CN113964821B - Small signal model modularized modeling method and device suitable for LCC-HVDC system - Google Patents
Small signal model modularized modeling method and device suitable for LCC-HVDC system Download PDFInfo
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
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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
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Abstract
The invention discloses a small signal model modularization modeling method and a small signal model modularization modeling device suitable for a high-voltage direct-current transmission (LCC-HVDC) system of a power grid converter, wherein the method comprises the following steps: the method comprises the steps of respectively processing each module of a rectification station converter, a rectification station controller, an inversion station converter, an inversion 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 modularized mathematical model; carrying out track linearization on the modularized mathematical model to obtain a linear periodic time-varying small signal model of the LCC-HVDC system; and applying a Fourier series and harmonic balance principle 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 prior modeling technology, and can better reflect the dynamic stability characteristics of the system.
Description
Technical Field
The invention relates to the technical field of modeling of power systems, in particular to a small signal model modularized modeling method and device suitable for an LCC-HVDC system.
Background
High-voltage direct current (HVDC) technology based on grid commutated converters (Line Commutated Converter, LCC) is widely applied to modern power systems by virtue of many advantages thereof, and as power electronic equipment is applied to modern power systems, dynamic characteristics of the modern power systems are greatly changed, new systematic stability problems are continuously gushed out, LCC-HVDC equipment is taken as an important constituent of the modern power systems, and modeling research of the dynamic characteristics of the LCC-HVDC equipment is also a problem that researchers have to pay attention to while changing dynamic behaviors of the modern power systems.
Trigonometric function operation in coordinate transformation of an LCC-HVDC control system and periodic on/off process of a converter switching device enable the system to display nonlinear periodic time-varying characteristics, a traditional modeling mode for transforming the system into a linear steady system faces great challenges due to nonlinearity and periodicity of the LCC-HVDC, and complexity increases sharply with increasing consideration orders. It is therefore desirable to provide a modeling method for LCC-HVDC nonlinear period time varying features that can reduce complexity and have a high scalability.
Disclosure of Invention
Aiming at the problems, the invention provides a small signal model modularized modeling method and device suitable for an LCC-HVDC system, which can effectively solve the problems of low portability, high complexity and difficult expansion of the existing modeling technology.
To achieve the above object, a first embodiment of the present invention provides a small signal model modularized modeling method applicable to an LCC-HVDC system, comprising the steps of:
s1, adopting a CIGRE HVDC standard model topological structure, respectively 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, establishing an original mathematical model of each module, and integrating to obtain an LCC-HVDC original nonlinear period time-varying modularized mathematical model.
S2, linearizing is carried out on a steady-state track of a modularized mathematical model with a time-varying LCC-HVDC original nonlinear period, and a linear period time-varying signal model of each module of the LCC-HVDC system is obtained.
S3, applying a Fourier series and harmonic balancing 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.
Meanwhile, the second embodiment of the invention correspondingly provides a small signal model modularized 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 the rectification station converter, the rectification station controller, the inversion station converter, the inversion station controller, the direct current network, the alternating current side main loop and the filter to obtain an original mathematical model of each module.
And a second processing module: and the method is used for linearizing the original mathematical model of each module to obtain the linear period time-varying small signal model of each module of the LCC-HVDC system.
And 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 a Fourier series and harmonic balance method to the linear period time-varying small signal model of each module.
Compared with the prior modeling technology, the small signal model modularization modeling method and device suitable for the LCC-HVDC system have the following beneficial effects:
the modularized small signal model can be established for the LCC-HVDC system, and the huge challenges of nonlinear periodic time-varying caused by the periodic on-off characteristic of a switching device and the trigonometric function operation of a controller in the LCC-HVDC system are effectively solved, wherein the HSS modeling can consider the frequency components of all orders, the modularized processing can well understand and know the interface relation among all modules of the LCC-HVDC system, and meanwhile, for a complex LCC-HVDC system, the modularized processing can effectively solve the problems of low portability, high complexity and difficult expansion of the conventional modeling technology.
Drawings
Fig. 1 is a schematic flow chart of a small-signal modular modeling method applicable to an LCC-HVDC system according to an embodiment of the present invention;
FIG. 2 is a block diagram of an LCC-HVDC original nonlinear periodic time-varying modular mathematical model constructed in accordance with an embodiment of the present invention;
FIG. 3 is a schematic diagram of an LCC-HVDC system topology;
FIG. 4 is a graph of time domain response results for a detailed nonlinear time domain model and modular HSS small signal model rectification station trigger angle;
FIG. 5 is a graph of time domain response results of DC current on DC side of a rectification station of a detailed nonlinear time domain model and a modularized HSS small signal model;
FIG. 6 is a plot of time domain response results for the inversion station trigger angle for the detailed nonlinear time domain model and the modular HSS small signal model;
fig. 7 is a graph of time domain response results of dc-side dc-current of an inverter station of a detailed nonlinear time domain model and a modularized HSS small signal model.
Detailed Description
The present invention will be further described in detail with reference to the drawings and examples, for the purpose of making the objects, technical solutions and advantages of the present invention more apparent, and it is apparent that the specific examples described herein are only for explaining the present invention and are not limiting the present invention. In addition, all other embodiments without making innovative work are intended to be within the scope of the invention
Example 1
The flow chart of the small signal model modularization modeling method suitable for the LCC-HVDC system is shown in figure 1, and the method comprises the following steps:
s1, adopting a CIGRE HVDC standard model topological structure, respectively 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, establishing an original mathematical model of each module, and integrating to obtain an LCC-HVDC original nonlinear period time-varying modularized mathematical model.
S2, linearizing is carried out on a steady-state track of a modularized mathematical model with a time-varying LCC-HVDC original nonlinear period, and a linear period time-varying signal model of each module of the LCC-HVDC system is obtained.
S3, applying a Fourier series and harmonic balancing 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.
Further, for step S1, a modularized mathematical model of LCC-HVDC original nonlinear period time-varying is obtained as shown in fig. 2, and the specific method for obtaining the original mathematical model of each module is as follows:
original mathematical model of rectifier station converter:
wherein: s is(s) rva 、s rvb 、s rvc Respectively the voltage switching functions of a phase, a phase and a phase c phase of the converter of the rectifying station, s ria 、s rib 、s ric The current switching functions of the phases a, b and c of the rectifier station converter are respectively shown.
The rectification station controller comprises a current controller module and a phase-locked loop controller module, wherein the current controller is an original mathematical model:
wherein: t (T) r For sampling the filter time constant, i drf Filtering for samplingOutput of the device, i dref For the direct current command value, alpha rord To trigger angle command value, k rpcc And k ricc Is the current controller PI parameter.
Original mathematical model of rectifier station phase-locked loop controller:
wherein: u (u) rαβ The voltage vector is the alternating current bus voltage vector of the rectification station under a two-phase static coordinate system; u (u) rdq U is the voltage vector of the alternating current bus of the rectification station under the rotating coordinate system rq For its q-axis component; k (k) rppll And k ripll Is a phase-locked loop controller PI parameter; t is constant amplitude Clark conversion; p (P) θ For Park rotation coordinate transformation, the input phase is dynamically determined by phase locking, so the transformation is nonlinear transformation; θ rpll The phase is output for the phase locked loop.
Original mathematical model of inverter station converter:
wherein: s is(s) iva 、s ivb 、s ivc Respectively the voltage switching functions of a phase, a phase and a phase c phase of the inverter station converter, s iia 、s iib 、s iic The current switching functions of the phase a, the phase b and the phase c of the inverter station converter are respectively shown.
The inversion station controller comprises a voltage controller module and a phase-locked loop controller module, wherein the voltage controller is an original mathematical model:
wherein: t (T) i For sampling the filter time constant, u idrf For the output of the sampling filter, u idref Is a direct-current voltage command value, beta in constant voltage control iord To put outArc angle command value, k ip And k ii Is the PI parameter of the constant voltage controller.
Inverter phase-locked loop controller original mathematical model:
wherein: u (u) iαβ The voltage vector is an alternating current bus voltage vector of the inversion station under a two-phase static coordinate system; u (u) rdq U is the voltage vector of the alternating current bus of the inversion station under the rotating coordinate system rq For its q-axis component; k (k) ippll And k iipll Is a phase-locked loop controller PI parameter; θ ipll The phase is output for the phase locked loop.
Original mathematical model of direct current network
Rectifying station alternating current main loop and filter original mathematical model:
wherein K is i11 ～K i78 Are all constant. Due to the coefficient K i18 The term introduces a switching function so that the LCC-HVDC original relation state equation contains periodic time variable, x is a, b, c three-phase, u cix ,u c2ix ,u 3cix ,u 4cix Respectively corresponding to the voltages of the capacitors in the filters of the inversion station, i 1ix ,i 2ix ,i 3ix Current of the inductor in the inverting station filter and the main loop respectively, u six The ac grid voltage is the inverter station.
Inverter station alternating current main loop and filter original mathematical model:
further, for step S2, linearizing is performed on a steady-state track of a modularized mathematical model that varies in time in an original nonlinear period of the LCC-HVDC system, so as to obtain a linear period varying small signal model of each module of the LCC-HVDC system, and the specific method is as follows:
linearization calculation of rectifier station converter module:
where Δ represents the disturbance quantity around the periodic steady-state trajectory of the corresponding variable, and the subscript "0" represents the periodic steady-state trajectory of the variable.
Linearization calculation of the rectifier station current controller:
linearization calculation of the rectifier station phase-locked loop controller:
linearization calculation of inverter station converter modules:
linearization calculation of the inverter station voltage controller module:
linearization calculation of the inverter phase-locked loop controller module:
and (3) linearization calculation of the direct current network module:
linearization calculation of a rectifier station alternating current side main loop and a filter module:
linearization calculation of the main loop and the filter module at the alternating current side of the inversion station:
further, for step S3, a fourier series and harmonic balancing method is applied to the LCC-HVDC system linear period time-varying small signal model, so as to obtain a modularized harmonic state space small signal model of the LCC-HVDC system, which comprises the following specific steps:
harmonic state space small signal model of rectifier station converter module:
where the symbol f 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:
wherein I represents an identity matrix of (2k+1) order, and Z represents a zero matrix of (2k+1) order; n is a diagonal matrix, and the specific form is:
N＝diag[-jkω,...,-jω,0,jω,...,jkω] (50)
harmonic state space small signal model of inverter station converter module:
harmonic state space small signal model of inverter station controller module:
harmonic state space small signal model of direct current network module:
harmonic state space small signal model of rectifier station alternating current side main loop and filter module:
(s+N)Δu c2rx ＝K r25 Δi 2rx (58)
(s+N)Δu c3rx ＝K r31 Δu crx +K r33 Δu c3rx +K r35 Δi 2rx (59)
(s+N)Δu c4rx ＝K r41 Δu crx +K r44 Δu c4rx +K r46 Δi 3rx (60)
(s+N)Δi 2rx ＝K r51 Δu crx +K r52 Δu c2rx +K r53 Δu c3rx +K r55 Δi 2rx (61)
(s+N)Δi 3rx ＝K r61 Δu crx +K r64 Δu c4rx (62)
(s+N)Δi 1rx ＝K r71 Δu crx +K r77 Δi 1rx +K r78 Δu srx (63)
harmonic state space small signal model of inverter station alternating current side main loop and filter module:
(s+N)Δu c2ix ＝K i25 Δi 2ix (65)
(s+N)Δu c3ix ＝K i31 Δu cix +K i33 Δu c3ix +K i35 Δi 2ix (66)
(s+N)Δu c4ix ＝K i41 Δu cix +K i44 Δu c4ix +K i46 Δi 3ix (67)
(s+N)Δi 2ix ＝K i51 Δu cix +K i52 Δu c2ix +K i53 Δu c3ix +K i55 Δi 2ix (68)
(s+N)Δi 3ix ＝K i61 Δu cix +K i64 Δu c4ix (69)
(s+N)Δi s1ix ＝K i71 Δu cix +K i77 Δi s1ix +K i78 Δu six +K i79 Δi s2ix (70)
(s+N)Δi s2ix ＝K i87 Δi s1ix +K i89 Δi s2ix (71)
in a specific embodiment, a detailed nonlinear time domain model of the system shown in fig. 3 is built in a PSCAD/EMTDC, and a modularized HSS small signal model of the system shown in fig. 3 is built according to a small signal model modularized modeling method suitable for an LCC-HVDC system according to a first embodiment of the present invention, where main parameters of the system refer to a CIGRE HVDC Benchmark standard model.
Referring to fig. 4, a time domain response result diagram of the trigger angles of the rectification station of the detailed nonlinear time domain model and the modularized HSS small signal model is shown, and when the reference value of the direct current controller instruction of the LCC-HVDC transmission end system falls from 1pu to 0.97pu at 0.02s, the time domain response results of the trigger angles of the rectification station of the detailed nonlinear time domain model and the modularized HSS small signal model are basically consistent.
Referring to fig. 5, a time domain response result diagram of the direct current on the direct current side of the rectification station of the detailed nonlinear time domain model and the modularized HSS small signal model is shown, and as can be seen from the time domain response result, when the command reference value of the direct current controller of the sending end system changes, the time domain response results of the direct current on the direct current side of the rectification station of the detailed nonlinear time domain model and the modularized HSS small signal model are basically consistent.
Referring to fig. 6, a time domain response result diagram of the trigger angles of the inversion stations of the detailed nonlinear time domain model and the modularized HSS small signal model is shown, and when the command reference value of the direct current controller of the sending end system changes, the time domain response results of the trigger angles of the inversion stations of the detailed nonlinear time domain model and the modularized HSS small signal model are basically consistent.
Referring to fig. 7, a time domain response result diagram of the direct current on the direct current side of the inversion station of the detailed nonlinear time domain model and the modularized HSS small signal model is shown, and as can be seen from the time domain response result, when the command reference value of the direct current controller of the sending end system changes, the time domain response results of the direct current on the direct current side of the inversion station of the detailed nonlinear time domain model and the modularized HSS small signal model are basically consistent.
In summary, according to the comparison of the detailed time domain response results of the nonlinear time domain model and the modularized HSS small signal model in the first embodiment of the invention, the correctness of the small signal model modularized modeling method suitable for the LCC-HVDC system is verified.
Example two
A small signal model modular modeling apparatus suitable for use in an LCC-HVDC system, comprising:
the first processing module is used for respectively processing each module of the rectifier station converter, the rectifier station controller, the inverter station converter, the inverter station controller, the direct current network, the alternating current side main loop and the filter by adopting a CIGRE HVDC standard model topological structure, establishing an original mathematical model of each module, and integrating to obtain an LCC-HVDC original nonlinear period time-varying modularized mathematical model;
the second processing module is used for carrying out track linearization on the modularized mathematical model with the time-varying LCC-HVDC original nonlinear period to obtain a linear period time-varying signal model of the LCC-HVDC system;
and the third processing module is used for applying a Fourier series and harmonic balancing 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.
Compared with the prior art, the small signal module modularized modeling method and device suitable for the LCC-HVDC system have the following beneficial effects:
the modularized small signal model can be established for LCC-HVDC, and the huge challenges of nonlinear periodic time-varying caused by periodic on-off characteristics of a switching device and trigonometric function operation of a controller in an LCC-HVDC system are effectively solved, wherein the HSS modeling can consider frequency components of all orders. The modularized processing can well understand and know the interface relation among all modules of the LCC-HVDC system, and meanwhile, for a 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 notable that: the above-described embodiments are provided for the purpose of illustrating the invention only and are not intended to limit the invention, and all other embodiments without innovative work and modifications, substitutions, etc. without departing from the principle of the invention are intended to be within the scope of the invention.
Claims (4)
1. A small signal model modular modeling method suitable for an LCC-HVDC system, comprising the steps of:
step S1, adopting a CIGRE HVDC standard model topological structure, respectively 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, establishing an original mathematical model of each module, and integrating to obtain an LCC-HVDC original nonlinear period time-varying modularized mathematical model;
s2, carrying out track linearization on a modularized mathematical model with time-varying LCC-HVDC original nonlinear period to obtain a linear period time-varying small signal model of the LCC-HVDC system;
s3, applying a Fourier series and harmonic balancing method to the LCC-HVDC system linear period time-varying signal model to obtain a linear steady system, namely, a LCC-HVDC system modularized harmonic state space small signal model;
in step S1, the original mathematical model after each module of the rectification station converter, the rectification station controller, the inversion station converter, the inversion station controller, the direct current network, the main loop at the ac side and the filter is processed respectively is specifically as follows:
original mathematical model of rectifier station converter:
wherein: s is(s) rva 、s rvb 、s rvc Respectively the voltage switching functions of a phase, a phase and a phase c phase of the converter of the rectifying station, s ria 、s rib 、s ric Current switching functions of phases a, b and c of the rectifier station converter, u cra 、u crb 、u crc Respectively the voltages of the alternating current bus, i ra 、i rb 、i rc Ac side ac current of rectifier station converter, u dcr For the direct-current voltage of the direct-current side of the converter of the rectifying station, i dcr Direct current at the direct current side of the rectifier station converter;
the rectification station controller comprises a current controller module and a phase-locked loop controller module, wherein the original mathematical model of the inversion station controller is as follows:
wherein: t (T) r For sampling the filter time constant, i drf I is the output of the sampling filter dref For the direct current command value, alpha rord To trigger angle command value, k rpcc And k ricc The PI parameter is a current controller;
phase-locked loop controller module primitive mathematical model of rectifier station controller:
wherein: u (u) cr The voltage vector is an alternating current bus voltage vector of the rectification station under a three-phase coordinate system; u (u) rαβ The voltage vector is the alternating current bus voltage vector of the rectification station under a two-phase static coordinate system; u (u) rdq U is the voltage vector of the alternating current bus of the rectification station under the rotating coordinate system rq For its q-axis component; k (k) rppll And k ripll Is a phase-locked loop controller PI parameter; t is constant amplitude Clark conversion; p (P) θ For Park rotation coordinate transformation, the input phase is dynamically determined by phase locking, so the transformation is nonlinear transformation; θ rpll Outputting a phase for the phase-locked loop;
original mathematical model of inverter station converter:
wherein: s is(s) iva 、s ivb 、s ivc Respectively the voltage switching functions of a phase, a phase and a phase c phase of the inverter station converter, s iia 、s iib 、s iic U is the current switching function of the phase a, b and c of the inverter station converter respectively cia 、u cib 、u cic Respectively the voltages of the alternating current bus, i ia 、i ib 、i ic Ac side ac current of rectifier station converter, u dci For the direct-current voltage of the direct-current side of the converter of the rectifying station, i dci For direct current at the direct current side of a converter of a rectifying station
The inversion station controller comprises a voltage controller module and a phase-locked loop controller module, wherein the voltage controller module is an original mathematical model:
wherein: t (T) i For sampling the filter time constant, u idrf For the output of the sampling filter, u idref Is a direct-current voltage command value, beta in constant voltage control iord For the arc extinction angle command value, k ip And k ii The PI parameter is a constant voltage controller;
the phase-locked loop controller module original mathematical model of the inversion station controller:
wherein: u (u) ci The voltage vector is an alternating current bus voltage vector of the inversion station under a three-phase coordinate system; u (u) iαβ The voltage vector is an alternating current bus voltage vector of the inversion station under a two-phase static coordinate system; u (u) rdq U is the voltage vector of the alternating current bus of the inversion station under the rotating coordinate system iq For its q-axis component; k (k) ippll And k iipll Is a phase-locked loop controller PI parameter; θ ipll Outputting a phase for the phase-locked loop;
original mathematical model of direct current network:
wherein: l (L) dcr And L dci Is a direct-current side smoothing reactor, R dcr And R is dci Is a direct current T-type equivalent network resistor, C dc Is the T-type equivalent network capacitance, u dc Is a capacitor voltage;
primary loop on ac side of rectifier station and original mathematical model of filter:
wherein K is r11 ～K r78 Are all constant due to the coefficient K r18 The term introduces a switching function so that the LCC-HVDC original relation state equation contains periodic time variable, x is a, b, c three-phase, u crx ,u c2rx ,u 3crx ,u 4crx Voltage of capacitor in filter of rectifying station, i 1rx ,i 2rx ,i 3rx Current corresponding to the rectifier station filter and the inductor in the main loop, u srx Alternating current network voltage for the rectifying station;
inverter station alternating current side main loop and filter original mathematical model:
wherein K is i11 ～K i89 Are all constants; due to the coefficient K i18 The term introduces a switching function so that the LCC-HVDC original relation state equation contains periodic time variable, x is a, b, c three-phase, u cix ,u c2ix ,u 3cix ,u 4cix Respectively corresponding to the voltages of the capacitors in the filters of the inversion station, i s1ix ,i s2ix ,i 2ix ,i 3ix Current of the inductor in the inverting station filter and the main loop respectively, u six The ac grid voltage is the inverter station.
2. A small signal model modeling method applicable to LCC-HVDC system in accordance with claim 1, wherein: in the step S2, carrying out track linearization on a modularized mathematical model with time-varying LCC-HVDC original nonlinear period to obtain a linear period time-varying small signal model of the LCC-HVDC system, wherein the method specifically comprises the following steps:
linearization calculation of rectifier station converter module:
wherein delta represents the disturbance quantity around the periodic steady-state track of the corresponding variable, and subscript "0" represents the periodic steady-state track of the variable;
linearization calculation of the rectifier station current controller:
linearization calculation of the rectifier station phase-locked loop controller:
linearization calculation of inverter station converter modules:
linearization calculation of the inverter station voltage controller module:
linearization calculation of the inverter phase-locked loop controller module:
and (3) linearization calculation of the direct current network module:
linearization calculation of a rectifier station alternating current side main loop and a filter module:
linearization calculation of the main loop and the filter module at the alternating current side of the inversion station:
3. a small signal model modeling method applicable to LCC-HVDC system in accordance with claim 1, wherein: step S3, applying a Fourier series and harmonic balancing method to the LCC-HVDC system linear period time-varying signal model to obtain a linear steady system, namely the LCC-HVDC system modularized harmonic state space small signal model, which comprises the following specific steps:
harmonic state space small signal model of rectifier station converter module:
wherein the symbol f 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:
wherein I represents an identity matrix of (2k+1) order, and Z represents a zero matrix of (2k+1) order; n is a diagonal matrix, and the specific form is:
N＝diag[-jkω,...,-jω,0,jω,...,jkω](50)
harmonic state space small signal model of inverter station converter module:
harmonic state space small signal model of inverter station controller module:
harmonic state space small signal model of direct current network module:
harmonic state space small signal model of rectifier station alternating current side main loop and filter module:
(s+N)Δu c2rx ＝K r25 Δi 2rx (58)
(s+N)Δu c3rx ＝K r31 Δu crx +K r33 Δu c3rx +K r35 Δi 2rx (59)
(s+N)Δu c4rx ＝K r41 Δu crx +K r44 Δu c4rx +K r46 Δi 3rx (60)
(s+N)Δi 2rx ＝K r51 Δu crx +K r52 Δu c2rx +K r53 Δu c3rx +K r55 Δi 2rx (61)
(s+N)Δi 3rx ＝K r61 Δu crx +K r64 Δu c4rx (62)
(s+N)Δi 1rx ＝K r71 Δu crx +K r77 Δi 1rx +K r78 Δu srx (63)
harmonic state space small signal model of inverter station alternating current side main loop and filter module:
(s+N)Δu c2ix ＝K i25 Δi 2ix (65)
(s+N)Δu c3ix ＝K i31 Δu cix +K i33 Δu c3ix +K i35 Δi 2ix (66)
(s+N)Δu c4ix ＝K i41 Δu cix +K i44 Δu c4ix +K i46 Δi 3ix (67)
(s+N)Δi 2ix ＝K i51 Δu cix +K i52 Δu c2ix +K i53 Δu c3ix +K i55 Δi 2ix (68)
(s+N)Δi 3ix ＝K i61 Δu cix +K i64 Δu c4ix (69)
(s+N)Δi s1ix ＝K i71 Δu cix +K i77 Δi s1ix +K i78 Δu six +K i79 Δi s2ix (70)
(s+N)Δi s2ix ＝K i87 Δi s1ix +K i89 Δi s2ix (71)。
4. a small signal model modular modeling apparatus for use in an LCC-HVDC system, comprising:
the first processing module is used for respectively processing each module of the rectifier station converter, the rectifier station controller, the inverter station converter, the inverter station controller, the direct current network, the alternating current side main loop and the filter by adopting a CIGRE HVDC standard model topological structure, establishing an original mathematical model of each module, and integrating to obtain an LCC-HVDC original nonlinear period time-varying modularized mathematical model;
the second processing module is used for carrying out track linearization on the modularized mathematical model with the time-varying LCC-HVDC original nonlinear period to obtain a linear period time-varying signal model of the LCC-HVDC system;
the third processing module is used for applying a Fourier series and harmonic balancing 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;
the first processing module respectively processes each module of the rectification station converter, the rectification station controller, the inversion station converter, the inversion station controller, the direct current network, the alternating current side main loop and the filter to establish an original mathematical model of each module, and specifically comprises the following steps:
original mathematical model of rectifier station converter:
wherein: s is(s) rva 、s rvb 、s rvc Respectively the voltage switching functions of a phase, a phase and a phase c phase of the converter of the rectifying station, s ria 、s rib 、s ric Current switching functions of phases a, b and c of the rectifier station converter, u cra 、u crb 、u crc Respectively the voltages of the alternating current bus, i ra 、i rb 、i rc Ac side ac current of rectifier station converter, u dcr For the direct-current voltage of the direct-current side of the converter of the rectifying station, i dcr Direct current at the direct current side of the rectifier station converter;
the rectification station controller comprises a current controller module and a phase-locked loop controller module, wherein the original mathematical model of the inversion station controller is as follows:
wherein: t (T) r For sampling the filter time constant, i drf I is the output of the sampling filter dref For the direct current command value, alpha rord To trigger angle command value, k rpcc And k ricc The PI parameter is a current controller;
phase-locked loop controller module primitive mathematical model of rectifier station controller:
wherein: u (u) cr The voltage vector is an alternating current bus voltage vector of the rectification station under a three-phase coordinate system; u (u) rαβ The voltage vector is the alternating current bus voltage vector of the rectification station under a two-phase static coordinate system; u (u) rdq U is the voltage vector of the alternating current bus of the rectification station under the rotating coordinate system rq For its q-axis component; k (k) rppll And k ripll Is a phase-locked loop controller PI parameter; t is constant amplitude Clark conversion; p (P) θ For Park rotation coordinate transformation, the input phase is dynamically determined by phase locking, so the transformation is nonlinear transformation; θ rpll Outputting a phase for the phase-locked loop;
original mathematical model of inverter station converter:
wherein: s is(s) iva 、s ivb 、s ivc Respectively the voltage switching functions of a phase, a phase and a phase c phase of the inverter station converter, s iia 、s iib 、s iic Inverter station converters a and b respectivelyC-phase current switching function, u cia 、u cib 、u cic Respectively the voltages of the alternating current bus, i ia 、i ib 、i ic Ac side ac current of rectifier station converter, u dci For the direct-current voltage of the direct-current side of the converter of the rectifying station, i dci For direct current at the direct current side of a converter of a rectifying station
The inversion station controller comprises a voltage controller module and a phase-locked loop controller module, wherein the voltage controller module is an original mathematical model:
wherein: t (T) i For sampling the filter time constant, u idrf For the output of the sampling filter, u idref Is a direct-current voltage command value, beta in constant voltage control iord For the arc extinction angle command value, k ip And k ii The PI parameter is a constant voltage controller;
the phase-locked loop controller module original mathematical model of the inversion station controller:
wherein: u (u) ci The voltage vector is an alternating current bus voltage vector of the inversion station under a three-phase coordinate system; u (u) iαβ The voltage vector is an alternating current bus voltage vector of the inversion station under a two-phase static coordinate system; u (u) rdq U is the voltage vector of the alternating current bus of the inversion station under the rotating coordinate system iq For its q-axis component; k (k) ippll And k iipll Is a phase-locked loop controller PI parameter; θ ipll Outputting a phase for the phase-locked loop;
original mathematical model of direct current network:
wherein: l (L) dcr And L dci Is a direct-current side smoothing reactor, R dcr And R is dci Is a direct current T-type equivalent network resistor, C dc Is the T-type equivalent network capacitance, u dc Is a capacitor voltage;
primary loop on ac side of rectifier station and original mathematical model of filter:
wherein K is r11 ～K r78 Are all constant due to the coefficient K r18 The term introduces a switching function so that the LCC-HVDC original relation state equation contains periodic time variable, x is a, b, c three-phase, u crx ,u c2rx ,u 3crx ,u 4crx Respectively corresponding rectifying stationVoltage of capacitor in filter, i 1rx ,i 2rx ,i 3rx Current corresponding to the rectifier station filter and the inductor in the main loop, u srx Alternating current network voltage for the rectifying station;
inverter station alternating current side main loop and filter original mathematical model:
wherein K is i11 ～K i89 Are all constants; due to the coefficient K i18 The term introduces a switching function so that the LCC-HVDC original relation state equation contains periodic time variable, x is a, b, c three-phase, u cix ,u c2ix ,u 3cix ,u 4cix Respectively corresponding to the voltages of the capacitors in the filters of the inversion station, i s1ix ,i s2ix ,i 2ix ,i 3ix Current of the inductor in the inverting station filter and the main loop respectively, u six The ac grid voltage is the inverter station.
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