CN113872229B - Flexible direct current transmission operation simulation method and device - Google Patents

Flexible direct current transmission operation simulation method and device Download PDF

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Publication number
CN113872229B
CN113872229B CN202111079708.7A CN202111079708A CN113872229B CN 113872229 B CN113872229 B CN 113872229B CN 202111079708 A CN202111079708 A CN 202111079708A CN 113872229 B CN113872229 B CN 113872229B
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direct current
electromechanical transient
flexible direct
passive side
model
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CN113872229A (en
Inventor
王炳辉
李�雨
安文宇
黄天啸
谢欢
曹天植
辛光明
陈瑞
王晓斐
张思琪
夏雪
易姝娴
刘瑛琳
任翔
卢文清
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State Grid Corp of China SGCC
Electric Power Research Institute of State Grid Jibei Electric Power Co Ltd
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State Grid Corp of China SGCC
Electric Power Research Institute of State Grid Jibei Electric Power Co Ltd
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    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02JCIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00Circuit arrangements for ac mains or ac distribution networks
    • H02J3/36Arrangements for transfer of electric power between ac networks via a high-tension dc link
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02JCIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00Circuit arrangements for ac mains or ac distribution networks
    • H02J3/24Arrangements for preventing or reducing oscillations of power in networks
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02JCIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/20Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
    • YGENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02EREDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E60/00Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation
    • Y02E60/60Arrangements for transfer of electric power between AC networks or generators via a high voltage DC link [HVCD]

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  • Engineering & Computer Science (AREA)
  • Power Engineering (AREA)
  • Supply And Distribution Of Alternating Current (AREA)
  • Inverter Devices (AREA)

Abstract

The embodiment of the application provides a flexible direct current transmission operation simulation method and device, and relates to the technical field of power systems. The method comprises the following steps: inputting current data of three alternating currents into a preset flexible direct current transmission passive side electromechanical transient model to obtain bus voltage of a passive side; and performing corresponding flexible direct current transmission operation according to the bus voltage of the passive side, wherein the passive side electromechanical transient model is used for simulating the electromechanical transient of the passive side in the flexible direct current transmission system. The method and the device can effectively simulate the electromechanical transient condition of the passive side of the flexible direct current transmission, intuitively reflect the process of the flexible direct current transmission operation, and are favorable for controlling the whole flexible direct current transmission operation more optimally.

Description

Flexible direct current transmission operation simulation method and device
Technical Field
The application relates to the technical field of power systems, in particular to a flexible direct current transmission operation simulation method and device.
Background
The transient modeling simulation of the flexible direct current converter for supplying power to the passive network comprises two types of electromagnetic transient modeling and electromechanical transient modeling. In the aspect of electromagnetic transient modeling, the switching process of the power electronic device is generally considered, a detailed model of each part of the MMC is established, and the model is accurate and specific and is suitable for researching the electromagnetic relation and the control strategy in the MMC; however, in the aspect of researching interaction between MMC and a power grid, problems of limited solving scale and speed, multiple parameters and the like exist, so that a simplified electromechanical transient model needs to be established. At present, the control technology and electromagnetic transient simulation development of a low inertia system after the low inertia system is connected into a large power grid through a direct current power grid are not mature enough, and the research of the electromagnetic transient simulation is also in an exploration stage.
In the patent 'an electromechanical transient simulation model (CN 108551178A) of a flexible direct current transmission system', an electromechanical transient simulation model of a flexible direct current transmission system is provided, including an electromechanical transient simulation model of a converter, an electromechanical transient simulation model of a direct current power grid, and an electromechanical transient simulation model of a three-winding transformer; the electromechanical transient simulation model of the converter is connected with the electromechanical transient simulation model of the direct current power grid and is connected with the alternating current power grid through the electromechanical transient simulation model of the three-winding transformer, and the electromechanical transient simulation model of the three-winding transformer comprises an alternating current power grid side winding, a load side winding and a valve side winding. The electromechanical transient simulation model of the flexible direct current transmission system provided by the invention has the flexible direct current transmission operation simulation function, and can provide a basis for stability analysis of the flexible direct current transmission system. However, the patent carries out electromechanical transient simulation modeling on the whole direct-current transmission system (including an inverter, a direct-current power grid and a three-winding transformer), and the main purpose is to simulate the operation of flexible direct-current transmission; the invention mainly researches the dynamic characteristics of the passive side alternating current system in the transient process, and only needs to perform electromechanical transient modeling on the passive side converter, and does not need to perform electromechanical transient modeling on the transmitting end alternating current system and the direct current system, so that the technology I has no reference significance.
The patent 'phase component-based MMC electromechanical transient simulation method and system (CN 112510746A)' relates to a phase component-based MMC-HVDC electromechanical transient simulation method and system, wherein the method comprises the following steps: obtaining PCC point voltage, PCC point current, transformer outlet voltage, transformer outlet current, converter outlet voltage and converter outlet current of an MMC-HVDC alternating current side; and phase shifting is carried out on the PCC point voltage, the PCC point current, the transformer outlet voltage, the transformer outlet current, the converter outlet voltage and the converter outlet current based on a phase component principle, and electromechanical transient simulation modeling is carried out according to each phase component. However, the transfer function of the inner loop control module in the electromechanical transient model built in the patent is 1, namely the dynamic characteristic of the inner loop of the controller is ignored, the invention focuses on researching the electromechanical transient equivalent modeling of the passive side converter, and under certain simulation parameters and simulation working conditions, the inner loop control system of the converter cannot be omitted, so that the technology II cannot be adopted.
Disclosure of Invention
Aiming at the problems in the prior art, the application provides a flexible direct current transmission operation simulation method and device, wherein the method comprises the following steps: inputting current data of three alternating currents into a preset flexible direct current transmission passive side electromechanical transient model to obtain bus voltage of a passive side; and performing corresponding flexible direct current transmission operation according to the bus voltage of the passive side, wherein the passive side electromechanical transient model is used for simulating the electromechanical transient of the passive side in the flexible direct current transmission system. The method and the device can effectively simulate the electromechanical transient condition of the passive side of the flexible direct current transmission, intuitively reflect the process of the flexible direct current transmission operation, and are favorable for controlling the whole flexible direct current transmission operation more optimally.
In one aspect of the present invention, there is provided a flexible direct current transmission operation simulation method, including:
inputting current data of three alternating currents into a preset flexible direct current transmission passive side electromechanical transient model to obtain bus voltage of a passive side;
and performing corresponding flexible direct current transmission operation according to the bus voltage of the passive side, wherein the passive side electromechanical transient model is used for simulating the electromechanical transient of the passive side in the flexible direct current transmission system.
In a preferred embodiment, further comprising:
and establishing an electromechanical transient model of the flexible direct-current transmission passive side.
In a preferred embodiment, the establishing an electromechanical transient model of the passive side of the flexible direct current transmission comprises:
establishing an electromechanical transient model of the passive side flexible direct current converter;
establishing an electromechanical transient model of an outer loop controller and an inner loop controller of the passive side flexible direct current converter;
and establishing a voltage source electromechanical transient model of the passive side flexible direct current converter.
In a preferred embodiment, the electromechanical transient model of the passive side flexible dc converter comprises:
converting the current data of the input three-phase alternating current into direct current data in a dq coordinate system;
generating an electromechanical transient time domain model of the passive side flexible direct current converter in the dq coordinate system according to the direct current data in the dq coordinate system:
L, R is the equivalent inductance and the equivalent resistance from the bus to the middle point of the bridge arm of the converter; u (u) d 、u q D and q axis components of the bus voltage are respectively represented; e, e d 、e q D and q axis components of virtual equipotential point voltages of upper and lower bridge arm reactors of the converter are respectively represented; i.e d 、i q The d and q axis components of the passive ac system current are represented, respectively.
In a preferred embodiment, the electromechanical transient model of the passive side flexible dc converter further comprises:
carrying out Laplace transformation on the electromechanical transient time domain model of the passive side flexible direct current converter in the dq coordinate system to generate the electromechanical transient frequency domain model of the passive side flexible direct current converter in the dq coordinate system:
in a preferred embodiment, establishing an electromechanical transient model of the flexible dc converter outer loop controller includes:
determining a circuit topology of the outer loop controller;
and determining d-axis components and q-axis components of the busbar voltage as input variables of a circuit topology structure of the outer loop controller, and determining d-axis components and q-axis components of a current reference value as output variables, so as to generate an electromechanical transient model of the outer loop controller.
In a preferred embodiment, establishing an electromechanical transient model of the flexible dc converter inner loop controller includes:
Determining a circuit topology of the inner loop controller;
determining a connection mode of the inner ring controller and the flexible direct current converter;
and determining d-axis components and q-axis components of virtual equipotential point voltages of upper and lower bridge arm reactors of the flexible direct current converter as output variables according to a connection mode of the inner loop controller and the flexible direct current converter, thereby generating an electromechanical transient model of the inner loop controller.
In a preferred embodiment, the connection mode of the inner ring controller and the flexible dc converter includes:
current decoupling connection mode.
In a preferred embodiment, further comprising:
determining control parameters of the inner ring controller according to the initial load;
if the initial load is larger than a first preset value, reducing the control parameters of the inner ring controller so as to increase the time for the output of the inner ring controller to reach the limiting value;
if the initial load is smaller than a second preset value, the control parameters of the inner ring controller are increased so as to improve the dynamic response speed of the system.
In a preferred embodiment, the establishing a voltage source electromechanical transient model of the passive side flexible dc converter includes:
determining a circuit topology of the voltage source;
and adding an inertial link structure in the circuit topology structure of the voltage source so as to generate the electromechanical transient model of the voltage source.
In still another aspect of the present invention, there is provided a flexible direct current transmission operation simulation apparatus including:
the model operation module inputs current data of three alternating currents to a preset flexible direct current transmission passive side electromechanical transient model to obtain bus voltage of a passive side;
and the simulation power transmission module is used for carrying out corresponding flexible direct current power transmission operation according to the bus voltage of the passive side, wherein the passive side electromechanical transient model is used for simulating the electromechanical transient of the passive side in the flexible direct current power transmission system.
In a preferred embodiment, further comprising:
and the model building module is used for building an electromechanical transient model of the flexible direct-current transmission passive side.
In a preferred embodiment, the modeling module includes:
the flexible direct current converter model building unit is used for building an electromechanical transient model of the passive side flexible direct current converter;
the controller model building unit is used for building electromechanical transient models of an outer loop controller and an inner loop controller of the passive side flexible direct current converter;
And the voltage source model building unit is used for building a voltage source electromechanical transient model of the passive side flexible direct current converter.
In yet another aspect of the present invention, an electronic device is provided, including a memory, a processor, and a computer program stored on the memory and executable on the processor, where the processor implements the flexible dc power transmission operation simulation method when executing the program.
In yet another aspect of the present invention, a computer readable storage medium is provided, on which a computer program is stored, which when executed by a processor implements the flexible direct current transmission operation simulation method.
According to the technical scheme, the flexible direct current transmission operation simulation method provided by the application comprises the following steps of: inputting current data of three alternating currents into a preset flexible direct current transmission passive side electromechanical transient model to obtain bus voltage of a passive side; and performing corresponding flexible direct current transmission operation according to the bus voltage of the passive side, wherein the passive side electromechanical transient model is used for simulating the electromechanical transient of the passive side in the flexible direct current transmission system. The method and the device can effectively simulate the electromechanical transient condition of the passive side of the flexible direct current transmission, intuitively reflect the process of the flexible direct current transmission operation, and are favorable for controlling the whole flexible direct current transmission operation more optimally.
Drawings
In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, and it is obvious that the drawings in the following description are some embodiments of the present application, and other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
Fig. 1 is a schematic flow chart of a flexible direct current transmission operation simulation method.
Fig. 2 is a schematic diagram of a structure in which flexible dc power is supplied to a passive network.
Fig. 3 is a schematic flow chart of an electromechanical transient model for establishing a passive side of flexible direct current transmission.
Fig. 4 is a schematic flow diagram of an electromechanical transient model for building a passive side flexible dc-to-ac converter.
Fig. 5 is a schematic flow diagram of an electromechanical transient model of the flexible dc converter outer loop controller.
Fig. 6 is a schematic diagram of the circuit topology of the outer loop controller.
Fig. 7 is a schematic flow diagram of an electromechanical transient model for establishing a flexible dc converter inner loop controller.
Fig. 8 is a schematic diagram of the circuit topology of the inner loop controller.
Fig. 9 is a schematic flow diagram of a voltage source electromechanical transient model for creating a passive side flexible dc converter.
Fig. 10 is a schematic diagram of the topology of an MMC passive-side electromechanical transient voltage source.
Fig. 11 shows simulation results of the first embodiment, where (a) in fig. 11 is a PCC bus voltage effective value curve, (b) in fig. 11 is a valve side current effective value curve, (c) in fig. 11 is a passive side active power curve, and (d) in fig. 11 is a passive side reactive power curve.
Fig. 12 is a simulation result of the implementation scenario two.
Fig. 13 is a schematic structural view of the flexible direct current power transmission operation simulation device.
Fig. 14 is a schematic structural diagram of an electronic device in an embodiment of the present application.
Detailed Description
For the purposes of making the objects, technical solutions and advantages of the embodiments of the present application more clear, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application, and it is apparent that the described embodiments are some embodiments of the present application, but not all embodiments. All other embodiments, which can be made by one of ordinary skill in the art based on the embodiments herein without making any inventive effort, are intended to be within the scope of the present application.
It should be noted that the flexible direct current transmission operation simulation method and device disclosed in the application can be used in the technical field of power systems, and can also be used in any field except the technical field of power systems, and the application field of the flexible direct current transmission operation simulation method and device disclosed in the application is not limited.
Flexible dc power transmission is a new generation of dc power transmission technology that is similar in structure to high voltage dc power transmission, yet is composed of a converter station and a dc power transmission line (typically, a dc cable).
The flexible direct current converter is power system equipment for performing alternating current-direct current conversion based on a flexible direct current transmission technology, and is called MMC for short.
The passive side refers to the side of the flexible dc converter that is connected to the grid of the synchronous power source (synchronous generator).
Electromechanical transients refer to transients that occur in the order of seconds to minutes due to an imbalance between mechanical or electromagnetic torque.
The transient modeling simulation of the flexible direct current converter for supplying power to the passive network comprises two types of electromagnetic transient modeling and electromechanical transient modeling. In the aspect of electromagnetic transient modeling, the switching process of the power electronic device is generally considered, a detailed model of each part of the MMC is established, and the model is accurate and specific and is suitable for researching the electromagnetic relation and the control strategy in the MMC; however, in the aspect of researching interaction between MMC and a power grid, problems of limited solving scale and speed, multiple parameters and the like exist, so that a simplified electromechanical transient model needs to be established. At present, the control technology and electromagnetic transient simulation development of a low inertia system after the low inertia system is connected into a large power grid through a direct current power grid are not mature enough, and the research of the electromagnetic transient simulation is also in an exploration stage.
In the patent 'an electromechanical transient simulation model (CN 108551178A) of a flexible direct current transmission system', an electromechanical transient simulation model of a flexible direct current transmission system is provided, including an electromechanical transient simulation model of a converter, an electromechanical transient simulation model of a direct current power grid, and an electromechanical transient simulation model of a three-winding transformer; the electromechanical transient simulation model of the converter is connected with the electromechanical transient simulation model of the direct current power grid and is connected with the alternating current power grid through the electromechanical transient simulation model of the three-winding transformer, and the electromechanical transient simulation model of the three-winding transformer comprises an alternating current power grid side winding, a load side winding and a valve side winding. The electromechanical transient simulation model of the flexible direct current transmission system provided by the invention has the flexible direct current transmission operation simulation function, and can provide a basis for stability analysis of the flexible direct current transmission system. However, the patent carries out electromechanical transient simulation modeling on the whole direct-current transmission system (including an inverter, a direct-current power grid and a three-winding transformer), and the main purpose is to simulate the operation of flexible direct-current transmission; the invention mainly researches the dynamic characteristics of the passive side alternating current system in the transient process, and only needs to perform electromechanical transient modeling on the passive side converter, and does not need to perform electromechanical transient modeling on the transmitting end alternating current system and the direct current system, so that the technology I has no reference significance.
The patent 'phase component-based MMC electromechanical transient simulation method and system (CN 112510746A)' relates to a phase component-based MMC-HVDC electromechanical transient simulation method and system, wherein the method comprises the following steps: obtaining PCC point voltage, PCC point current, transformer outlet voltage, transformer outlet current, converter outlet voltage and converter outlet current of an MMC-HVDC alternating current side; and phase shifting is carried out on the PCC point voltage, the PCC point current, the transformer outlet voltage, the transformer outlet current, the converter outlet voltage and the converter outlet current based on a phase component principle, and electromechanical transient simulation modeling is carried out according to each phase component. However, the transfer function of the inner loop control module in the electromechanical transient model built in the patent is 1, namely the dynamic characteristic of the inner loop of the controller is ignored, the invention focuses on researching the electromechanical transient equivalent modeling of the passive side converter, and under certain simulation parameters and simulation working conditions, the inner loop control system of the converter cannot be omitted, so that the technology II cannot be adopted.
Aiming at the problems in the prior art, the application provides a flexible direct current transmission operation simulation method and device, wherein the method comprises the following steps: inputting current data of three alternating currents into a preset flexible direct current transmission passive side electromechanical transient model to obtain bus voltage of a passive side; and performing corresponding flexible direct current transmission operation according to the bus voltage of the passive side, wherein the passive side electromechanical transient model is used for simulating the electromechanical transient of the passive side in the flexible direct current transmission system. The method and the device can effectively simulate the electromechanical transient condition of the passive side of the flexible direct current transmission, intuitively reflect the process of the flexible direct current transmission operation, and are favorable for controlling the whole flexible direct current transmission operation more optimally.
The flexible direct current transmission operation simulation method and device provided by the invention are described in detail below with reference to the accompanying drawings.
In a specific embodiment, a flexible dc power transmission operation simulation method is provided, as shown in fig. 1, including:
s1, current data of three alternating currents are input into a preset flexible direct current transmission passive side electromechanical transient model to obtain bus voltage of a passive side;
specifically, fig. 2 is a schematic structural diagram of a flexible dc power transmission to supply power to a passive network, wherein MMCl operates in a rectifying state to transfer active power from the active network to the dc network, and MMC2 operates in an inverting state to transfer active and reactive power to the passive network. The three-phase AC power system is composed of three AC circuits with the same frequency, equal potential amplitude and 120-degree phase difference, and is produced by three groups of symmetrical windings of a three-phase generator, each winding and an external loop thereof are called a phase, A, B, C is respectively marked, and corresponding currents can be marked as ia, ib and ic. On the other hand, the power of the power plant is required to be increased to high voltage for transmission, the power is reduced to the user side through a transformer, the line of the high voltage side before being connected with the transformer is a bus, and the bus generally adopts a bare wire or stranded wire with a rectangular or circular section, and the function of the bus is to collect, distribute and transmit electric energy. It is understood that the bus voltage is the high voltage of the power transmission before the transformer is not transformed.
In a specific embodiment, the flexible dc power transmission passive side includes a flexible dc converter, a controller for the converter and a voltage source, so that the creating an electromechanical transient model of the flexible dc power transmission passive side, as shown in fig. 3, includes:
s11, establishing an electromechanical transient model of the passive side flexible direct current converter;
specifically, the passive side flexible dc converter refers to a side flexible dc converter connected to a passive network that operates in an inverted state.
In a specific embodiment, the building an electromechanical transient model of the passive side flexible dc converter, as shown in fig. 4, includes:
s111, converting the current data of the input three-phase alternating current into direct current data in a dq coordinate system;
specifically, in order to simplify the mathematical model of the flexible direct current converter, a park transformation is adopted to transform sinusoidal alternating current quantity under a three-phase coordinate system into direct current quantity under a dq coordinate system. The park transformation is to project three-phase currents of a, b and c of the stator onto a direct axis (d axis) rotating along with the rotor, and a quadrature axis (q axis) and a zero axis (0 axis) perpendicular to the dq plane, so that diagonalization of a stator inductance matrix is realized, and the operation analysis of the synchronous motor is simplified.
S112, generating an electromechanical transient time domain model of the passive side flexible direct current converter in the dq coordinate system according to the direct current data in the dq coordinate system:
l, R is the equivalent inductance and the equivalent resistance from the bus to the middle point of the bridge arm of the converter; u (u) d 、u q D and q axis components of the bus voltage are respectively represented; e, e d 、e q D and q axis components of virtual equipotential point voltages of upper and lower bridge arm reactors of the converter are respectively represented; i.e d 、i q The d and q axis components of the passive ac system current are represented, respectively.
Specifically, only the positive sequence fundamental component is considered when the characteristics of the alternating current side of the converter are researched, so that an electromechanical transient modeling is performed by adopting a fundamental frequency dynamic mathematical model of the alternating current side of the MMC, and an electromechanical transient time domain model of the passive side flexible direct current converter in a dq coordinate system is generated.
In another specific embodiment, an electromechanical transient frequency domain model of the converter can be obtained, and the specific steps are as follows:
s113, carrying out Laplace transformation on an electromechanical transient time domain model of the passive side flexible direct current converter in the dq coordinate system to generate an electromechanical transient frequency domain model of the passive side flexible direct current converter in the dq coordinate system:
specifically, as can be understood from the frequency domain model, the ac output current of the MMC depends only on the ac system voltage and the bridge arm differential mode voltage. If the system voltage is determined, the ac output current is dependent only on the bridge arm differential mode voltage.
S12, establishing an electromechanical transient model of an outer loop controller and an inner loop controller of the passive side flexible direct current converter;
specifically, the control of the inverter is divided into an outer loop control and an inner loop control. Wherein the inner loop control is a fast current control and the outer loop control is a direct voltage and frequency control.
In a specific embodiment, establishing an electromechanical transient model of the outer ring controller of the flexible dc converter, as shown in fig. 5, includes:
s121, determining a circuit topology structure of the outer loop controller;
specifically, as shown in fig. 6, the circuit topology of the outer ring controller is that the outer ring controller is controlled by passive side ac voltage and frequency, and because the frequency of the passive power grid is a given value, the electrical angle θ=ω 0 t is unchanged, and if the voltage and frequency rating of the passive network are to be kept, only u is controlled d =U m 、u q =0, a valve side current clipping link is added considering the overcurrent capability of the inverter.
S122, determining a d-axis component and a q-axis component of bus voltage as input variables of a circuit topology structure of the outer loop controller, determining a d-axis component and a q-axis component of a current reference value as output variables, and further generating an electromechanical transient model of the outer loop controller.
In particular, the method comprises the steps of,
in a specific embodiment, establishing an electromechanical transient model of the inner loop controller of the flexible dc converter, as shown in fig. 7, includes:
S1201, determining a circuit topology structure of the inner loop controller;
specifically, the inner loop controller controls the common mode current and the phase current of the MMC to desired reference current values. The circuit topology of the inner loop controller is shown in FIG. 8, and the inner loop controller adjusts the output voltage e of the MMC d 、e q Let the AC side i d 、i q Fast tracking current reference value i output by outer loop controller dref 、i qref
S1202, determining a connection mode of the inner ring controller and the flexible direct current converter;
specifically, the inner ring controller is connected with the flexible direct current converter in a current decoupling connection mode. It is understood that current decoupling refers to the voltage of the d-axis controlling the current of the d-axis and the voltage of the q-axis controlling the current of the q-axis. In a specific embodiment, the current decoupling is achieved by a PI controller.
And S1203, determining d-axis components and q-axis components of the virtual equipotential point voltages of the upper bridge arm reactor and the lower bridge arm reactor of the flexible direct current converter as output variables according to the connection mode of the inner loop controller and the flexible direct current converter, and further generating an electromechanical transient model of the inner loop controller.
In a specific embodiment, the control parameters of the inner ring controller are also determined according to the initial load when the electromechanical transient model of the inner ring controller is used. If the initial load is larger than a first preset value, reducing the control parameters of the inner ring controller so as to increase the time for the output of the inner ring controller to reach the limiting value; and if the initial load is smaller than the second preset value for a plurality of years, increasing the control parameters of the inner ring controller so as to improve the dynamic response speed of the system. The selection of the first preset value and the second preset value is determined according to the size of the load.
It can be understood that, since the outer loop output quantity of the electromechanical transient voltage source model is to be the given value of the inner loop controller, the actual control input quantity of the system is e output by the inner loop controller d 、e q When a large disturbance is applied to the passive system, the output i of the outer loop controller is due to dref 、i qref And if the parameter selection of the inner loop controller is improper, the output of the inner loop PI controller easily reaches the limiting value, and the current limiting link cannot work any more at the moment, so that the current of the valve side is over-limited. If the initial load is large, the inner loop controller k should be properly reduced p The parameter is properly increased, so that when large disturbance occurs, the time for the output of the inner ring PI controller to reach the limiting value is increased, and the valve side current limiting node can be ensured to work; if the initial load is smaller, the inner loop controller k can be properly increased p Parameters to obtain faster system dynamic response.
And S13, establishing a voltage source electromechanical transient model of the passive side flexible direct current converter.
In a specific embodiment, the step of establishing a voltage source electromechanical transient model of the passive side flexible dc converter, as shown in fig. 9, includes:
s131, determining a circuit topology structure of the voltage source;
s132, adding an inertia link structure in the circuit topology structure of the voltage source so as to generate the electromechanical transient model of the voltage source.
Specifically, the electromechanical transient simulation modeling is carried out on the passive system, the complex dynamic process in the MMC is ignored, only the passive system and the inner and outer ring controllers are reserved, and the whole converter station is equivalent to a controlled voltage source; in order to simulate the measurement part of an actual system, an inertia link is applied to the model, so that an MMC passive side electromechanical transient voltage source model is established, and a specific structural block diagram of the MMC passive side electromechanical transient voltage source model is shown in FIG. 10.
And S2, performing corresponding flexible direct current transmission operation according to the passive side electromechanical transient model, wherein the passive side electromechanical transient model is used for simulating the passive side electromechanical transient in a flexible direct current transmission system.
In a specific embodiment, PSCAD is adopted as a simulation platform for simulating power transmission operation by using a passive side electromagnetic transient model and a passive side electromechanical transient model, a PI controller with internal and external limiting is adopted, and the same PI control parameters are adopted in electromagnetic transient and electromechanical transient simulation; to simplify the calculation, the relevant electrical quantities in the model are per-unit processed.
The invention will be further described with reference to a specific implementation scenario.
Scene one:
the occurrence of a three-phase metallic ground at the PCC bus results in an electromechanical transient simulation of the passive system PCC bus voltage dropping rapidly to 0.
The single-ended active flexible direct current converter shown in fig. 1 is simulated to the passive network power transmission operation, wherein the MMC1 side is a transmitting end, constant direct current voltage control and constant reactive power control are adopted, the MMC2 side is a receiving end, constant frequency control and constant alternating current voltage control are adopted, PSCAD is adopted as an electromagnetic transient model and an electromechanical transient model simulation platform of an MMC system, a PI controller with internal and external limiting is adopted, and the same PI control parameters are adopted in electromagnetic transient and electromechanical transient simulation. The original load of the passive system is 800MW, after the system stably runs for 1.0s, three-phase metallic grounding occurs at the PCC bus, faults are cleared after the three-phase metallic grounding lasts for 0.2s, as shown in FIG. 11 (including (a) in FIG. 11, and (b) in FIG. 11, and (c) in FIG. 11 and (d) in FIG. 11) are dynamic changes in the simulation process of the passive system, the simulation result shows that the electromagnetic transient model is approximately the same as the dynamic process of the electromechanical transient model under large disturbance, and the main difference is that the electromagnetic transient model has a modulation process and contains a certain high-frequency component, and the electromechanical transient model only considers the fundamental component; the electromagnetic transient model is analyzed, the valve side current is found to be suddenly increased at the moment of short circuit and exceeds the limiting value, then the current is firstly reduced and then increased, finally the current is stabilized at the limiting value, the current suddenly decreases at the moment of fault removal, and the current is restored to the original value after about 100 ms.
Analyzing the electromechanical transient model, finding that after three-phase metallic grounding occurs at the PCC bus, the voltage of the PCC bus of the passive system is rapidly reduced to 0, the voltage is slowly increased within 100ms after the fault is removed, and the voltage is restored to the original control value after 100 ms; the valve side current is suddenly increased at the moment of short circuit and exceeds the limiting value, but the current is firstly reduced and then increased after 10ms, finally the current is stabilized at the limiting value, the overcurrent is again generated at the moment of fault removal, and then the current is firstly reduced and then increased, and is restored to the original value after about 100 ms. The active power slowly drops after the fault is applied, drops to 0 after 100ms, and slowly rises within 200ms after the fault is removed, and returns to the original level after 200 ms; the reactive power fluctuates within 20ms after fault removal, after which it quickly returns to 0.
It can be seen that the passive system corresponding to the electromechanical transient voltage source model can be kept stable under large disturbance, and the simulation result of the model is basically consistent with that of the electromagnetic transient accurate model.
Scene II:
an electromechanical transient simulation occurs at different initial loads where the passive system PCC bus voltage drops rapidly to 0.
As can be seen from the simulation results shown in fig. 12, three different initial loads are selected, the power of which is 600mw,800mw,1000mw, respectively, and the inner loop controller k is adjusted according to the adjustment method provided in the present application p Parameters, respectively, were determined as 0.5,0.8,1.1. Using corresponding k p The parameters are simulated, three-phase metallic grounding is assumed to occur at the PCC bus after the system stably operates for 1.0s, faults are cleared after the PCC bus continues for 0.2s, and when the passive system is stable, the simulation result verifies the effectiveness of the inner ring controller parameter selection method.
As can be seen from the above description, the method for simulating the flexible direct current transmission operation provided by the invention comprises the following steps: inputting current data of three alternating currents into a preset flexible direct current transmission passive side electromechanical transient model to obtain bus voltage of a passive side; and performing corresponding flexible direct current transmission operation according to the bus voltage of the passive side, wherein the passive side electromechanical transient model is used for simulating the electromechanical transient of the passive side in the flexible direct current transmission system. The method and the device can effectively simulate the electromechanical transient condition of the passive side of the flexible direct current transmission, intuitively reflect the process of the flexible direct current transmission operation, and are favorable for controlling the whole flexible direct current transmission operation more optimally.
In another aspect, the present application provides an embodiment of a flexible dc power transmission operation simulation apparatus for executing all or part of the content in the flexible dc power transmission operation simulation method, referring to fig. 13, where the flexible dc power transmission operation simulation apparatus specifically includes the following content:
The model operation module 1 inputs current data of three alternating currents to a preset flexible direct current transmission passive side electromechanical transient model to obtain bus voltage of a passive side;
and the simulation power transmission module 2 is used for carrying out corresponding flexible direct current power transmission operation according to the bus voltage of the passive side, wherein the passive side electromechanical transient model is used for simulating the electromechanical transient of the passive side in the flexible direct current power transmission system.
In a specific embodiment, the flexible direct current transmission operation simulation device further includes:
and a model building module for building a flexible direct-current transmission passive side electromechanical transient model.
Specifically, the flexible direct current power transmission passive side comprises a flexible direct current converter, a controller of the converter and a voltage source, so that the model building module is divided into a flexible direct current converter model building unit, a controller model building unit and a voltage source model building unit.
In a preferred embodiment, the flexible dc converter model building unit comprises:
a coordinate conversion unit converting current data of the input three-phase alternating current into direct current data in a dq coordinate system;
the time domain model building unit is used for generating an electromechanical transient time domain model of the passive side flexible direct current converter in the dq coordinate system according to the direct current data in the dq coordinate system:
L, R is the equivalent inductance and the equivalent resistance from the bus to the middle point of the bridge arm of the converter; u (u) d 、u q D and q axis components of the bus voltage are respectively represented; e, e d 、e q D and q axis components of virtual equipotential point voltages of upper and lower bridge arm reactors of the converter are respectively represented; i.e d 、i q The d and q axis components of the passive ac system current are represented, respectively.
In a preferred embodiment, the flexible dc converter model building unit further includes:
the frequency domain model building unit is used for carrying out Laplace transformation on the electromechanical transient time domain model of the passive side flexible direct current converter in the dq coordinate system to generate the electromechanical transient frequency domain model of the passive side flexible direct current converter in the dq coordinate system:
in a preferred embodiment, the controller module building unit comprises:
the outer loop controller model building unit builds an electromechanical transient model of the outer loop controller;
specifically, firstly, determining a circuit topology structure of the outer loop controller; and then determining d-axis components and q-axis components of the busbar voltage as input variables of a circuit topology structure of the outer loop controller, and determining d-axis components and q-axis components of a current reference value as output variables, so as to generate an electromechanical transient model of the outer loop controller.
And the inner ring controller model building unit is used for building an electromechanical transient model of the inner ring controller.
Specifically, firstly, determining a circuit topology structure of the inner loop controller; then determining a connection mode of the inner ring controller and the flexible direct current converter; and then determining d-axis components and q-axis components of the virtual equipotential point voltages of the upper bridge arm reactor and the lower bridge arm reactor of the flexible direct current converter as output variables according to the connection mode of the inner loop controller and the flexible direct current converter, and further generating an electromechanical transient model of the inner loop controller.
In a specific embodiment, the connection mode of the inner ring controller and the flexible direct current converter adopts a current decoupling connection mode, so that the d-axis of the bus voltage is only controlled by d-axis control current, and the q-axis of the bus voltage is only controlled by q-axis control current. The selection of the control parameters of the inner ring controller is determined according to the initial load, if the initial load is larger than a first preset value, the control parameters of the inner ring controller are reduced, so that the time for the output of the inner ring controller to reach the limiting value is prolonged; if the initial load is smaller than a second preset value, the control parameters of the inner ring controller are increased so as to improve the dynamic response speed of the system.
In a preferred embodiment, the voltage source modeling unit includes: firstly, determining a circuit topology structure of the voltage source; and adding an inertial link structure into the circuit topology structure of the voltage source to generate the electromechanical transient model of the voltage source.
Specifically, the electromechanical transient simulation modeling is carried out on the passive system, the complex dynamic process in the MMC is ignored, only the passive system and the inner and outer ring controllers are reserved, and the whole converter station is equivalent to a controlled voltage source; and in order to simulate the measurement part of an actual system, an inertia link is applied to the model, so that an MMC passive side electromechanical transient voltage source model is established.
As can be seen from the above description, the flexible direct current transmission operation simulation device provided by the invention has the advantages that the model operation module 1 inputs current data of three alternating currents to a preset flexible direct current transmission passive side electromechanical transient model to obtain bus voltage of a passive side; and the simulation power transmission module 2 is used for carrying out corresponding flexible direct current power transmission operation according to the bus voltage of the passive side, wherein the passive side electromechanical transient model is used for simulating the electromechanical transient of the passive side in the flexible direct current power transmission system. The method and the device can effectively simulate the electromechanical transient condition of the passive side of the flexible direct current transmission, intuitively reflect the process of the flexible direct current transmission operation, and are favorable for controlling the whole flexible direct current transmission operation more optimally.
From the aspect of hardware, the application provides an embodiment of an electronic device for implementing all or part of the content in a flexible direct current transmission operation simulation method, where the electronic device specifically includes the following content:
fig. 14 is a schematic block diagram of a system configuration of an electronic device 9600 of an embodiment of the present application. As shown in fig. 14, the electronic device 9600 may include a central processor 9100 and a memory 9140; the memory 9140 is coupled to the central processor 9100. Notably, this fig. 14 is exemplary; other types of structures may also be used in addition to or in place of the structures to implement telecommunications functions or other functions.
In one embodiment, the flexible dc power transmission operation simulation function may be integrated into the central processor. Wherein the central processor may be configured to control:
s1, current data of three alternating currents are input into a preset flexible direct current transmission passive side electromechanical transient model to obtain bus voltage of a passive side;
and S2, performing corresponding flexible direct current transmission operation according to the bus voltage of the passive side, wherein the passive side electromechanical transient model is used for simulating the electromechanical transient of the passive side in the flexible direct current transmission system.
From the above description, the method and the device can effectively simulate the electromechanical transient condition of the passive side of the flexible direct current transmission, intuitively reflect the process of the flexible direct current transmission operation, and are beneficial to controlling the whole flexible direct current transmission operation more optimally.
In another embodiment, the flexible dc power transmission operation simulation device may be configured separately from the central processor 9100, for example, the flexible dc power transmission operation simulation device may be configured as a chip connected to the central processor 9100, and the flexible dc power transmission operation simulation function is implemented by control of the central processor.
As shown in fig. 14, the electronic device 9600 may further include: a communication module 9110, an input unit 9120, an audio processor 9130, a display 9160, and a power supply 9170. It is noted that the electronic device 9600 need not include all of the components shown in fig. 14; in addition, the electronic device 9600 may further include components not shown in fig. 14, and reference may be made to the related art.
As shown in fig. 14, the central processor 9100, sometimes referred to as a controller or operational control, may include a microprocessor or other processor device and/or logic device, which central processor 9100 receives inputs and controls the operation of the various components of the electronic device 9600.
The memory 9140 may be, for example, one or more of a buffer, a flash memory, a hard drive, a removable media, a volatile memory, a non-volatile memory, or other suitable device. The information about failure may be stored, and a program for executing the information may be stored. And the central processor 9100 can execute the program stored in the memory 9140 to realize information storage or processing, and the like.
The input unit 9120 provides input to the central processor 9100. The input unit 9120 is, for example, a key or a touch input device. The power supply 9170 is used to provide power to the electronic device 9600. The display 9160 is used for displaying display objects such as images and characters. The display may be, for example, but not limited to, an LCD display.
The memory 9140 may be a solid state memory such as Read Only Memory (ROM), random Access Memory (RAM), SIM card, etc. But also a memory which holds information even when powered down, can be selectively erased and provided with further data, an example of which is sometimes referred to as EPROM or the like. The memory 9140 may also be some other type of device. The memory 9140 includes a buffer memory 9141 (sometimes referred to as a buffer). The memory 9140 may include an application/function storage portion 9142, the application/function storage portion 9142 storing application programs and function programs or a flow for executing operations of the electronic device 9600 by the central processor 9100.
The memory 9140 may also include a data store 9143, the data store 9143 for storing data, such as contacts, digital data, pictures, sounds, and/or any other data used by an electronic device. The driver storage portion 9144 of the memory 9140 may include various drivers of the electronic device for communication functions and/or for performing other functions of the electronic device (e.g., messaging applications, address book applications, etc.).
The communication module 9110 is a transmitter/receiver 9110 that transmits and receives signals via an antenna 9111. A communication module (transmitter/receiver) 9110 is coupled to the central processor 9100 to provide input signals and receive output signals, as in the case of conventional mobile communication terminals.
Based on different communication technologies, a plurality of communication modules 9110, such as a cellular network module, a bluetooth module, and/or a wireless local area network module, etc., may be provided in the same electronic device. The communication module (transmitter/receiver) 9110 is also coupled to a speaker 9131 and a microphone 9132 via an audio processor 9130 to provide audio output via the speaker 9131 and to receive audio input from the microphone 9132 to implement usual telecommunications functions. The audio processor 9130 can include any suitable buffers, decoders, amplifiers and so forth. In addition, the audio processor 9130 is also coupled to the central processor 9100 so that sound can be recorded locally through the microphone 9132 and sound stored locally can be played through the speaker 9131.
The embodiments of the present application further provide a computer readable storage medium capable of implementing all the steps in the flexible dc power transmission operation simulation method in the above embodiments, where the computer readable storage medium stores a computer program, and when the computer program is executed by a processor, the computer program implements all the steps in the flexible dc power transmission operation simulation method in which the execution subject in the above embodiments is a server or a client, for example, the processor implements the following steps when executing the computer program:
s1, current data of three alternating currents are input into a preset flexible direct current transmission passive side electromechanical transient model to obtain bus voltage of a passive side;
and S2, performing corresponding flexible direct current transmission operation according to the bus voltage of the passive side, wherein the passive side electromechanical transient model is used for simulating the electromechanical transient of the passive side in the flexible direct current transmission system.
From the above description, the method and the device can effectively simulate the electromechanical transient condition of the passive side of the flexible direct current transmission, intuitively reflect the process of the flexible direct current transmission operation, and are beneficial to controlling the whole flexible direct current transmission operation more optimally.
It will be apparent to those skilled in the art that embodiments of the present invention may be provided as a method, apparatus, or computer program product. Accordingly, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present invention 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 invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (devices), and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations 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 principles and embodiments of the present invention have been described in detail with reference to specific examples, which are provided to facilitate understanding of the method and core ideas of the present invention; meanwhile, as those skilled in the art will have variations in the specific embodiments and application scope in accordance with the ideas of the present invention, the present description should not be construed as limiting the present invention in view of the above.

Claims (10)

1. A flexible direct current transmission operation simulation method, characterized by comprising:
inputting current data of three-phase alternating current into a preset flexible direct current transmission passive side electromechanical transient model to obtain bus voltage of a passive side;
performing corresponding flexible direct current transmission operation according to the bus voltage of the passive side, wherein the passive side electromechanical transient model is used for simulating the electromechanical transient of the passive side in a flexible direct current transmission system;
Establishing an electromechanical transient model of a flexible direct current transmission passive side;
the establishing of the electromechanical transient model of the flexible direct current transmission passive side comprises the following steps:
establishing an electromechanical transient model of the passive side flexible direct current converter;
establishing an electromechanical transient model of an outer loop controller and an inner loop controller of the passive side flexible direct current converter;
establishing a voltage source electromechanical transient model of the passive side flexible direct current converter;
determining a control parameter k of the inner ring controller according to the initial load p
If the initial load is larger than a first preset value, reducing the control parameter k of the inner ring controller p So that the time for the output of the inner loop controller to reach the limiting value is increased;
if the initial load is smaller than the second preset value, increasing the control parameter k of the inner ring controller p To improve the dynamic response speed of the system.
2. A method of simulating operation of a flexible dc power transmission according to claim 1, wherein the electromechanical transient model of the passive side flexible dc converter comprises:
converting the current data of the input three-phase alternating current into direct current data in a dq coordinate system;
generating an electromechanical transient time domain model of the passive side flexible direct current converter in the dq coordinate system according to the direct current data in the dq coordinate system:
L, R is the equivalent inductance and the equivalent resistance from the bus to the middle point of the bridge arm of the converter; u (u) d 、u q D and q axis components of the bus voltage are respectively represented; e, e d 、e q D and q axis components of virtual equipotential point voltages of upper and lower bridge arm reactors of the converter are respectively represented; i.e d 、i q The d and q axis components of the passive ac system current are represented, respectively.
3. The method for simulating flexible dc power transmission operation according to claim 2, wherein the electromechanical transient model of the passive-side flexible dc converter further comprises:
carrying out Laplace transformation on the electromechanical transient time domain model of the passive side flexible direct current converter in the dq coordinate system to generate the electromechanical transient frequency domain model of the passive side flexible direct current converter in the dq coordinate system:
4. the method for simulating flexible dc power transmission operation according to claim 1, wherein establishing an electromechanical transient model of the flexible dc converter outer loop controller comprises:
determining a circuit topology of the outer loop controller;
and determining d-axis components and q-axis components of the busbar voltage as input variables of a circuit topology structure of the outer loop controller, and determining d-axis components and q-axis components of a current reference value as output variables, so as to generate an electromechanical transient model of the outer loop controller.
5. The method for simulating flexible dc power transmission operation according to claim 1, wherein establishing an electromechanical transient model of the flexible dc converter inner loop controller comprises:
determining a circuit topology of the inner loop controller;
determining a connection mode of the inner ring controller and the flexible direct current converter;
and determining d-axis components and q-axis components of virtual equipotential point voltages of upper and lower bridge arm reactors of the flexible direct current converter as output variables according to a connection mode of the inner loop controller and the flexible direct current converter, thereby generating an electromechanical transient model of the inner loop controller.
6. The method for simulating flexible dc power transmission operation according to claim 5, wherein the connection mode between the inner ring controller and the flexible dc converter comprises:
current decoupling connection mode.
7. The method for simulating flexible dc power transmission operation according to claim 1, wherein the step of establishing a voltage source electromechanical transient model of the passive-side flexible dc converter comprises:
Determining a circuit topology of the voltage source;
and adding an inertial link structure in the circuit topology structure of the voltage source so as to generate the electromechanical transient model of the voltage source.
8. A flexible direct current transmission operation simulation device, comprising:
the model operation module is used for inputting current data of the three-phase alternating current into a preset flexible direct current transmission passive side electromechanical transient model to obtain bus voltage of the passive side;
the simulation power transmission module is used for carrying out corresponding flexible direct current power transmission operation according to the bus voltage of the passive side, wherein the passive side electromechanical transient model is used for simulating the electromechanical transient of the passive side in a flexible direct current power transmission system;
the model building module is used for building an electromechanical transient model of the flexible direct-current transmission passive side;
the model building module comprises:
the flexible direct current converter model building unit is used for building an electromechanical transient model of the passive side flexible direct current converter;
the controller model building unit is used for building electromechanical transient models of an outer loop controller and an inner loop controller of the passive side flexible direct current converter;
the voltage source model building unit is used for building a voltage source electromechanical transient model of the passive side flexible direct current converter;
The controller model building unit is specifically configured to:
determining a control parameter k of the inner ring controller according to the initial load p
If the initial load is larger than a first preset value, reducing the control parameter k of the inner ring controller p So that the time for the output of the inner loop controller to reach the limiting value is increased;
if the initial load is smaller than the second preset value, increasing the control parameter k of the inner ring controller p To improve the dynamic response speed of the system.
9. An electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the processor implements the flexible direct current transmission operation simulation method of any of claims 1 to 7 when the program is executed by the processor.
10. A computer readable storage medium having stored thereon a computer program, characterized in that the computer program, when executed by a processor, implements the flexible direct current transmission operation simulation method of any of claims 1 to 7.
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