CN110212575A - The small signal stability modal analysis method of double-fed blower one machine infinity bus system - Google Patents

The small signal stability modal analysis method of double-fed blower one machine infinity bus system Download PDF

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CN110212575A
CN110212575A CN201910500553.6A CN201910500553A CN110212575A CN 110212575 A CN110212575 A CN 110212575A CN 201910500553 A CN201910500553 A CN 201910500553A CN 110212575 A CN110212575 A CN 110212575A
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loop control
generator
rotor
state
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古庭赟
伍华伟
徐长宝
林呈辉
吕黔苏
高吉普
李军
龙秋风
范强
顾威
徐梅梅
牛唯
张俊玮
肖小兵
刘明顺
陈相吉
汪明媚
孟令雯
陈敦辉
刘斌
苏立
李博文
祝健杨
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Guizhou Power Grid 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
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    • 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
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    • Y02EREDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
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Abstract

The invention discloses a kind of analysis on Small Disturbance Stability methods of double-fed blower one machine infinity bus system, it includes the following steps: (1) to model to the dynamic mathematical models of one machine infinity bus system;Step 2 carries out linearization process to the mathematical model of system at equalization point;Obtain corresponding state matrix;Step 3 obtains system features value and pattern class, according to participation factor predicted state variable and mode relationship;Step 4, according to system parameter or operating status and external network parameter, calculate the size and Mode variation of different characteristic value;It is directed to the stability study of blower grid-connected system, the model of the existing model for not setting up some elements in system in detail such as transmission system and the model of control system in the prior art;The influence under detailed model for system parameters for system mode does not carry out the technical problem such as studying.

Description

The small signal stability modal analysis method of double-fed blower one machine infinity bus system
Technical field
The invention belongs to double-fed blower one machine infinity bus system technologies;More particularly to a kind of double-fed blower Infinite bus power system system The small signal stability modal analysis method of system.
Background technique
Since recent decades global energy consumes energy deficiency caused by steady-state growth and problem of environmental pollution increasingly Seriously, generation of electricity by new energy especially wind-power electricity generation is more and more paid attention to, and also plays in the power system increasingly heavier The role wanted.Due to the randomness of wind energy and the uncertainty of access power grid, for the stability study of blower access power grid It is increasingly becoming focus.Blower grid-connected system will be stablized, and first have to guarantee that it is small interference stability, therefore there are many scholars to wind The stability of machine grid-connected system is studied.Some study the Infinite bus power system model for establishing blower, and establish its small interference Analysis model probes into its small signal stability;Some analyze to the mode of blower grid-connected system and have probed into some systems Influence of the parameter of uniting to system mode.The prior art there are following innings of technologies to lack the stability study of blower grid-connected system It falls into: having the model for the model such as transmission system for setting up some elements in system in detail and the model of control system;Do not exist The system parameters of influence under detailed model for to(for) system mode is further probed into.
Summary of the invention
The technical problem to be solved by the present invention is providing a kind of small signal stability of double-fed blower one machine infinity bus system Modal analysis method, it is existing not establish in detail to solve to be directed to the stability study of blower grid-connected system in the prior art The model of the model such as transmission system of some elements and the model of control system in the system of rising;Not under detailed model for Influence of the system parameters for system mode carries out the technical problem such as studying.
The technical scheme is that
A kind of analysis on Small Disturbance Stability method of double-fed blower one machine infinity bus system, it includes:
Step 1 models the dynamic mathematical models of one machine infinity bus system;
Step 2 carries out linearization process to the mathematical model of system at equalization point;Obtain corresponding state matrix;
Step 3 obtains system features value and pattern class, according to participation factor predicted state variable and mode relationship;
Step 4, according to system parameter or operating status and external network parameter, calculate different characteristic value size and Mode variation.
The dynamic mathematical models include wind turbine model, transmission system double quality model, generator model, inverter moulds Type and external network model;
Transitive relation of the wind turbine model between wind energy and mechanical energy:
In formula, PtIt is the mechanical output of wind turbine output, unit kW;vwindIt is wind speed, unit is m/s;CpIt is dimensionless Power coefficient;AwtIt is the area that blade scans, unit is m2;ρ is atmospheric density, unit kg/m3;λ is blade tip speed Than;θ is incidence angle of the wind in turbo blade.
The transmission system double quality blocks model, one is used for steam turbine, and one is used for generator, each mass block and biography The dynamical equation of moving axis are as follows:
In formula: ωtWith ωrIt is the revolving speed of wind turbine and generator, θ respectivelytwIt is shafting torsion angle, HtAnd HgIt is wind respectively The inertia time constant of turbine and generator, ωe1BFor benchmark electrical rotate-speed, PtIt is the mechanical output of the capture of wind turbine, TshWith TeIt is shafting torque and generator electrical torque respectively,
K and c is axis rigidity and damped coefficient, E ' respectively in formulaqDWith E 'dDIt is the transient state rotor electricity of q axis and d axis respectively Pressure, IqsWith IdsIt is the q shaft current and d shaft current of generator unit stator side respectively;
Generator model is two shaft models, using 90 ° of dq coordinate system of the advanced d axis of q axis, and is defined in this coordinate system such as Lower variable:
In formula: T '0It is transient state open circuit time constant, X 'sIt is transient state reactance, XmIt is the mutual impedance between stator and rotor, Xs =Xls+XmIt is stator reactance, Xr=Xlr+XmIt is rotor reactance, ωsFor synchronous rotational speed;ψqrAnd ψdrIt is the temporary of q axis and d axis respectively State magnetic linkage.
Ignore the change procedure of stator magnetic linkage, simplified model are as follows:
In formula: RsFor stator resistance, IdrFor rotor d shaft current, IqrFor rotor q shaft current, VdrFor rotor d shaft voltage, Vqr For rotor q shaft voltage, VDFor stator terminal voltage, PgenAnd QgenIt is targeted to the active power and reactive power of grid side respectively;
The foundation of inverter model: d is worked as in decoupling of the inverter rotor-side control design case based on active output and idle output When axis is stator magnetic linkage oriented, the voltage V of stator sideqs=VD, Vds=0, control system is controlled using proportional, integral (P-I), mould Type are as follows:
In formula: x1It is active outer loop control integrating state amount, KI1It is active outer loop control integral coefficient, KP1It is active outer ring Control proportionality coefficient, x2It is current inner loop control integrating state amount, KI2It is current inner loop control integral coefficient, KP2It is current inner loop Control proportionality coefficient, x3It is idle outer loop control integrating state amount, KI3It is idle outer loop control integral coefficient, KP3It is idle outer ring Control proportionality coefficient, x4It is current inner loop control integrating state amount, KI4It is current inner loop control integral coefficient, KP4It is current inner loop Control proportionality coefficient;PrefFor active power reference value;QrefFor active power reference value.
External network model:
External system is infinitely great power supply, and the network equation of external network model indicates are as follows:
In formula R and X be respectively be connected with infinite busbar transmission line resistance and reactance, V be the voltage of infinite busbar, VDWith θDThe respectively voltage and phase angle of generator generator terminal;PrIt is the active power that rotor flows through, IGIt is that generator terminal injects the grid-connected change of current The electric current of device, IpAnd IqIt is the electric current of generator terminal injection network under synchronous coordinate system, is expressed as follows:
The mathematical model of pair system established described in step 2 carries out linearization process at equalization point;Obtain corresponding shape The method of state matrix are as follows:
Mathematical model is collectively expressed as a series of differential-algebraic equationsG (x, y)=0, x, y difference For the state variable and algebraic variable of system;F and g is respectively differential equation group and Algebraic Equation set;Ignore the two of Taylor series Rank and the above dimensionless of second order, the state space equation of system are represented by
It enablesThen state space is
Δ y is eliminated to obtain
MatrixReferred to as coefficient matrix or state matrix.
The invention has the advantages that:
The present invention considers the model of wind turbine, transmission system, generator, inverter and its external network respectively, uses The actuation system models of double quality blocks, control system is using classical two close cycles PI control;First according to the number of whole system Its linear differential equation system of model foundation is learned, and carries out linearisation in equalization point and obtains its state matrix, and then carry out system Analysis on Small Disturbance Stability;And then the characteristic value of system and its relevant mode are analyzed, is probed into out and phase Answer the maximally related state variable of mode.Different parameters are probed into for system finally by change different system parameter and operating parameter The influence of mode, and find the parameter area for making system be in more stable state.
It is of the invention to be advantageous in that: 1. completely to consider the grid-connected dynamic mathematical models of double-fed blower and 2. completely consider wind Machine operating status and system parameter influence system mode.Improve the analysis on Small Disturbance Stability of system accuracy and comprehensively Property;Solve the stability study for being directed to blower grid-connected system in the prior art, it is existing not set up in detail one in system The model of the model such as transmission system of a little elements and the model of control system;Not for system parameters under detailed model Influence for system mode carries out the technical problem such as studying.
Detailed description of the invention
Fig. 1 is analysis on Small Disturbance Stability linearized system eigenvalue λ and corresponding mode relation schematic diagram;
Fig. 2 is the eigenvalue schematic diagram for changing transmission system parameter Hg rotator electromechanical mode;
Fig. 3 is the eigenvalue schematic diagram of current inner loop control mode when changing generator parameter Xr.
Fig. 4 is the eigenvalue schematic diagram of rotor electrical mode when changing system operating point.
Specific embodiment
It completely include wind turbine, legacy system, generator, inverter and outer based on double-fed blower one machine infinity bus system Portion's network model;Wherein wind turbine is made of blade and wheel hub, by maximum power tracing control mode obtain mechanical energy by its Send generator to;Transmission system is connected using double quality blocks model with generator;Generator unit stator side is connected with external network; AC-DC-a-c transducer includes two pulse width module inverters.Rotor-side inverter, will as controlled voltage source The alternating voltage of slip-frequency injects DFIG rotor.Net side inverter keeps the voltage of direct current connection permanent as controlled current source Alternating current fixed and to network injection mains frequency.
A kind of small signal stability modal analysis method based on double-fed blower one machine infinity bus system, the analysis method The following steps are included:
(A) the dynamic mathematical models modeling of one machine infinity bus system includes the double quality models of transmission system, generator model, changes Flow device model and external network model.
1. wherein transitive relation of the model of wind turbine between wind energy and mechanical energy are as follows:
In formula, PtIt is the mechanical output of wind turbine output, unit kW.CpIt is nondimensional power coefficient.λ is leaf Tip-speed ratio;θ is incidence angle of the wind in turbo blade.ρ is atmospheric density, unit kg/m3。AwtIt is the area that blade scans, it is single Position is m2。vwindIt is wind speed, unit is m/s.
2. the mathematical model of transmission system uses double quality blocks model, one is used for steam turbine, and one is used for generator, often The dynamical equation of a mass block and transmission shaft are as follows:
Wherein ωtWith ωrIt is the revolving speed of wind turbine and generator, θ respectivelytwIt is shafting torsion angle, HtAnd HgIt is wind wheel respectively The inertia time constant of machine and generator, ωe1BFor benchmark electrical rotate-speed, PtIt is the mechanical output (vacation here of the capture of wind turbine It is set to constant), TshAnd TeIt is shafting torque and generator electrical torque respectively, is expressed as follows:
Wherein k and c is axis rigidity and damped coefficient, E ' respectivelyqDWith E 'dDIt is the transient state rotor electricity of q axis and d axis respectively Pressure, IqsWith IdsIt is the q shaft current and d shaft current of generator unit stator side respectively.
3. generator uses two shaft models, using 90 ° of dq coordinate system of the advanced d axis of q axis, and define in this coordinate system such as Lower variable:
Wherein T0' it is transient state open circuit time constant, X 'sIt is transient state reactance, XmIt is the mutual impedance between stator and rotor, Xs =Xls+XmIt is stator reactance, Xr=Xlr+XmIt is rotor reactance, ωsFor synchronous rotational speed.Wherein XlsFor stator leakage impedance, XmIt is fixed Mutual impedance between son and rotor.ψqrAnd ψdrIt is the transient state magnetic linkage of q axis and d axis respectively.
The change procedure for ignoring stator magnetic linkage uses, the model of this simplified double-fed induction blower are as follows:
Wherein RsFor stator resistance, IdrFor rotor d shaft current, IqrFor rotor q shaft current, VdrFor rotor d shaft voltage, Vqr For rotor q shaft voltage, VDFor stator terminal voltage, PgenAnd QgenIt is targeted to the active power and reactive power of grid side respectively.
4. decoupling of the inverter rotor-side control design case based on active output and idle output.When d axis is fixed for stator magnetic linkage Xiang Shi, the voltage V of stator sideqs=VD, Vds=0, and control system is controlled using the most common proportional, integral (P-I), mould Type are as follows:
Wherein x1It is active outer loop control integrating state amount, KI1It is active outer loop control integral coefficient, KP1It is active outer ring Control proportionality coefficient, x2It is current inner loop control integrating state amount, KI2It is current inner loop control integral coefficient, KP2It is current inner loop Control proportionality coefficient, x3It is idle outer loop control integrating state amount, KI3It is idle outer loop control integral coefficient, KP3It is idle outer ring Control proportionality coefficient, x4It is current inner loop control integrating state amount, KI4It is current inner loop control integral coefficient, KP4It is current inner loop Control proportionality coefficient;PrefFor active power reference value;QrefFor active power reference value.
5. external system is infinitely great power supply, the network equation of the system be may be expressed as:
Wherein R and X be respectively be connected with infinite busbar transmission line resistance and reactance, V be the voltage of infinite busbar, VDWith θDThe respectively voltage and phase angle of generator generator terminal.PrIt is the active power that rotor flows through, IGIt is that generator terminal injects the grid-connected change of current The electric current of device, IpAnd IqIt is the electric current of generator terminal injection network under synchronous coordinate system, can be expressed as follows:
(B) mathematical model is linearized at equalization point.The mathematical model of the system is collectively expressed as a series of differential- Algebraic equationG (x, y)=0.Wherein, x, y are respectively the state variable and algebraic variable of system;F and g are respectively Differential equation group and Algebraic Equation set.Ignore the second order and the above dimensionless of second order of Taylor series, the state space side of system Journey is represented by
It enablesThen state space is
Δ y is eliminated to obtain
Wherein, matrixCommonly known as coefficient matrix or state matrix.Pass through research state matrixCharacteristic valueCan analysis system dynamic process.
X=[E 'qD E′dD wt θ wr x1 x2 x3 x4]
Y=[Ids Iqs Idr Iqr Vdr Vqr VDθD Pgen Qgen]。
(C) system features value and pattern class are obtained, according to participation factor predicted state variable and mode relationship.
(D) system parameter/operating status and external network parameter, the size and mode for calculating different characteristic value become Change.
Specific embodiment:
The mathematical model of system is collectively expressed as a series of differential-algebraic equationsG (x, y)=0.Its In, x, y are respectively the state variable and algebraic variable of system;F and g is respectively differential equation group and Algebraic Equation set.Ignore Thailand The second order and the above dimensionless of second order, the state space equation of system for strangling series are represented by
It enablesThen state space is
Δ y is eliminated to obtain
Wherein, matrixCommonly known as coefficient matrix or state matrix.Pass through research state matrixCharacteristic valueCan analysis system dynamic process.Under normal circumstances, if generator voltage be 1p.u., active power 1p.u., And revolving speed is specified synchronous rotational speed.Assuming that double-fed blower DFIG is directly connected with infinite busbar, reactive power output is 0, Terminal voltage remains unchanged.Linearization process near a little, gained state are balanced to double-fed blower one machine infinity bus system Characteristic value corresponding to matrix and corresponding mode are as shown in Figure 1.
Change transmission system parameter and generator system parameter respectively, Fig. 2, Fig. 3 are obtained system parameter to system The significant bias effect of different modalities characteristic value.
Changing system operating point keeps other parameters constant, and Fig. 4 is that obtained system operating point changes to different modalities The bias effect of corresponding eigenvalue.
Change exterior network parameter, obtains influence of the outside line reactance to system mode characteristic value.

Claims (3)

1. a kind of analysis on Small Disturbance Stability method of double-fed blower one machine infinity bus system, it includes:
Step 1 models the dynamic mathematical models of one machine infinity bus system;
Step 2 carries out linearization process to the mathematical model of system at equalization point;Obtain corresponding state matrix;
Step 3 obtains system features value and pattern class, according to participation factor predicted state variable and mode relationship;
Step 4, according to system parameter or operating status and external network parameter, calculate the size and mode of different characteristic value Variation.
2. a kind of analysis on Small Disturbance Stability method of double-fed blower one machine infinity bus system according to claim 1, Be characterized in that: the dynamic mathematical models include wind turbine model, transmission system double quality model, generator model, inverters Model and external network model;
Transitive relation of the wind turbine model between wind energy and mechanical energy:
In formula, PtIt is the mechanical output of wind turbine output, unit kW;vwindIt is wind speed, unit is m/s;CpIt is nondimensional wind It can usage factor;AwtIt is the area that blade scans, unit is m2;ρ is atmospheric density, unit kg/m3;λ is tip speed ratio;θ For wind turbo blade incidence angle.
The transmission system double quality blocks model, one is used for steam turbine, and one is used for generator, each mass block and transmission shaft Dynamical equation are as follows:
In formula: ωtWith ωrIt is the revolving speed of wind turbine and generator, θ respectivelytwIt is shafting torsion angle, HtAnd HgIt is wind turbine respectively With the inertia time constant of generator, ωe1BFor benchmark electrical rotate-speed, PtIt is the mechanical output of the capture of wind turbine, TshAnd TePoint It is not shafting torque and generator electrical torque,
K and c is axis rigidity and damped coefficient, E ' respectively in formulaqDWith E 'dDIt is the transient state rotor voltage of q axis and d axis, I respectivelyqs With IdsIt is the q shaft current and d shaft current of generator unit stator side respectively;
Generator model is two shaft models, using 90 ° of dq coordinate system of the advanced d axis of q axis, and is defined as follows change in this coordinate system Amount:
In formula: T0' it is transient state open circuit time constant, X 'sIt is transient state reactance, XmIt is the mutual impedance between stator and rotor, Xs=Xls +XmIt is stator reactance, Xr=Xlr+XmIt is rotor reactance, ωsFor synchronous rotational speed;ψqrAnd ψdrIt is the transient state magnetic of q axis and d axis respectively Chain.
Ignore the change procedure of stator magnetic linkage, simplified model are as follows:
In formula: RsFor stator resistance, IdrFor rotor d shaft current, IqrFor rotor q shaft current, VdrFor rotor d shaft voltage, VqrTo turn Sub- q shaft voltage, VDFor stator terminal voltage, PgenAnd QgenIt is targeted to the active power and reactive power of grid side respectively;
The foundation of inverter model: decoupling of the inverter rotor-side control design case based on active output and idle output, when d axis is When stator magnetic linkage oriented, the voltage V of stator sideqs=VD, Vds=0, control system is controlled using proportional, integral (P-I), model Are as follows:
In formula: x1It is active outer loop control integrating state amount, KI1It is active outer loop control integral coefficient, KP1It is active outer loop control Proportionality coefficient, x2It is current inner loop control integrating state amount, KI2It is current inner loop control integral coefficient, KP2It is current inner loop control Proportionality coefficient, x3It is idle outer loop control integrating state amount, KI3It is idle outer loop control integral coefficient, KP3It is idle outer loop control Proportionality coefficient, x4It is current inner loop control integrating state amount, KI4It is current inner loop control integral coefficient, KP4It is current inner loop control Proportionality coefficient;PrefFor active power reference value;QrefFor active power reference value.
External network model:
External system is infinitely great power supply, and the network equation of external network model indicates are as follows:
In formula R and X be respectively be connected with infinite busbar transmission line resistance and reactance, V be the voltage of infinite busbar, VDWith θDThe respectively voltage and phase angle of generator generator terminal.PrIt is the active power that rotor flows through, IGIt is that generator terminal injects grid-connected inverter Electric current, IpAnd IqIt is the electric current of generator terminal injection network under synchronous coordinate system, is expressed as follows:
3. a kind of analysis on Small Disturbance Stability method of double-fed blower one machine infinity bus system according to claim 1, Be characterized in that: the mathematical model of pair system established described in step 2 carries out linearization process at equalization point;Obtain corresponding shape The method of state matrix are as follows:
Mathematical model is collectively expressed as a series of differential-algebraic equationsG (x, y)=0, x, y are respectively to be The state variable and algebraic variable of system;F and g is respectively differential equation group and Algebraic Equation set;Ignore Taylor series second order and The above dimensionless of second order, the state space equation of system are represented by
It enablesThen state space is
Δ y is eliminated to obtain
MatrixReferred to as coefficient matrix or state matrix.
CN201910500553.6A 2019-06-11 2019-06-11 The small signal stability modal analysis method of double-fed blower one machine infinity bus system Pending CN110212575A (en)

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CN110970925A (en) * 2019-12-11 2020-04-07 贵州电网有限责任公司 Double-fed fan based damping and modeling method for improving system through fast active power modulation
CN111884215A (en) * 2020-07-30 2020-11-03 海南电网有限责任公司海口供电局 Uncertainty-containing single-machine infinite power system optimization control method
CN112526262A (en) * 2020-11-26 2021-03-19 国网宁夏电力有限公司电力科学研究院 Method for judging stability of direct-current transmission end power grid accessed by high-proportion new energy
CN113901670A (en) * 2021-10-25 2022-01-07 国网四川省电力公司电力科学研究院 Rapid assessment method for dynamic stability characteristics of full-power variable-speed constant-frequency pumping and storage unit
CN114268116A (en) * 2021-10-18 2022-04-01 国网浙江省电力有限公司丽水供电公司 State space modeling method of master-slave alternating-current micro-grid considering communication time delay

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Cited By (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN110970925A (en) * 2019-12-11 2020-04-07 贵州电网有限责任公司 Double-fed fan based damping and modeling method for improving system through fast active power modulation
CN111884215A (en) * 2020-07-30 2020-11-03 海南电网有限责任公司海口供电局 Uncertainty-containing single-machine infinite power system optimization control method
CN111884215B (en) * 2020-07-30 2023-04-28 海南电网有限责任公司海口供电局 Uncertainty-containing single machine infinite power system optimization control method
CN112526262A (en) * 2020-11-26 2021-03-19 国网宁夏电力有限公司电力科学研究院 Method for judging stability of direct-current transmission end power grid accessed by high-proportion new energy
CN114268116A (en) * 2021-10-18 2022-04-01 国网浙江省电力有限公司丽水供电公司 State space modeling method of master-slave alternating-current micro-grid considering communication time delay
CN114268116B (en) * 2021-10-18 2023-09-15 国网浙江省电力有限公司丽水供电公司 State space modeling method of master-slave alternating-current micro-grid considering communication time delay
CN113901670A (en) * 2021-10-25 2022-01-07 国网四川省电力公司电力科学研究院 Rapid assessment method for dynamic stability characteristics of full-power variable-speed constant-frequency pumping and storage unit
CN113901670B (en) * 2021-10-25 2023-04-21 国网四川省电力公司电力科学研究院 Rapid evaluation method for dynamic stability characteristics of full-power variable-speed constant-frequency pumping and storage unit

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Application publication date: 20190906