical model to obtain an LCC-HVDC system linear period time-varying small signal model, specifically:
and (3) carrying out linearization calculation on the converter module of the rectification station:
Figure FDA0003306836970000056
in the formula, delta represents the disturbance amount around the periodic steady-state track of the corresponding variable, and subscript "0" represents the periodic steady-state track of the variable;
and (3) carrying out linearization calculation on the current controller of the rectifying station:
Figure FDA0003306836970000061
and (3) linear calculation of a rectifier station phase-locked loop controller:
Figure FDA0003306836970000062
and (3) carrying out linearization calculation on the inverter station converter module:
Figure FDA0003306836970000063
and (3) linear calculation of the inverter station voltage controller module:
Figure FDA0003306836970000064
and (3) linear calculation of the inverter station phase-locked loop controller module:
Figure FDA0003306836970000071
and (3) linear calculation of the direct current network module:
Figure FDA0003306836970000072
and (3) carrying out linearization calculation on a main loop and a filter module on the alternating current side of the rectification station:
Figure FDA0003306836970000073
Figure FDA0003306836970000074
Figure FDA0003306836970000075
Figure FDA0003306836970000076
Figure FDA0003306836970000077
Figure FDA0003306836970000078
Figure FDA0003306836970000079
and (3) carrying out linearization calculation on a main loop and a filter module at the alternating current side of the inverter station:
Figure FDA0003306836970000081
Figure FDA0003306836970000082
Figure FDA0003306836970000083
Figure FDA0003306836970000084
Figure FDA0003306836970000085
Figure FDA0003306836970000086
Figure FDA0003306836970000087
Figure FDA0003306836970000088
4. the small-signal model modeling method suitable for the LCC-HVDC system in accordance with claim 1, wherein: step S3, applying Fourier series and harmonic balance method to the LCC-HVDC system linear period time-varying small signal model to obtain a linear steady system, namely the LCC-HVDC system modularized harmonic state space small signal model, specifically:
harmonic state space small signal model of rectifier station transverter module:
Figure FDA0003306836970000089
wherein the symbol t represents the Toeplitz matrix and the subscript "0" represents the steady state value of the variable;
harmonic state space small signal model of rectifier station controller module:
Figure FDA0003306836970000091
Figure FDA0003306836970000092
Figure FDA0003306836970000093
Figure FDA0003306836970000094
wherein I represents an identity matrix of order (2k +1) and Z represents a zero matrix of order (2k + 1); n is a diagonal matrix, and the specific form is as follows:
N＝diag[-jkω,...,-jω,0,jω,...,jkω] (50)
harmonic state space small signal model of inverter station transverter module:
Figure FDA0003306836970000095
harmonic state space small signal model of inverter controller module:
Figure FDA0003306836970000096
Figure FDA0003306836970000101
Figure FDA0003306836970000102
Figure FDA0003306836970000103
harmonic state space small signal model of the direct current network module:
Figure FDA0003306836970000104
the harmonic state space small signal model of the main loop at the alternating current side of the rectification station and the filter module is as follows:
Figure FDA0003306836970000105
(s+N)Δuc2rx＝Kr25Δi2rx (58)
(s+N)Δuc3rx＝Kr31Δucrx+Kr33Δuc3rx+Kr35Δi2rx (59)
(s+N)Δuc4rx＝Kr41Δucrx+Kr44Δuc4rx+Kr46Δi3rx (60)
(s+N)Δi2rx＝Kr51Δucrx+Kr52Δuc2rx+Kr53Δuc3rx+Kr55Δi2rx (61)
(s+N)Δi3rx＝Kr61Δucrx+Kr64Δuc4rx (62)
(s+N)Δi1rx＝Kr71Δucrx+Kr77Δi1rx+Kr78Δusrx (63)
the harmonic state space small signal model of the main loop at the alternating current side of the inverter station and the filter module is as follows:
Figure FDA0003306836970000106
(s+N)Δuc2ix＝Ki25Δi2ix (65)
(s+N)Δuc3ix＝Ki31Δucix+Ki33Δuc3ix+Ki35Δi2ix (66)
(s+N)Δuc4ix＝Ki41Δucix+Ki44Δuc4ix+Ki46Δi3ix (67)
(s+N)Δi2ix＝Ki51Δucix+Ki52Δuc2ix+Ki53Δuc3ix+Ki55Δi2ix (68)
(s+N)Δi3ix＝Ki61Δucix+Ki64Δuc4ix (69)
(s+N)Δis1ix＝Ki71Δucix+Ki77Δis1ix+Ki78Δusix+Ki79Δis2ix (70)
(s+N)Δis2ix＝Ki87Δis1ix+Ki89Δis2ix (71)。
5. a small signal model modular modeling device suitable for an LCC-HVDC system is characterized by comprising:
the first processing module is used for respectively processing modules of a rectifier station converter, a rectifier station controller, an inverter station converter, an inverter station controller, a direct current network, an alternating current side main loop and a filter by adopting an CIGRE HVDC Benchmark standard model topological structure, establishing an original mathematical model of each module, and integrating to obtain an LCC-HVDC original nonlinear cycle time-varying modular mathematical model;
the second processing module is used for carrying out track linearization on the LCC-HVDC original nonlinear period time-varying modular mathematical model to obtain a LCC-HVDC system linear period time-varying small signal model;
and the third processing module is used for applying Fourier series and harmonic balance methods to the LCC-HVDC system linear period time-varying small signal model to obtain a linear steady system, namely the LCC-HVDC system modularized harmonic state space small signal model.
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