CN111509704A - Dynamic interaction analysis method for multi-energy system containing DFIG-SOFC (doubly Fed induction Generator) -based SSSC (solid State gas insulated switchgear) - Google Patents

Dynamic interaction analysis method for multi-energy system containing DFIG-SOFC (doubly Fed induction Generator) -based SSSC (solid State gas insulated switchgear) Download PDF

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CN111509704A
CN111509704A CN202010326860.XA CN202010326860A CN111509704A CN 111509704 A CN111509704 A CN 111509704A CN 202010326860 A CN202010326860 A CN 202010326860A CN 111509704 A CN111509704 A CN 111509704A
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voltage
sssc
sofc
dfig
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CN111509704B (en
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和萍
赵琛
陶玉昆
李从善
饶宇飞
祁盼
杨红卫
南春雷
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Zhengzhou University of Light Industry
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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
    • 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
    • H02J3/18Arrangements for adjusting, eliminating or compensating reactive power in networks
    • H02J3/1807Arrangements for adjusting, eliminating or compensating reactive power in networks using series compensators
    • 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
    • H02J3/38Arrangements for parallely feeding a single network by two or more generators, converters or transformers
    • H02J3/381Dispersed generators
    • 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]
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02JCIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2300/00Systems for supplying or distributing electric power characterised by decentralized, dispersed, or local generation
    • H02J2300/20The dispersed energy generation being of renewable origin
    • H02J2300/28The renewable source being wind energy
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02JCIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2300/00Systems for supplying or distributing electric power characterised by decentralized, dispersed, or local generation
    • H02J2300/30The power source being a fuel cell
    • 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
    • Y02E40/00Technologies for an efficient electrical power generation, transmission or distribution
    • Y02E40/30Reactive power compensation

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  • Control Of Eletrric Generators (AREA)

Abstract

The invention provides a dynamic interaction analysis method of a DFIG-SOFC (doubly Fed induction heating-solid oxide fuel cell) multi-energy system based on SSSC (static synchronous series compensator), which comprises the following steps: firstly, an SOFC power station and an SSSC are connected to a bus of a power system, and a voltage algebraic equation of the power system is constructed; secondly, performing Park transformation on a voltage algebraic equation of the power system to obtain a terminal current dq component, substituting the terminal current dq component into each element mathematical model, and performing linearization processing at a stable point to obtain a state matrix of the linearization power system; finally, relevant parameters influencing the stability of the power system can be obtained from the state matrix, and the system is verified by using the change of the compensation quantity of the SSSC. The method adds SSSC into a multi-energy power system containing DFIG and SOFC, constructs a linear model of the system, analyzes the dynamic interaction of the system from the mechanism, and verifies the correctness of the method on a four-machine two-area system by changing the compensation quantity of a static synchronous series compensator.

Description

Dynamic interaction analysis method for multi-energy system containing DFIG-SOFC (doubly Fed induction Generator) -based SSSC (solid State gas insulated switchgear)
Technical Field
The invention relates to the technical field of power systems, in particular to a dynamic interaction analysis method of a DFIG-SOFC (doubly Fed induction Generator-solid State Fuel cell) multi-energy system based on SSSC (static synchronous series converter).
Background
With the increasing severity of environmental and energy problems, the use of clean energy to generate electricity has become an important measure for the sustainable development of countries in the world. The wind energy is used as a green pollution-free clean energy, not only optimizes the energy structure, but also plays an important role in improving the ecological environment. Wind power generation technology, especially double-fed asynchronous Generator (DFIG) power generation, has been widely applied to modern power systems. The fuel cell has wide sources and environmental protection, is acknowledged as the first choice of the next generation of clean energy, and the international energy world also predicts that the fuel cell is one of the most attractive power generation methods in the 21 st century. Among them, Solid Oxide Fuel Cells (SOFC) have great influence on future power systems due to their characteristics of modularization, high efficiency and no pollution and rapid development of their power generation technologies. Although the grid-connected DFIG and SOFC power generation have many advantages, the low-frequency oscillation phenomenon of the grid-connected system is inevitable.
In recent years, the power grid has low-frequency oscillation accidents for many times, and the safe and stable operation of the power grid is greatly threatened. Flexible Alternating Current Transmission Systems (FACTS) are widely used in power grids to increase system damping and improve system stability. As a novel series reactive power compensation device, a Static Series Synchronous Compensator (SSSC) has the advantages of flexible control, simple structure, and capability of rapidly regulating and controlling power flow, and is also widely used in power systems. The influence of an SSSC control mode on the stability of a traditional power system and a power system containing wind power is considered in most of the existing research results, but the influence of the SSSC control mode on the stability of the power system of a multi-energy system containing a DFIG-SOFC is rarely researched.
Disclosure of Invention
The invention provides a dynamic interaction analysis method of a DFIG-SOFC multi-energy system based on SSSC, aiming at the technical problem that the system has low-frequency oscillation after the DFIG-SOFC is connected with the grid, and the dynamic interaction analysis method is used for analyzing the dynamic influence of the SSSC on the DFIG-SOFC multi-energy system.
The technical scheme of the invention is realized as follows:
a dynamic interaction analysis method of a DFIG-SOFC-containing multi-energy system based on SSSC comprises the following steps:
s1, the SOFC power station and the SSSC are connected to a bus node of the power system, a voltage equation of a branch equivalent reactance in the power system is obtained through ohm' S law, and a voltage algebraic equation of the power system is constructed according to the voltage equation of the branch equivalent reactance, wherein the branch equivalent reactance comprises an equivalent reactance from a synchronous generator node to the bus node, an equivalent reactance from a DFIG wind power station node to the bus node, an equivalent reactance from the SOFC power station node to the bus node, and an equivalent reactance from the SSSC node to the bus node;
s2, respectively constructing a synchronous generator model, a DFIG wind power plant model, an SOFC power plant model and an SSSC model;
s3, performing Park conversion on the voltage algebraic equation of the power system in the step S1 to obtain a current dq component of a branch equivalent reactance in the power system, respectively substituting the current dq component of the branch equivalent reactance into the synchronous generator model, the DFIG wind power plant model, the SOFC power station model and the SSSC model in the step S2, and performing linearization processing at a stable point to obtain a state matrix of a linearized power system;
s4, obtaining relevant parameters influencing the stability of the power system from the state matrix in the step S3;
and S5, judging the stability of the power system by changing the compensation amount of the static synchronous series compensator in the related parameters.
The voltage equation of the branch equivalent reactance in the power system is as follows:
Figure BDA0002463532630000021
wherein the content of the first and second substances,
Figure BDA0002463532630000022
is the voltage at the node of the synchronous generator,
Figure BDA0002463532630000023
is the voltage of the DFIG wind farm node,
Figure BDA0002463532630000024
is the voltage at the node of the SOFC power station,
Figure BDA0002463532630000025
is the voltage at the node of the bus bar,
Figure BDA0002463532630000026
is the voltage of the node at infinity and,
Figure BDA0002463532630000027
is the equivalent voltage of the SSSC node; x is the number oftsIs the equivalent reactance, x, from the node of the synchronous generator to the node of the bustwIs equivalent reactance, x, from DFIG wind farm node to bus nodesIs the equivalent reactance, x, from SOFC power station node to bus nodelIs the equivalent reactance from the infinite node to the bus node;
Figure BDA0002463532630000028
is the current injected at the node of the synchronous generator,
Figure BDA0002463532630000029
is the current injected into the DFIG windfarm node,
Figure BDA00024635326300000210
is injected into SOFC power stationCurrent at the node, j representing an imaginary unit;
adding the voltage equations of the branch equivalent reactances to cancel the voltage of the bus node
Figure BDA00024635326300000211
Obtaining a voltage algebraic equation of the power system:
Figure BDA00024635326300000212
the synchronous generator model is as follows:
Figure BDA00024635326300000213
wherein p (-) represents a differential function, is the rotor power angle, ω is the rotor angular velocity of the synchronous machine, ω is0Is the synchronous angular velocity, TJIs the inertia time constant, T'd0Is the time constant of the field winding, TaIs the excitation system time constant, PmIs the mechanical power of the prime mover, PeIs electromagnetic power, E'qIs q-axis transient electromotive force, EqeIs a forced no-load electromotive force, EqIs no-load electromotive force, KaIs the amplification factor, V, of the excitation systemtIs the voltage amplitude, V, of the synchronous generator nodetrefIs the excitation regulator set voltage;
the DFIG wind power plant model is as follows:
Figure BDA0002463532630000031
wherein R issIs stator resistance, XsIs stator reactance, X'sIs the stator transient reactance, ωsIs the synchronous angular velocity, omega, of the synchronous generatorrIs the angular speed of the rotor, ωtIs the angular velocity of the wind turbine shaft, LmStator-rotor mutual inductance, LrrIs rotor self-inductance, VwdsIs the d-axis component of the stator voltage, VwqsIs the stator voltage q-axis component, VwdrIs rotor electricityD-axis component of pressure, VwqrIs the q-axis component, i, of the rotor voltagewdsIs the d-axis component of the stator current, iwqsIs the q-axis component, e 'of the stator current'dIs the d-axis component, e ', of the post-stator transient potential'qIs the q-axis component, T ', of the post-stator transient potential'0Is the rotor time constant, TmIs the mechanical torque of the fan, TshIs the torque between two masses, TeIs the electromagnetic torque of the generator, thetatwIs the twist angle of the shaft of the low-speed fan relative to the shaft of the high-speed generator, HtIs the inertia time constant of the fan, HgIs the inertial time constant of the generator;
the SOFC power station model is as follows:
Figure BDA0002463532630000032
wherein, VdcIs a DC capacitor C in SOFC power stationdcVoltage across, PfcIs the fuel cell power, m is the modulation ratio of the inverter, k is the transformation ratio of the inverter, IsdIs the d-axis component, I, of the current injected at the SOFC power station nodesqIs the q-axis component of the current injected at the SOFC power station node, psi is the phase of the voltage at the SOFC power station node, CdcIs the dc capacitance capacity;
the SSSC model is as follows:
Figure BDA0002463532630000033
wherein the content of the first and second substances,
Figure BDA0002463532630000041
is the first derivative of the dc capacitor voltage versus time t in the SSSC structure,
Figure BDA0002463532630000042
is the equivalent voltage, V, of the SSSC nodescdIs the d-axis component, V, of the equivalent voltage of the SSSC nodescqIs the q-axis component, V ', of the equivalent voltage of the SSSC node'dcIs the DC capacitor voltage in the SSSC structure,' isAmplitude V of SSSC equivalent voltagescRelative to the phase angle of the q axis, k 'is the transformer transformation ratio, m' is the inverter pulse width modulation coefficient, and C is the capacitance; i isdIs the current flowing into infinite node
Figure BDA0002463532630000047
D-axis component of (I)qIs flowing into infinite node current
Figure BDA0002463532630000046
Q-axis component of (a).
The electromagnetic power PeNo-load electromotive force EqVoltage amplitude V of synchronous generator nodetThe calculation method comprises the following steps:
Figure RE-GDA0002502195090000045
wherein x isdIs d-axis reactance of the generator, xqIs the q-axis reactance of the generator, x'dIs the d-axis transient reactance of the generator, ItsdD-axis current of generator stator, ItsqIs the generator stator q-axis current, VtdIs the d-axis component of the port voltage, VtqIs the q-axis component of the port voltage.
Torque T between the two massesshElectromagnetic torque T of generatoreThe calculation method comprises the following steps:
Figure BDA0002463532630000044
wherein, KshIs the stiffness coefficient of the shaft, DshIs the damping coefficient of the shaft.
The current dq component of the branch equivalent reactance in the power system is as follows:
Figure BDA0002463532630000045
wherein x istsIs the equivalent reactance, x, from the node of the synchronous generator to the node of the bustwIs DFIG windEquivalent reactance, x, from electric field node to bus nodesIs the equivalent reactance, x, from SOFC power station node to bus nodelIs an equivalent reactance from an infinite node to a bus node; x is the number ofqIs the q-axis reactance of the generator, x'dIs the d-axis transient reactance of the generator, ItsdD-axis current of generator stator, ItsqIs the generator stator q-axis current, IsdIs the d-axis component, I, of the current injected at the SOFC power station nodesqIs the q-axis component, I, of the current injected at the SOFC power station nodewdIs the d-axis component, I, of the current injected into the DFIG windfarm nodewqIs a q-axis component of current injected into the DFIG windfarm node; vcIs the voltage amplitude, V, of the DFIG wind farm nodebVoltage amplitude, V, of infinite nodescIs the magnitude of the SSSC equivalent voltage; vdwIs the d-axis component, V, of the voltage at the DFIG wind farm nodeqwIs the q-axis component of the voltage at the DFIG wind farm node; e'qIs the q-axis transient electromotive force of the synchronous generator; is the rotor power angle; psi is the phase of the SOFC plant node voltage; ' is the amplitude V of the SSSC equivalent voltagescPhase angle with respect to the q-axis.
Adopting a Lyapunov linearization method at a stable operation point, and respectively substituting the current dq components of the branch equivalent reactance of the power system into a synchronous generator model, a DFIG wind power plant model, an SOFC power plant model and an SSSC model to obtain a state equation of the linearized power system as follows:
Figure BDA0002463532630000051
wherein the content of the first and second substances,
Figure BDA0002463532630000052
Figure BDA0002463532630000053
is to calculate the first derivative of the system state variable matrix, X ' is the system state variable matrix, A ' is the coefficient matrix of the system state variable, B ' is the coefficient matrix of the system control variable, U is the system control variable, △ is the rotorVariation of work angle, variation of △ ω rotor angular velocity of synchronous machine, Δ E'qIs the amount of change, Δ E, in the q-axis transient electromotive forceqeIs the amount of change, Δ i, in the forced no-load electromotive forcewdsIs the d-axis component variation, Δ i, of the stator currentwqsIs the q-axis component variation of the stator current, Δ e'dIs the d-axis component variation, Δ e ', of the post-stator transient potential'qVariation of q-axis component of post-stator transient potential, Δ ωrIs the rotor angular velocity variation, Δ ωtIs the variation of angular velocity, Delta theta, of the wind turbine shafttwIs the amount of change, Δ V, in the twist angle of the shaft of the low-speed fan relative to the shaft of the high-speed generatordcIs a DC capacitor C in SOFC power stationdcVoltage variation at two ends, △ m is inverter modulation ratio variation in SOFC power station, Δ ψ is voltage phase variation of SOFC power station node, Δ m 'is inverter pulse width modulation coefficient variation in SSSC, △' is amplitude V of SSSC equivalent voltagescDelta T of phase angle variation with respect to q-axismIs the variation of mechanical torque of the fan, Δ VwdrD-axis component variation, Δ V, of rotor voltage in DFIGwqrIs the amount of change in the q-axis component of the rotor voltage in the DFIG.
The beneficial effect that this technical scheme can produce: the method adds SSSC into a multi-energy power system containing DFIG and SOFC, constructs a linear model of the system, analyzes the dynamic interaction of the system from the mechanism, and verifies the correctness of the analysis method on a four-machine two-area system by taking the variable of the SSSC as an example.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to these drawings without creative efforts.
FIG. 1 is a block diagram of the system of the present invention;
FIG. 2 is a diagram of a four-machine two-area grid system according to an embodiment of the present invention;
FIG. 3 is a response curve of the power angle of the synchronous generator with different compensation degrees according to the embodiment of the present invention;
fig. 4 is a response curve of the reactive power of the synchronous generator at different compensation degrees according to the embodiment of the invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be described clearly and completely with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without any inventive step, are within the scope of the present invention.
As shown in fig. 1, an embodiment of the present invention provides a dynamic interaction analysis method for a DFIG-SOFC-containing multi-energy system based on SSSC, which includes the following specific steps:
s1, the SOFC power station and the SSSC are connected to a bus node of the power system, a voltage equation of a branch equivalent reactance in the power system is obtained through ohm' S law, and a voltage algebraic equation of the power system is constructed according to the voltage equation of the branch equivalent reactance, wherein the branch equivalent reactance comprises an equivalent reactance from a synchronous generator node to the bus node, an equivalent reactance from a DFIG wind power station node to the bus node, an equivalent reactance from the SOFC power station node to the bus node, and an equivalent reactance from the SSSC node to the bus node; :
Figure BDA0002463532630000061
wherein the content of the first and second substances,
Figure BDA0002463532630000062
is the voltage at the node of the synchronous generator,
Figure BDA0002463532630000063
is the voltage of the DFIG wind farm node,
Figure BDA0002463532630000064
is the voltage at the node of the SOFC power station,
Figure BDA0002463532630000065
is the voltage at the node of the bus bar,
Figure BDA0002463532630000066
is the voltage of the node at infinity and,
Figure BDA0002463532630000067
is the equivalent voltage of the SSSC node; x is the number oftsIs the equivalent reactance, x, from the node of the synchronous generator to the node of the bustwIs equivalent reactance, x, from DFIG wind farm node to bus nodesIs the equivalent reactance, x, from SOFC power station node to bus nodelIs the equivalent reactance from the infinite node to the bus node;
Figure BDA0002463532630000068
is the current injected at the node of the synchronous generator,
Figure BDA0002463532630000069
is the current injected into the DFIG windfarm node,
Figure BDA00024635326300000610
is the current injected at the SOFC power station node.
Adding voltage equations of equivalent reactances of all branches of the system to eliminate voltage of bus nodes
Figure BDA00024635326300000611
Obtaining:
Figure BDA00024635326300000612
s2, respectively constructing a synchronous generator model, a DFIG wind power plant model, an SOFC power plant model and an SSSC model; as can be seen from FIG. 1, the power system includes a synchronous generator, a DFIG wind farm, a SOFC power plant, and a SSSC; therefore, the dynamic influence of the SSSC on the DFIG-SOFC multi-energy system is analyzed through the constructed synchronous generator model, the DFIG wind power plant model, the SOFC power plant model and the SSSC model.
The synchronous generator model is as follows:
Figure BDA0002463532630000071
wherein p (-) represents a differential function, is the rotor power angle, ω is the rotor angular velocity of the synchronous machine, ω is0Is the synchronous angular velocity, TJIs the inertia time constant, T'd0Is the time constant of the field winding, TaIs the excitation system time constant, PmIs the mechanical power of the prime mover, PeIs electromagnetic power, E'qIs q-axis transient electromotive force, EqeIs a forced no-load electromotive force, EqIs no-load electromotive force, KaIs the amplification factor, V, of the excitation systemtIs the voltage amplitude, V, of the synchronous generator nodetrefIs the excitation regulator set voltage.
The electromagnetic power PeNo-load electromotive force EqVoltage amplitude V of synchronous generator nodetThe calculation method comprises the following steps:
Figure BDA0002463532630000072
wherein x isdIs d-axis reactance of the generator, xqIs the q-axis reactance of the generator, x'dIs the d-axis transient reactance of the generator, ItsdD-axis current of generator stator, ItsqIs the generator stator q-axis current, VtdIs the d-axis component of the port voltage, VtqIs the q-axis component of the port voltage.
The DFIG wind power plant model is as follows:
Figure BDA0002463532630000073
wherein R issIs stator resistance, XsIs stator reactance, X'sIs the stator transient reactance, ωsIs the synchronous angular velocity, omega, of the synchronous generatorrIs the angular speed of the rotor, ωtIs the angular velocity of the wind turbine shaft, LmStator-rotor mutual inductance, LrrIs rotor self-inductance, VwdsIs the d-axis component of the stator voltage, VwqsIs the stator voltage q-axis component, VwdrIs the d-axis component of the rotor voltage, VwqrIs the q-axis component, i, of the rotor voltagewdsIs the d-axis component of the stator current, iwqsIs the q-axis component, e 'of the stator current'dIs the d-axis component, e ', of the post-stator transient potential'qIs the q-axis component, T ', of the post-stator transient potential'0Is the rotor time constant, TmIs the mechanical torque of the fan, TshIs the torque between two masses, TeIs the electromagnetic torque of the generator, thetatwIs the twist angle of the shaft of the low-speed fan relative to the shaft of the high-speed generator, HtIs the inertia time constant of the fan, HgIs the inertia time constant of the generator.
Torque T between the two massesshElectromagnetic torque T of generatoreThe calculation method comprises the following steps:
Figure BDA0002463532630000081
wherein, KshIs the stiffness coefficient of the shaft, DshIs the damping coefficient of the shaft.
The SOFC power station model is as follows:
Figure BDA0002463532630000082
wherein, VdcIs a DC capacitor C in SOFC power stationdcVoltage across, PfcIs the fuel cell power, m is the modulation ratio of the inverter, k is the transformation ratio of the inverter, IsdIs the d-axis component, I, of the current injected at the SOFC power station nodesqIs the q-axis component of the current injected at the SOFC power station node, psi is the phase of the voltage at the SOFC power station node, CdcIs the dc capacitance.
The SSSC model is as follows:
Figure BDA0002463532630000083
wherein the content of the first and second substances,
Figure BDA0002463532630000084
is the first derivative of the dc capacitor voltage versus time t in the SSSC structure,
Figure BDA0002463532630000085
is the equivalent voltage, V, of the SSSC nodescdIs the d-axis component, V, of the equivalent voltage of the SSSC nodescqIs the q-axis component, V ', of the equivalent voltage of the SSSC node'dcIs the DC capacitor voltage in the SSSC structure, is the amplitude V of the SSSC equivalent voltagescRelative to the phase angle of the q axis, k 'is the transformer transformation ratio, m' is the inverter pulse width modulation coefficient, and C is the capacitance; i isdIs the current flowing into infinite node
Figure BDA0002463532630000087
D-axis component of (I)qIs flowing into infinite node current
Figure BDA0002463532630000086
Q-axis component of (a).
S3, performing Park conversion on a voltage algebraic equation of the power system to obtain a current dq component of a branch equivalent reactance in the power system, respectively substituting the current dq component of the branch equivalent reactance into the synchronous generator model, the DFIG wind power plant model, the SOFC power station model and the SSSC model in the step S2, and performing linearization processing at a stable point to obtain a state matrix of the linearized power system;
the current dq component of the branch equivalent reactance in the power system is as follows:
Figure BDA0002463532630000091
wherein x istsIs the equivalent reactance, x, from the node of the synchronous generator to the node of the bustwIs DFIG windEquivalent reactance, x, from electric field node to bus nodesIs the equivalent reactance, x, from SOFC power station node to bus nodelIs an equivalent reactance from an infinite node to a bus node; x is the number ofqIs the q-axis reactance of the generator, x'dIs the d-axis transient reactance of the generator, ItsdD-axis current of generator stator, ItsqIs the generator stator q-axis current, IsdIs the d-axis component, I, of the current injected at the SOFC power station nodesqIs the q-axis component, I, of the current injected at the SOFC power station nodewdIs the d-axis component, I, of the current injected into the DFIG windfarm nodewqIs a q-axis component of current injected into the DFIG windfarm node; vcIs the voltage amplitude, V, of the DFIG wind farm nodebVoltage amplitude, V, of infinite nodescIs the magnitude of the SSSC equivalent voltage; vdwIs the d-axis component, V, of the voltage at the DFIG wind farm nodeqwIs the q-axis component of the voltage at the DFIG wind farm node; e'qIs the q-axis transient electromotive force of the synchronous generator; is the rotor power angle; psi is the phase of the SOFC plant node voltage; ' is the amplitude V of the SSSC equivalent voltagescPhase angle with respect to the q-axis.
At a stable operation point, a Lyapunov linearization method is adopted to carry out linearization processing on the dq component of the end current of the power system, and V is processedsc、Vc、Vdw、VqwThe variation of (a) is replaced by a corresponding expression:
Figure BDA0002463532630000092
wherein, Delta ItsqIs the amount of change, Δ I, in the q-axis current of the stator of the generatorsqVariation of q-axis component, Δ I, of current injected at SOFC power station nodewqIs the q-axis component variation of the current injected into the DFIG wind farm node, Δ is the rotor power angle variation, △ m 'is the inverter pulse width modulation coefficient variation in the SSSC, Δ' is the amplitude V of the SSSC equivalent voltagescAmount of phase angle change with respect to q-axis, Δ VdcIs a DC capacitor C in SOFC power stationdcVoltage variation at both ends, where Δ m is the inverter modulation ratio variation in SOFC power stationAnd delta phi is the voltage phase variation of the SOFC power station node, delta e'dIs a d-axis component variation, Δ e ', of the post-stator transient potential'qAmount of change of q-axis component of post-stator transient potential, Δ iwdsIs the d-axis component variation, Δ i, of the stator currentwqsIs the q-axis component variation amount, X 'of the stator current'sIs the stator transient reactance, Δ E'qIs the variation of the q-axis transient electromotive force, A is a q-axis impedance matrix, and B is a d-axis impedance matrix.
Figure BDA0002463532630000101
Figure BDA0002463532630000102
Converting the linearized electric power system terminal current dq component into a state equation:
Figure BDA0002463532630000103
wherein X ═ Δ Δ E'qΔVdcΔm Δψ ΔiwdsΔiwqsΔe′dΔe′qΔm′ Δ′]TIs a state variable matrix, C and D are unambiguous matrices, and F is a coefficient matrix of state variables in the linearized power system terminal current dq component state equation. F is a matrix of 6 rows and 11 columns, the element being Fij(i is an integer of 1-6, and j is an integer of 1-11).
Figure BDA0002463532630000104
Figure BDA0002463532630000105
Electromagnetic power P according to current dq component of equivalent reactance of branch in linearized power systemeNo-load electromotive force EqVoltage amplitude V of synchronous generator nodetThe equation of (a) is linearized to obtain:
Figure BDA0002463532630000106
wherein, Δ PeIs the amount of change in electromagnetic power, Δ EqIs the amount of change in no-load electromotive force, Δ VtIs the voltage amplitude variation of the synchronous generator node.
Linearizing the synchronous generator model by a Lyapunov linearization method at a stable operation point and substituting a formula (16) into the linear generator model to obtain:
Figure BDA0002463532630000111
wherein, Delta is the variation of the rotor power angle, Delta omega is the variation of the rotor angular speed of the synchronous machine, Delta E'qIs the variation of the q-axis transient electromotive force, Δ EqeIs the amount of change in the forced no-load electromotive force.
Kp=E′qf11+(xq-x′d)Itsdf11+(xq-x′d)Itsqf41;Kpq=Itsq+E′qf12+(xq-x′d)Itsdf12+(xq-x′d)Itsqf42
Kpdc=E′qf13+(xq-x′d)Itsdf13+(xq-x′d)Itsqf43;Kpm=E′qf14+(xq-x′d)Itsdf14+(xq-x′d)Itsqf44
K=E′qf15+(xq-x′d)Itsdf15+(xq-x′d)Itsqf45;Kpds=E′qf16+(xq-x′d)Itsdf16+(xq-x′d)Itsqf46
Kpqs=E′qf17+(xq-x′d)Itsdf17+(xq-x′d)Itsqf47;Kped=E′qf18+(xq-x′d)Itsdf18+(xq-x′d)Itsqf48
Kpeq=E′qf19+(xq-x′d)Itsdf19+(xq-x′d)Itsqf49;Kpm′=E′qf1,10+(xq-x′d)Itsdf1,10+(xq-x′d)Itsqf4,10
Kp′=E′qf1,11+(xq-x′d)Itsdf1,11+(xq-x′d)Itsqf4,11;Ke=(xd-x′d)f41;Keq=1+(xd-x′d)f42
Kedc=(xd-x′d)f43;Kem=(xd-x′d)f44;K=(xd-x′d)f45;Keds=(xd-x′d)f46Keqs=(xd-x′d)f47
Keed=(xd-x′d)f48;Keeq=(xd-x′d)f49;Kem′=(xd-x′d)f4,10;Ke′=(xd-x′d)f4,11
Figure BDA0002463532630000112
Figure BDA0002463532630000113
Figure BDA0002463532630000114
Figure BDA0002463532630000115
At a stable operation point, linearizing the DFIG wind power plant model by adopting a Lyapunov linearization method to obtain:
Figure BDA0002463532630000121
wherein, Δ ωrVariation of angular speed of rotor, Δ ωtIs the variation of angular velocity, Delta theta, of the wind turbine shafttwIs the amount of change, Δ T, in the twist angle of the shaft of the low-speed fan relative to the shaft of the high-speed generatormIs the variation of the mechanical torque of the fan.
Linearizing the model of the SOFC power station by adopting a Lyapunov linearization method at a stable operation point to obtain:
Figure BDA0002463532630000122
wherein the content of the first and second substances,
Figure BDA0002463532630000123
a2=kIsdcosψ+kIsqsinψ;a5=km sinψ;a3=kmIsqcosψ-kmIsdsinψ;a4=km cosψ;
the state equation of the linearized power system obtained from equations (17) - (19) is:
Figure BDA0002463532630000124
wherein the content of the first and second substances,
Figure BDA0002463532630000125
Figure BDA0002463532630000126
obtaining a first derivative of a system state variable, X 'is the system state variable, A' is a coefficient matrix of a power system state variable, B 'is a coefficient matrix of a system control variable, U is the system control variable, delta is the variation of a rotor power angle, delta omega is the variation of a rotor angular speed of a synchronous machine, and delta E'qIs the amount of change, Δ E, in the q-axis transient electromotive forceqeIs the amount of change, Δ i, in the forced no-load electromotive forcewdsIs the d-axis component variation, Δ i, of the stator currentwqsIs the q-axis component variation of the stator current, Δ e'dIs the d-axis component variation of the post-stator transient potential, △ e'qVariation of q-axis component of post-stator transient potential, Δ ωrIs the rotor angular velocity variation, Δ ωtIs the angular velocity variation of the wind turbine shaft, △ thetatwIs the variation of the twist angle of the low-speed fan shaft relative to the high-speed generator shaft, △ VdcIs a DC capacitor C in SOFC power stationdcVoltage variation at two ends, △ m is inverter modulation ratio variation in SOFC power station, Δ ψ is voltage phase variation of SOFC power station node, Δ m 'is inverter pulse width modulation coefficient variation in SSSC, and Δ' is amplitude V of SSSC equivalent voltagescDelta T of phase angle variation with respect to q-axismIs the variation of mechanical torque of the fan, Δ VwdrD-axis component variation, Δ V, of rotor voltage in DFIGwqrThe amount of change in the q-axis component of the rotor voltage in the DFIG. a is12=ω0
Figure BDA0002463532630000131
Figure BDA0002463532630000132
a56=2ωs
Figure BDA0002463532630000133
a65=-2ωs
Figure BDA0002463532630000134
Figure BDA0002463532630000135
a78=ωsr; a79=-e′q
Figure BDA0002463532630000136
a87=-(ωsr);
Figure BDA0002463532630000137
Figure BDA0002463532630000138
a11,9=-1;a11,10=1;
Figure BDA0002463532630000139
Figure BDA00024635326300001310
Figure BDA00024635326300001311
Figure BDA00024635326300001312
The remaining elements in the matrices a ', B' are all 0. The matrix A' is a 12-row and 12-column matrix with the element ai’j’(i ', j ' is an integer of 1-12), B ' is a matrix of 12 rows and 7 columns, and the element is Bi”j”(i 'is an integer of 1-12, and j' is an integer of 1-7).
S4, obtaining parameter vectors influencing the stability of the power system from the state matrix in the step S2; as can be seen from the elements of the matrix a', the compensation amount of the SSSC is closely related to the system state matrix, and changing the compensation amount causes the system state matrix to change, thereby changing the system stability.
And S5, changing the state matrix of the power system by changing the compensation quantity of the static synchronous series compensator in the related parameters, and judging the stability of the power system by solving the characteristic value of the state matrix.
Adding an SOFC power station and an SSSC model into a power grid system, wherein the model is a four-machine two-area system, and the system comprises 2 similar area systems: the area 1 and the area 2 are connected by a weak connecting line; each zone contained 2 tightly coupled units, with a system reference capacity of 100MVA and a frequency of 50Hz, as shown in fig. 2. The DFIG output is set to be 30MW, the SOFC output is set to be 100MW, and the compensation amount of SSSC is 0(Case 1), 25% (Case 2) and 45% (Case 3). The system simulation running time is set to 20s, and the system simulation continues to run to 20s, assuming that the three-phase short circuit suddenly occurs when t is 1s, and the fault is cleared when t is 1.1 s.
Taking the power angle, reactive power response curve of a Synchronous Generator (SG) G1 as an example, as shown in fig. 3 and 4: as can be seen from fig. 3, the initial value of the power angle and the oscillation amplitude decrease with the increase of the degree of SSSC compensation, and the settling time gradually decreases. As can be seen from fig. 4, the oscillation amplitude of the reactive power also decreases with the increase of the degree of compensation of the SSSC, and the convergence speed also becomes faster and faster. Therefore, by changing the amount of compensation of the SSSC, the state matrix of the system changes, showing a change in the stability of the system.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, but rather as the subject matter of the invention is to be construed in all aspects and equivalents thereof.

Claims (7)

1. A dynamic interaction analysis method for a DFIG-SOFC-containing multi-energy system based on SSSC is characterized by comprising the following steps:
s1, the SOFC power station and the SSSC are connected to a bus node of the power system, a voltage equation of branch equivalent reactance in the power system is obtained through ohm' S law, and a voltage algebraic equation of the power system is constructed according to the voltage equation of the branch equivalent reactance, wherein the branch equivalent reactance comprises equivalent reactance from a synchronous generator node to the bus node, equivalent reactance from a DFIG wind power plant node to the bus node, equivalent reactance from the SOFC power station node to the bus node, and equivalent reactance from the SSSC node to the bus node;
s2, respectively constructing a synchronous generator model, a DFIG wind power plant model, an SOFC power plant model and an SSSC model;
s3, performing Park conversion on the voltage algebraic equation of the power system in the step S1 to obtain a current dq component of a branch equivalent reactance in the power system, respectively substituting the current dq component of the branch equivalent reactance into the synchronous generator model, the DFIG wind power plant model, the SOFC power station model and the SSSC model in the step S2, and performing linearization processing at a stable point to obtain a state matrix of the linearized power system;
s4, obtaining relevant parameters influencing the stability of the power system from the state matrix in the step S3;
and S5, judging the stability of the power system by changing the compensation amount of the static synchronous series compensator in the related parameters.
2. The SSSC-based DFIG-SOFC-containing multi-energy system dynamic interaction analysis method according to claim 1, wherein the voltage equation of the branch equivalent reactance in the power system is as follows:
Figure FDA0002463532620000011
wherein the content of the first and second substances,
Figure FDA0002463532620000012
is the voltage at the node of the synchronous generator,
Figure FDA0002463532620000013
is the voltage of the DFIG wind farm node,
Figure FDA0002463532620000014
is the voltage at the node of the SOFC power station,
Figure FDA0002463532620000015
is the voltage at the node of the bus bar,
Figure FDA0002463532620000016
is the voltage of the node at infinity and,
Figure FDA0002463532620000017
is the equivalent voltage of the SSSC node; x is the number oftsIs the equivalent reactance, x, from the node of the synchronous generator to the node of the bustwIs equivalent reactance, x, from DFIG wind farm node to bus nodesIs the equivalent reactance, x, from SOFC power station node to bus nodelIs the equivalent reactance from the infinite node to the bus node;
Figure FDA0002463532620000018
is the current injected at the node of the synchronous generator,
Figure FDA0002463532620000019
is the current injected into the DFIG windfarm node,
Figure FDA00024635326200000110
is the current injected at the SOFC power station node, j represents the imaginary unit;
adding the voltage equations of the branch equivalent reactances to cancel the voltage of the bus node
Figure FDA00024635326200000111
Obtaining a voltage algebraic equation of the power system:
Figure FDA00024635326200000112
3. the SSSC-based DFIG-SOFC-containing multi-energy system dynamic interaction analysis method according to claim 1, wherein the synchronous generator model is:
Figure FDA0002463532620000021
wherein p (-) represents a differential function, is the rotor power angle, ω is the rotor angular velocity of the synchronous machine, ω is0Is the synchronous angular velocity, TJIs the inertia time constant, T'd0Is the time constant of the field winding, TaIs the excitation system time constant, PmIs the mechanical power of the prime mover, PeIs electromagnetic power, E'qIs q-axis transient electromotive force, EqeIs a forced no-load electromotive force, EqIs no-load electromotive force, KaIs the amplification factor, V, of the excitation systemtIs the voltage amplitude, V, of the synchronous generator nodetrefIs the excitation regulator set voltage;
the DFIG wind power plant model is as follows:
Figure FDA0002463532620000022
wherein R issIs stator resistance, XsIs stator reactance, X'sIs the stator transient reactance, ωsIs the synchronous angular velocity, omega, of the synchronous generatorrIs the angular speed of the rotor, ωtIs the angular velocity of the wind turbine shaft, LmStator-rotor mutual inductance, LrrIs rotor self-inductance, VwdsIs the d-axis component of the stator voltage, VwqsIs the stator voltage q-axis component, VwdrIs the d-axis component of the rotor voltage, VwqrIs the q-axis component, i, of the rotor voltagewdsIs the d-axis component of the stator current, iwqsIs the q-axis component, e 'of the stator current'dIs the d-axis component, e ', of the post-stator transient potential'qIs the q-axis component, T ', of the post-stator transient potential'0Is the rotor time constant, TmIs the mechanical torque of the fan, TshIs the torque between two masses, TeIs the electromagnetic torque of the generator, thetatwIs the twist angle of the shaft of the low-speed fan relative to the shaft of the high-speed generator, HtIs the inertia time constant of the fan, HgIs the inertial time constant of the generator;
the SOFC power station model is as follows:
Figure FDA0002463532620000031
wherein, VdcIs a DC capacitor C in SOFC power stationdcVoltage across, PfcIs the fuel cell power, m is the modulation ratio of the inverter, k is the transformation ratio of the inverter, IsdIs the d-axis component, I, of the current injected at the SOFC power station nodesqIs the q-axis component of the current injected at the SOFC power station node, psi is the phase of the voltage at the SOFC power station node, CdcIs the dc capacitance capacity;
the SSSC model is as follows:
Figure FDA0002463532620000032
wherein the content of the first and second substances,
Figure FDA0002463532620000033
is the first derivative of the dc capacitor voltage over time t in the SSSC structure,
Figure FDA0002463532620000034
is the equivalent voltage, V, of the SSSC nodescdIs the d-axis component, V, of the equivalent voltage of the SSSC nodescqIs the q-axis component, V ', of the equivalent voltage of the SSSC node'dcIs the DC capacitor voltage in the SSSC structure, is the amplitude V of the SSSC equivalent voltagescRelative to the phase angle of the q axis, k 'is the transformer transformation ratio, m' is the inverter pulse width modulation coefficient, and C is the capacitance; i isdIs flowing into infinite node current
Figure FDA0002463532620000035
D-axis component of (I)qIs flowing into infinite node current
Figure FDA0002463532620000036
Q-axis component of (a).
4. The SSSC-based DFIG-SOFC-containing multi-energy system dynamic interaction analysis method according to claim 3, wherein the electromagnetic power P iseNo-load electromotive force EqVoltage amplitude V of synchronous generator nodetThe calculation method comprises the following steps:
Figure FDA0002463532620000037
wherein x isdIs d-axis reactance of the generator, xqIs the q-axis reactance of the generator, x'dIs the d-axis transient reactance of the generator, ItsdD-axis current of generator stator, ItsqIs the generator stator q-axis current, VtdIs the d-axis component of the port voltage, VtqIs the q-axis component of the port voltage.
5. The SSSC-based DFIG-SOFC-containing multi-energy system dynamic interaction analysis method according to claim 3, wherein the torque T between the two mass blocksshElectromagnetic torque T of generatoreThe calculation method comprises the following steps:
Figure FDA0002463532620000038
wherein, KshIs the stiffness coefficient of the shaft, DshIs the damping coefficient of the shaft.
6. The SSSC-based DFIG-SOFC-containing multi-energy system dynamic interaction analysis method according to claim 1, wherein the current dq component of the branch equivalent reactance in the power system is:
Figure FDA0002463532620000041
wherein x istsIs the equivalent reactance, x, from the node of the synchronous generator to the node of the bustwIs DFIG wind powerEquivalent reactance, x, from field node to bus nodesIs the equivalent reactance, x, from SOFC power station node to bus nodelIs the equivalent reactance from the infinite node to the bus node; x is the number ofqIs the q-axis reactance of the generator, x'dIs the d-axis transient reactance of the generator, ItsdD-axis current of generator stator, ItsqIs the generator stator q-axis current, IsdIs the d-axis component, I, of the current injected at the SOFC power station nodesqIs the q-axis component, I, of the current injected at the SOFC power station nodewdIs the d-axis component, I, of the current injected into the DFIG windfarm nodewqIs a q-axis component of current injected into the DFIG windfarm node; vcIs the voltage amplitude, V, of the DFIG wind farm nodebIs the voltage amplitude, V, of the infinite nodescIs the magnitude of the SSSC equivalent voltage; vdwIs the d-axis component, V, of the voltage at the DFIG wind farm nodeqwIs the q-axis component of the voltage at the DFIG wind farm node; e'qIs the q-axis transient electromotive force of the synchronous generator; is the rotor power angle; psi is the phase of the SOFC plant node voltage; ' is the amplitude V of the SSSC equivalent voltagescPhase angle with respect to the q-axis.
7. The dynamic interaction analysis method for the multi-energy system containing the DFIG-SOFC based on the SSSC according to claim 6, characterized in that a Lyapunov linearization method is adopted at a stable operation point, and the current dq components of the branch equivalent reactance of the power system are respectively substituted into a synchronous generator model, a DFIG wind power plant model, an SOFC power plant model and an SSSC model to obtain the state equation of the linearized power system as follows:
Figure FDA0002463532620000042
wherein the content of the first and second substances,
Figure FDA0002463532620000043
Figure FDA0002463532620000044
is to the system stateObtaining a first derivative of a variable matrix, wherein X 'is a system state variable matrix, A' is a coefficient matrix of a system state variable, B 'is a coefficient matrix of a system control variable, U is the system control variable, delta is the variation of a rotor power angle, delta omega is the variation of a rotor angular speed of a synchronous machine, and delta E'qIs the amount of change, Δ E, in the q-axis transient electromotive forceqeIs the amount of change, Δ i, in the forced no-load electromotive forcewdsIs the d-axis component variation, Δ i, of the stator currentwqsIs the q-axis component variation of the stator current, Δ e'dIs the d-axis component variation, Δ e ', of the post-stator transient potential'qVariation of q-axis component of post-stator transient potential, Δ ωrIs the rotor angular velocity variation, Δ ωtIs the variation of angular velocity, Delta theta, of the wind turbine shafttwIs the amount of change, Δ V, in the twist angle of the shaft of the low-speed fan relative to the shaft of the high-speed generatordcIs a DC capacitor C in SOFC power stationdcVoltage variation at two ends, wherein delta m is inverter modulation ratio variation in the SOFC power station, delta psi is voltage phase variation of the SOFC power station node, delta m 'is inverter pulse width modulation coefficient variation in the SSSC, and delta' is amplitude V of SSSC equivalent voltagescDelta T of phase angle variation with respect to q-axismIs the variation of mechanical torque of the fan, Δ VwdrD-axis component variation, Δ V, of rotor voltage in DFIGwqrIs the amount of change in the q-axis component of the rotor voltage in the DFIG.
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