CN109327043A - A kind of voltage source converter grid-connected system inner loop control parsing transfer function modeling method and system - Google Patents
A kind of voltage source converter grid-connected system inner loop control parsing transfer function modeling method and system Download PDFInfo
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Abstract
The invention discloses a kind of voltage source converter grid-connected system inner loop controls to parse transfer function modeling method, and method includes: to establish to consider grid strength and the dynamic voltage source converter grid-connected system mathematical model of phaselocked loop based on the first assumed condition；Voltage source converter grid-connected system mathematical model is subjected to linearization process；Based on the second assumed condition, the simplification transmission function of the inner loop control of electric current is obtained；According to transmission function is simplified, the dynamic output phase expression formula of phaselocked loop is embodied, the inner loop control for establishing the voltage source converter grid-connected current for considering phaselocked loop dynamic effects parses transmission function；Parameter designing is and guided based on inner loop control parsing transfer function analysis voltage source converter grid-connected system inner loop control instability Mechanism.
Description
Technical Field
The invention relates to the technical field of electric power, in particular to a voltage source type converter grid-connected system inner ring control analysis transfer function modeling method and system.
Background
When a fan converter, a photovoltaic inverter, a flexible direct current (VSC) and other Voltage source converters are connected to a weak alternating current power grid, instability risks exist, and a set of modeling and stability analysis methods of a VSC grid-connected system of the VSC are needed as tools for analyzing and solving problems. At present, a voltage source converter VSC grid-connected system modeling method mainly comprises a state space modeling method, an input impedance method and a complex torque method, and the problems existing when the stability mechanism of the voltage source converter VSC grid-connected system is analyzed by applying the models are as follows: the state space modeling method is too detailed, and only characteristic root analysis and participation factor analysis can be utilized to calculate main participation variables of a instability mode, so that the instability mechanism cannot be accurately explained; the input impedance method model is over simplified, whether the system is unstable or not can be judged only by calculating equivalent input impedance, but the instability mechanism cannot be intuitively disclosed; the complex torque method model is too simplified, a voltage source converter VSC system can only be divided into two subsystems, equivalent synchronization and damping torque are calculated to reveal a instability mechanism, and the instability mechanism cannot be intuitively explained. The prior art cannot explain the instability mechanism of a voltage source converter VSC grid-connected system.
Therefore, a technique is needed to implement the method for modeling the inner-loop control analysis transfer function of the grid-connected system of the voltage source converter.
Disclosure of Invention
The technical scheme of the invention provides a voltage source type converter grid-connected system inner ring control analysis transfer function modeling method and system, which are used for solving the problem of how to control the voltage source type converter grid-connected system to be unstable and the problem of how to guide the design of voltage source type converter grid-connected system inner ring control parameters.
In order to solve the above problem, the present invention provides a method for modeling an inner loop control analysis transfer function of a voltage source converter grid-connected system, where the method includes:
establishing a voltage source type converter grid-connected system mathematical model considering the power grid strength and the phase-locked loop dynamics based on a first assumed condition;
carrying out linearization processing on the voltage source type converter grid-connected system mathematical model;
acquiring a simplified transfer function of inner loop control of the current based on a second assumed condition; according to the simplified transfer function, the dynamic output phase expression of the phase-locked loop is specified, and an inner loop control analysis transfer function of the grid-connected current of the voltage source type converter considering the dynamic influence of the phase-locked loop is established;
and analyzing an inner ring control instability mechanism of the voltage source type converter grid-connected system and guiding parameter design based on the inner ring control analytic transfer function.
Preferably, the first assumption condition is:
only the strength of the electrical connection is considered, the inner loop current feedback value can track the inner loop current reference value in real time, the filter capacitor of the common connection point is ignored, the delay in the modulation process and the sampling delay are ignored, and the loss is ignored.
Preferably, the grid-connected system mathematical model includes:
a main circuit mathematical model, a phase-locked loop dynamic mathematical model and an inner loop control mathematical model.
Preferably, the main circuit mathematical model is:
the mathematical model of the main circuit part is as follows under dq coordinate system
Wherein L iseq＝Lt+Larm/2，Req＝Rt+Rarm/2，Lac＝Leq+Lg，Rac＝Req+RgS denotes a differential operator, ReqIs the equivalent resistance between the PCC bus and the converter valve side, LeqIs the equivalent inductance between the PCC bus and the converter valve side, LtIs the equivalent inductance, L, of an AC mains transformerarmIs an MMC bridge arm inductor, RtIs an equivalent resistance of an AC network transformer, LacIs equivalent between an inverter and an infinite system (ideal power supply)Inductance, RacIs the equivalent resistance from the inverter to the infinite system (ideal power supply), icdFor the d-axis component of the converter output current icqFor the converter output current q-axis component, ucdIs d-axis component, u, of the converter equivalent output voltagesdIs the d-axis component, ω, of the PCC bus voltage1At a nominal angular frequency, ucqFor the q-axis component of the converter equivalent output voltage, usqIs the q-axis component of the PCC bus voltage, LgIs an equivalent inductance of an AC network, RgIs the equivalent resistance of the AC network, ugdD-axis component, u, of infinite system (ideal power supply) voltagegqThe d-axis component of the infinite system (ideal power supply) voltage.
Preferably, the dynamic mathematical model of the phase-locked loop is:
wherein,
wherein, thetaPLLFor dynamically outputting phase, theta, to a phase-locked looppllFor phase-locked loop output phase thetaPLLAnd omega1Difference of t ω1t is an initial phase of 0 at a constant angular velocity ω1Phase of rotating dq coordinate system, kp_pllFor phase-locked loop dynamic proportional integral controller proportionality coefficient, Ti_pllIntegrating time constant, u, for a phase locked loop dynamic proportional integral controllersqFor the q-axis component of the PCC bus voltage, ω 1 is the rated angular velocity of the dq coordinate system, s is the Laplace operator, GpllIs a proportional-integral controller for a phase-locked loop,the q-axis component of the equivalent output voltage of the converter in the dq coordinate system of the control system.
Preferably, the dynamic mathematical model of the phase-locked loop is designed to have a second-order response characteristic and a parameter calculation formula thereof is as follows:
wherein, ω ispllFor dynamically designing the bandwidth of the phase-locked loop, the damping ratio ξ is 0.707 usd0Is a steady-state value of the d-axis component of the PCC bus voltage.
Preferably, the inner-loop control mathematical model is:
wherein,
wherein,for reference values of the d-axis component of the inverter output voltage in the control system coordinate system,to control the reference value of the q-axis component of the inverter output voltage in the system coordinate system,to control the value of the d-axis component of the inverter output voltage in the system coordinate system,for controlling the value of the q-axis component of the converter output voltage in the system coordinate system, omegafIs the voltage filter bandwidth, TfIs the time constant of the voltage filter, omegaCLIs the inner loop bandwidth, kp_clIs the inner loop PI controller proportionality coefficient, Ti_clProportional coefficient, integral time constant, G, of inner loop controllerfIs a PCC bus voltage filter, GCLIs an inner ring proportional-integral controller,for reference values of the d-axis component of the inverter output current in the control system coordinate system,for reference values of the q-axis component of the inverter output current in the control system coordinate system,to control the value of the d-axis component of the inverter output current in the system coordinate system,for controlling the value of the q-axis component of the converter output current in the system coordinate system, omega1At a nominal angular frequency, LeqIs the equivalent inductance between the PCC bus and the converter valve side, s is the Laplace operator, ReqIs the equivalent resistance between the PCC bus and the converter valve side.
Preferably, the mathematical model of the modulation process is:
wherein G isd＝e-sTd，TdFor the equivalent delay of the flexible-straight control system, ucdIs d-axis component, u, of the equivalent output voltage at the AC side of the convertercqFor the q-axis component of the equivalent output voltage at the AC side of the converter, udcIs a DC side voltage, Udc0Is a steady-state value of the DC side voltage, thetapllFor phase-locked loop output phase thetaPLLAnd omega1the difference between the values of t and t,for reference values of the d-axis component of the inverter output voltage in the control system coordinate system,for reference values of q-axis components of converter output voltage in a control system coordinate system, GdIs a time delay simulation link.
Based on another aspect of the present invention, there is provided a voltage source converter grid-connected system inner loop control analysis transfer function modeling system, including:
the first establishing unit is used for establishing a voltage source type converter grid-connected system mathematical model considering the power grid strength and the phase-locked loop dynamic state based on a first assumed condition;
the processing unit is used for carrying out linearization processing on the voltage source type converter grid-connected system mathematical model;
a second establishing unit for acquiring a simplified transfer function of inner loop control of the current based on a second assumption condition; according to the simplified transfer function, the dynamic output phase expression of the phase-locked loop is specified, and an inner loop control analysis transfer function of the grid-connected current of the voltage source type converter considering the dynamic influence of the phase-locked loop is established;
and the design unit is used for analyzing the inner ring control instability mechanism of the voltage source type converter grid-connected system and guiding parameter design based on the inner ring control analytic transfer function.
Preferably, the first assumption condition is:
only the strength of the electrical connection is considered, the inner loop current feedback value can track the inner loop current reference value in real time, the filter capacitor of the common connection point is ignored, the delay in the modulation process and the sampling delay are ignored, and the loss is ignored.
Preferably, the grid-connected system mathematical model includes:
a main circuit mathematical model, a phase-locked loop dynamic mathematical model and an inner loop control mathematical model.
Preferably, the main circuit mathematical model is:
the mathematical model of the main circuit part is as follows under dq coordinate system
Wherein L iseq＝Lt+Larm/2，Req＝Rt+Rarm/2，Lac＝Leq+Lg，Rac＝Req+RgS denotes a differential operator, ReqIs the equivalent resistance between the PCC bus and the converter valve side, LeqIs the equivalent inductance between the PCC bus and the converter valve side, LtIs the equivalent inductance, L, of an AC mains transformerarmIs an MMC bridge arm inductor, RtIs an equivalent resistance of an AC network transformer, LacIs the equivalent inductance from the inverter to the infinite system (ideal power supply), RacIs the equivalent resistance from the inverter to the infinite system (ideal power supply), icdFor the d-axis component of the converter output current icqFor the converter output current q-axis component, ucdIs d-axis component, u, of the converter equivalent output voltagesdIs the d-axis component, ω, of the PCC bus voltage1At a nominal angular frequency, ucqFor the q-axis component of the converter equivalent output voltage, usqIs the q-axis component of the PCC bus voltage, LgIs an equivalent inductance of an AC network, RgIs the equivalent resistance of the AC network, ugdD-axis component, u, of infinite system (ideal power supply) voltagegqThe d-axis component of the infinite system (ideal power supply) voltage. Preferably, the dynamic mathematical model of the phase-locked loop is:
wherein,
wherein, thetaPLLFor dynamically outputting phase, theta, to a phase-locked looppllFor phase-locked loop output phase thetaPLLAnd omega1Difference of t, ω1t is an initial phase of 0 at a constant angular velocity ω1Phase of rotating dq coordinate system, kp_pllFor phase-locked loop dynamic proportional integral controller proportionality coefficient, Ti_pllIntegrating time constant, u, for a phase locked loop dynamic proportional integral controllersqIs the q-axis component, ω, of the PCC bus voltage1Is the nominal angular velocity of dq coordinate system, s is the Laplace operator, GpllIs a proportional-integral controller for a phase-locked loop,the q-axis component of the equivalent output voltage of the converter in the dq coordinate system of the control system.
Preferably, the dynamic mathematical model of the phase-locked loop is designed to have a second-order response characteristic and a parameter calculation formula thereof is as follows:
wherein, ω ispllFor dynamically designing the bandwidth of the phase-locked loop, the damping ratio ξ is 0.707 usd0For PCC bus-bar electricitySteady state values of the d-axis component of pressure.
Preferably, the inner-loop control mathematical model is:
wherein,
wherein,for reference values of the d-axis component of the inverter output voltage in the control system coordinate system,to control the reference value of the q-axis component of the inverter output voltage in the system coordinate system,to control the value of the d-axis component of the inverter output voltage in the system coordinate system,for controlling the value of the q-axis component of the converter output voltage in the system coordinate system, omegafIs the voltage filter bandwidth, TfIs the time constant of the voltage filter, omegaCLIs the inner loop bandwidth, kp_clIs the inner loop PI controller proportionality coefficient, Ti_clProportional coefficient, integral time constant, G, of inner loop controllerfIs a PCC bus voltage filter, GCLIs an inner ring proportional-integral controller,for reference values of the d-axis component of the inverter output current in the control system coordinate system,for reference values of the q-axis component of the inverter output current in the control system coordinate system,to control the value of the d-axis component of the inverter output current in the system coordinate system,for controlling the value of the q-axis component of the converter output current in the system coordinate system, omega1At a nominal angular frequency, LeqIs the equivalent inductance between the PCC bus and the converter valve side, s is the Laplace operator, ReqIs the equivalent resistance between the PCC bus and the converter valve side.
Preferably, the mathematical model of the modulation process is:
wherein G isd＝e-sTd，TdFor the equivalent delay of the flexible-straight control system, ucdIs d-axis component, u, of the equivalent output voltage at the AC side of the convertercqFor the q-axis component of the equivalent output voltage at the AC side of the converter, udcIs a DC side voltage, Udc0Is a steady-state value of the DC side voltage, thetapllFor phase-locked loop output phase thetaPLLAnd omega1the difference between the values of t and t,for reference values of the d-axis component of the inverter output voltage in the control system coordinate system,for controlling q-axis component of converter output voltage in system coordinate systemReference value of GdIs a time delay simulation link.
The technical scheme of the invention provides a method and a system for modeling an inner ring control analysis transfer function of a voltage source type converter grid-connected system, wherein the method comprises the following steps: establishing a voltage source type converter grid-connected system mathematical model considering the power grid strength and the phase-locked loop dynamics based on a first assumed condition; carrying out linearization processing on a voltage source type converter grid-connected system mathematical model; acquiring a simplified transfer function of inner loop control of the current based on a second assumed condition; according to the simplified transfer function, the dynamic output phase expression of the phase-locked loop is embodied, and an inner loop control analysis transfer function of the voltage source converter grid-connected current considering the dynamic influence of the phase-locked loop is established; and analyzing an inner ring control instability mechanism of the voltage source type converter grid-connected system based on the inner ring control analytic transfer function and guiding parameter design. The voltage source converter VSC grid-connected system analytic transfer function model with the proper simplification degree established by the technical scheme of the invention can intuitively explain the instability mechanism of the voltage source converter VSC grid-connected system, can also guide the design of the inner ring control parameters of the voltage source converter VSC grid-connected system, and has positive significance for guiding the design of the control strategy. The VSC grid-connected system of the voltage source converter mainly comprises inner ring control and outer ring control, wherein the inner ring control is more than ten times faster than the outer ring control, the outer ring can be assumed to be in a stable state when the inner ring control is researched, and the dynamic process of the inner ring control can be ignored when the outer ring control is researched.
Drawings
A more complete understanding of exemplary embodiments of the present invention may be had by reference to the following drawings in which:
fig. 1 is a flowchart of an inner loop control analysis transfer function modeling method of a voltage source converter grid-connected system according to a preferred embodiment of the invention;
fig. 2 is a structural diagram of a main circuit and a control system of a voltage source converter VSC grid-connected system according to a preferred embodiment of the invention;
FIG. 3 is a schematic diagram of the main circuit and control system coordinate system according to the preferred embodiment of the present invention;
FIG. 4 is a schematic diagram of a dynamic PLL of a phase locked loop in accordance with a preferred embodiment of the present invention;
FIG. 5 is a schematic diagram of an inner loop current control block according to a preferred embodiment of the present invention;
FIG. 6 is a block diagram illustrating an inner loop current control analytic transfer function model in accordance with a preferred embodiment of the present invention;
FIG. 7 is a block diagram illustrating an inner loop current control analytic transfer function model in accordance with a preferred embodiment of the present invention;
fig. 8 is a structural diagram of an inner loop control analysis transfer function modeling system of a grid-connected system of a voltage source converter according to a preferred embodiment of the invention.
Detailed Description
The exemplary embodiments of the present invention will now be described with reference to the accompanying drawings, however, the present invention may be embodied in many different forms and is not limited to the embodiments described herein, which are provided for complete and complete disclosure of the present invention and to fully convey the scope of the present invention to those skilled in the art. The terminology used in the exemplary embodiments illustrated in the accompanying drawings is not intended to be limiting of the invention. In the drawings, the same units/elements are denoted by the same reference numerals.
Unless otherwise defined, terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. Further, it will be understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the relevant art and will not be interpreted in an idealized or overly formal sense.
Fig. 1 is a flowchart of a method for modeling an inner loop control analysis transfer function of a grid-connected system of a voltage source converter according to a preferred embodiment of the invention. The embodiment of the invention provides a method for modeling an inner ring control analysis transfer function of a voltage source type converter grid-connected system, which comprises the following four steps: establishing a voltage source converter VSC grid-connected system mathematical model considering power grid strength and phase-locked Loop (PLL) dynamics based on assumed conditions, linearizing the voltage source converter VSC grid-connected system mathematical model, solving to obtain an inner-Loop control analytic transfer function model, analyzing an inner-Loop control instability mechanism of the voltage source converter VSC grid-connected system based on the inner-Loop control analytic transfer function model, and guiding control parameter selection. As shown in fig. 1, a method for modeling an inner loop control analysis transfer function of a grid-connected system of a voltage source converter includes:
preferably, in step 101: and establishing a voltage source type converter grid-connected system mathematical model considering the power grid strength and the phase-locked loop dynamics based on the first assumed condition. Preferably, the first assumption condition is: only the strength of the electrical connection is considered, the inner loop current feedback value can track the inner loop current reference value in real time, the filter capacitor of the common connection point is ignored, the delay in the modulation process and the sampling delay are ignored, and the loss is ignored. Preferably, the grid-connected system mathematical model comprises: a main circuit mathematical model, a phase-locked loop dynamic mathematical model and an inner loop control mathematical model.
The assumed condition for establishing the voltage source converter VSC grid-connected system mathematical model is that only the strength of electrical connection is considered, the inner loop current feedback value can track the inner loop current reference value in real time, the filter capacitor of the common connection point is ignored, the modulation process delay and the sampling delay are ignored, and the loss is ignored. The power and current reference directions are shown in fig. 2.
The VSC grid-connected system mathematical model comprises: a main circuit mathematical model, a PLL mathematical model and an inner loop control mathematical model.
Preferably, after considering the first assumption condition, the mathematical model of the main circuit is:
the mathematical model of the main circuit part is as follows under dq coordinate system
Wherein L iseq＝Lt+Larm/2，Req＝Rt+Rarm/2，Lac＝Leq+Lg，Rac＝Req+RgS denotes a differential operator, ReqIs the equivalent resistance between the PCC bus and the converter valve side, LeqIs the equivalent inductance between the PCC bus and the converter valve side, LtIs the equivalent inductance, L, of an AC mains transformerarmIs an MMC bridge arm inductor, RtIs an equivalent resistance of an AC network transformer, LacIs the equivalent inductance from the inverter to the infinite system (ideal power supply), RacIs the equivalent resistance from the inverter to the infinite system (ideal power supply), icdFor the d-axis component of the converter output current icqFor the converter output current q-axis component, ucdIs d-axis component, u, of the converter equivalent output voltagesdIs the d-axis component, ω, of the PCC bus voltage1At a nominal angular frequency, ucqFor the q-axis component of the converter equivalent output voltage, usqIs the q-axis component of the PCC bus voltage, LgIs an equivalent inductance of an AC network, RgIs the equivalent resistance of the AC network, ugdD-axis component, u, of infinite system (ideal power supply) voltagegqThe d-axis component of the infinite system (ideal power supply) voltage. Using PCC point voltage Us∠θsThe directional control system coordinate system and the main circuit coordinate system are shown in FIG. 3, wherein the coordinate system defined by the d-axis and the q-axis is the main circuit coordinate systemRoad coordinate system, from dcf、qcfThe determined coordinate system is a control system coordinate system, fd、fqBeing the component of the vector F in the main circuit coordinate system,is the component of the vector F in the control system coordinate system. The position of the control system coordinate system is determined by the PLL output, and U is adopted in the applications∠θsD-axis and U of coordinate system of control system in orientation and steady states∠θsCoincidence, thetapll＝θsTransient process after disturbance thetapll≠θs. The relationship between the projection components of the voltage vector and the current vector under two coordinate systems is as follows:
wherein f is a variable us、uc、ug、icAnd the like.
Preferably, the dynamic mathematical model of the phase-locked loop is:
wherein,
wherein, thetaPLLFor dynamically outputting phase, theta, to a phase-locked looppllFor phase-locked loop output phase thetaPLLAnd omega1Difference of t, ω1t is an initial phase of 0 at a constant angular velocity ω1Rotating dq coordinate systemPhase of (a), kp_pllFor phase-locked loop dynamic proportional integral controller proportionality coefficient, Ti_pllIntegrating time constant, u, for a phase locked loop dynamic proportional integral controllersqFor the q-axis component of the PCC bus voltage, ω 1 is the rated angular velocity of the dq coordinate system, s is the Laplace operator, GpllIs a proportional-integral controller for a phase-locked loop,the q-axis component of the equivalent output voltage of the converter in the dq coordinate system of the control system.
Preferably, the dynamic mathematical model of the phase-locked loop is designed as a parameter calculation formula of the second-order response characteristic:
wherein, ω ispllFor dynamically designing the bandwidth of the phase-locked loop, the damping ratio ξ is 0.707 usd0Is a steady-state value of the d-axis component of the PCC bus voltage.
Preferably, the inner loop control mathematical model is:
wherein,
wherein,referencing d-axis components of inverter output voltage in control system coordinate systemThe value of the one or more of,to control the reference value of the q-axis component of the inverter output voltage in the system coordinate system,to control the value of the d-axis component of the inverter output voltage in the system coordinate system,for controlling the value of the q-axis component of the converter output voltage in the system coordinate system, omegafIs the voltage filter bandwidth, TfIs the time constant of the voltage filter, omegaCLIs the inner loop bandwidth, kp_clIs the inner loop PI controller proportionality coefficient, Ti_clProportional coefficient, integral time constant, G, of inner loop controllerfIs a PCC bus voltage filter, GCLIs an inner ring proportional-integral controller,for reference values of the d-axis component of the inverter output current in the control system coordinate system,for reference values of the q-axis component of the inverter output current in the control system coordinate system,to control the value of the d-axis component of the inverter output current in the system coordinate system,for controlling the value of the q-axis component of the converter output current in the system coordinate system, omega1At a nominal angular frequency, LeqIs the equivalent inductance between the PCC bus and the converter valve side, s is the Laplace operator, ReqIs the equivalent resistance between the PCC bus and the converter valve side. Application TfTypically 300 us.
Preferably, the mathematical model of the modulation process is:
wherein G isd＝e-sTd，TdFor the equivalent delay of the flexible-straight control system, ucdIs d-axis component, u, of the equivalent output voltage at the AC side of the convertercqFor the q-axis component of the equivalent output voltage at the AC side of the converter, udcIs a DC side voltage, Udc0Is a steady-state value of the DC side voltage, thetapllFor phase-locked loop output phase thetaPLLAnd omega1the difference between the values of t and t,for reference values of the d-axis component of the inverter output voltage in the control system coordinate system,for reference values of q-axis components of converter output voltage in a control system coordinate system, GdIs a time delay simulation link. T isdThe equivalent delay time of the flexible-straight control system is generally 400-500 us.
Preferably, at step 102: and carrying out linearization processing on the voltage source type converter grid-connected system mathematical model.
A voltage source converter VSC grid-connected system mathematical model is a typical nonlinear model, and in order to research the stability of a grid-connected system, the voltage source converter VSC grid-connected system mathematical model needs to be linearized, and each variable f in the formulas (41) to (52) is changed into f with small disturbance f0Substituting the form of + Δ f to eliminate the steady state quantity can obtain a linearized model.
In order to obtain a detailed VSC grid-connected current expression, the linearization models of the joint type (41) to (52) are arranged to obtain an inner loop current control linearization closed-loop expression considering the influences of PLL, time delay, a voltage filter and direct current voltage disturbance as follows:
ignoring the secondary factors, a second assumption is made as follows:
(1) the delay of the whole converter system is very small, generally 400-500 us, and T is assumedd0, then Gd＝1；
(2) The delay of the voltage sampling filter is very small and generally takes 300us, Tf0, then Gf＝1；
(3) The DC voltage being maintained at a constant value, Δ udc＝0；
In view of the above second assumption, the simplified transfer function for the resulting current inner loop control is:
in the formula Zic＝sLeq+Req+GCLThe equation (54) shows that d-axis and q-axis current disturbance of the grid-connected VSC is mainly affected by current reference value disturbance and PLL output disturbance, and respectively represents the influence of outer loop control and PLL on current inner loop control.
Preferably, in step 103: acquiring a simplified transfer function of inner loop control of the current based on a second assumed condition; according to the simplified transfer function, the dynamic output phase of the phase-locked loop is embodied, and an inner loop control analysis transfer function of the voltage source converter grid-connected current considering the dynamic influence of the phase-locked loop is established.
In order to obtain a current inner loop control analysis transfer function model considering the influence of the PLL and the AC power grid intensity, a PLL output phase disturbance expression in an expression (54) needs to be specified, and delta theta is eliminatedpllA closed loop is established from the control system to the main circuit.
From formulae (54) and ugd＝0，ugqAvailable as 0:
can be obtained by finishing
Fig. 5 is a block diagram of equation (56) to visually illustrate the effect of the PLL on the inner loop current control.
The solving formula (56) can obtain a grid-connected VSC current inner loop control analytic expression considering PLL influence
Wherein
A block diagram of a transfer function expression for analyzing a small signal in current inner loop control of a grid-connected VSC system is shown in fig. 6. From the equations (57) and (59), it can be seen that the equivalent inductance Lg representing the ac network strength plays a decisive role in the PLL interaction with the current inner loop control, LgThe magnitude of (c) determines the severity of the interaction between the two. When the AC power grid is an infinite system, Rg≈0，Lg≈0，Gdd＝Gqq＝0，Gdq＝GqdAnd when the value is 0, the value is B, C and 0, the PLL and the current inner loop control have no influence, and the current inner loop control has no influence on the d and q axis control. When the AC power grid strength is small, LgNot equal to 0, the interaction between PLL and current inner loop is strengthened, and is characterized by the formula (59)I magnitude of work and reactive powercd0、Icq0The larger the interaction, the more significant the interaction.
Preferably, at step 104: and analyzing an inner ring control instability mechanism of the voltage source type converter grid-connected system based on the inner ring control analytic transfer function and guiding parameter design.
From the equation (61), the characteristic equation for determining the stability of the inner loop current control is
G0Is composed of three parts, GCL/ZicReflecting the effect of the inner loop control in the ideal case, without taking into account the PLL and the grid strength, GPLLThe influence of the PLL is reflected, and the rest reflects the influence of the grid strength, the active current (active power), and the reactive current (reactive power). Under the assumption of unity power factor:
by combining the formula (61) with the stability criterion on the Bode graph or the Nyquist graph shown in fig. 7, the influence of factors such as the power grid strength, the active power, the PLL bandwidth and the like on the inner-loop control stability can be analyzed, and the PLL bandwidth and the inner-loop control bandwidth parameter design are guided. The equivalent reactance of the power grid determines the initial position of the Bode diagram, the bandwidth of the phase-locked loop determines the position of the maximum value of the amplitude, and the bandwidth of the inner loop does not influence the maximum value of the amplitude. The parameters of the bandwidth of the phase-locked loop can be reasonably selected according to the strength of the power grid and the bandwidth of the inner loop, and the condition that the maximum value of the Bode graph amplitude is less than 0 is met is guaranteed.
Fig. 2 is a structural diagram of a main circuit and a control system of a voltage source converter VSC grid-connected system according to a preferred embodiment of the invention. The meanings of the variables in FIG. 2 are explained in Table 1.
TABLE 1 VSC grid-connected system variables
The application provides a modeling analysis method for inner loop control analysis transfer functions of a VSC grid-connected system under a weak current grid, which can be used for analyzing a destabilization mechanism of inner loop control of the VSC grid-connected system under the weak current grid and guiding control parameter selection. According to the VSC grid-connected system inner ring control analytic modeling method, the influence of each factor on stability can be intuitively explained due to the fact that the transfer function is adopted for analytic modeling, main influencing factors are located, and model explanatory power is high. The instability mechanism analysis method based on the VSC grid-connected system inner ring control analysis model can visually reveal the influence of various influencing factors on the stability of the VSC grid-connected system inner ring control, guides the design of control parameters of the VSC grid-connected system inner ring control such as a fan converter and a photovoltaic inverter, and can create obvious economic benefits.
Fig. 8 is a structural diagram of an inner loop control analysis transfer function modeling system of a grid-connected system of a voltage source converter according to a preferred embodiment of the invention. As shown in fig. 8, an inner loop control analysis transfer function modeling system of a voltage source converter grid-connected system includes:
the first establishing unit 801 is configured to establish a voltage source converter grid-connected system mathematical model considering grid strength and phase-locked loop dynamics based on a first assumed condition. Preferably, the first assumption condition is: only the strength of the electrical connection is considered, the inner loop current feedback value can track the inner loop current reference value in real time, the filter capacitor of the common connection point is ignored, the delay in the modulation process and the sampling delay are ignored, and the loss is ignored. Preferably, the grid-connected system mathematical model comprises: a main circuit mathematical model, a phase-locked loop dynamic mathematical model and an inner loop control mathematical model.
Preferably, the main circuit mathematical model is:
the mathematical model of the main circuit part is as follows under dq coordinate system
Wherein L iseq＝Lt+Larm/2，Req＝Rt+Rarm/2，Lac＝Leq+Lg，Rac＝Req+RgS denotes a differential operator, ReqIs the equivalent resistance between the PCC bus and the converter valve side, LeqIs the equivalent inductance between the PCC bus and the converter valve side, LtIs the equivalent inductance, L, of an AC mains transformerarmIs an MMC bridge arm inductor, RtIs an equivalent resistance of an AC network transformer, LacIs the equivalent inductance from the inverter to the infinite system (ideal power supply), RacIs the equivalent resistance from the inverter to the infinite system (ideal power supply), icdFor the d-axis component of the converter output current icqFor the converter output current q-axis component, ucdIs d-axis component, u, of the converter equivalent output voltagesdIs d-axis component of PCC bus voltage, omega 1 is rated angular frequency, ucqFor the q-axis component of the converter equivalent output voltage, usqIs the q-axis component of the PCC bus voltage, LgIs an equivalent inductance of an AC network, RgIs the equivalent resistance of the AC network, ugdD-axis component, u, of infinite system (ideal power supply) voltagegqThe d-axis component of the infinite system (ideal power supply) voltage. Preferably, the dynamic mathematical model of the phase-locked loop is:
wherein,
wherein, thetaPLLFor dynamically outputting phase, theta, to a phase-locked looppllFor phase-locked loop output phase thetaPLLAnd omega1Difference of t, ω1t is an initial phase of 0 at a constant angular velocity ω1Phase of rotating dq coordinate system, kp_pllFor phase-locked loop dynamic proportional integral controller proportionality coefficient, Ti_pllIntegrating time constant, u, for a phase locked loop dynamic proportional integral controllersqFor the q-axis component of the PCC bus voltage, ω 1 is the rated angular velocity of the dq coordinate system, s is the Laplace operator, GpllIs a proportional-integral controller for a phase-locked loop,the q-axis component of the equivalent output voltage of the converter in the dq coordinate system of the control system. Preferably, the dynamic mathematical model of the phase-locked loop is designed as a parameter calculation formula of the second-order response characteristic:
wherein, ω ispllFor dynamically designing the bandwidth of the phase-locked loop, the damping ratio ξ is 0.707 usd0Is a steady-state value of the d-axis component of the PCC bus voltage.
Preferably, the inner loop control mathematical model is:
wherein,
wherein,for reference values of the d-axis component of the inverter output voltage in the control system coordinate system,to control the reference value of the q-axis component of the inverter output voltage in the system coordinate system,to control the value of the d-axis component of the inverter output voltage in the system coordinate system,for controlling the value of the q-axis component of the converter output voltage in the system coordinate system, omegafIs the voltage filter bandwidth, TfIs the time constant of the voltage filter, omegaCLIs the inner loop bandwidth, kp_clIs the inner loop PI controller proportionality coefficient, Ti_clProportional coefficient, integral time constant, G, of inner loop controllerfIs a PCC bus voltage filter, GCLIs an inner ring proportional-integral controller,for reference values of the d-axis component of the inverter output current in the control system coordinate system,for reference values of the q-axis component of the inverter output current in the control system coordinate system,to control the value of the d-axis component of the inverter output current in the system coordinate system,for controlling the value of the q-axis component of the converter output current in the system coordinate system, omega1At a nominal angular frequency, LeqIs the equivalent inductance between the PCC bus and the converter valve side, s is the Laplace operator, ReqIs the equivalent resistance between the PCC bus and the converter valve side.
Preferably, the mathematical model of the modulation process is:
wherein G isd＝e-sTd，TdFor the equivalent delay of the flexible-straight control system, ucdIs d-axis component, u, of the equivalent output voltage at the AC side of the convertercqFor the q-axis component of the equivalent output voltage at the AC side of the converter, udcIs a DC side voltage, Udc0Is a steady-state value of the DC side voltage, thetapllFor phase-locked loop output phase thetaPLLAnd omega1the difference between the values of t and t,for reference values of the d-axis component of the inverter output voltage in the control system coordinate system,for reference values of q-axis components of converter output voltage in a control system coordinate system, GdIs a time delay simulation link.
And the processing unit 802 is configured to perform linearization processing on the voltage source converter grid-connected system mathematical model. A voltage source converter VSC grid-connected system mathematical model is a typical nonlinear model, and in order to research the stability of a grid-connected system, the voltage source converter VSC grid-connected system mathematical model needs to be linearized, and each variable f in the formulas (62) to (71) is changed into f by small disturbance f0Substituting the form of + Δ f to eliminate the steady state quantity can obtain a linearized model.
In order to obtain a detailed VSC grid-connected current expression, a joint type (62) - (71) linearization model is arranged to obtain a linearization closed-loop expression of inner loop current control considering the influences of PLL, time delay, a voltage filter and direct-current voltage disturbance, wherein the linearization closed-loop expression comprises the following steps:
ignoring the secondary factors, a second assumption is made as follows:
(1) the delay of the whole converter system is very small, generally 400-500 us, and T is assumedd0, then Gd＝1；
(2) The delay of the voltage sampling filter is very small and generally takes 300us, Tf0, then Gf＝1；
(3) The DC voltage being maintained at a constant value, Δ udc＝0；
In view of the above second assumption, the simplified transfer function for the resulting current inner loop control is:
in the formula Zic＝sLeq+Req+GCLThe equation (73) shows that d-axis and q-axis current disturbance of the grid-connected VSC is mainly influenced by PLL output disturbance and current reference value disturbance, and respectively represents the influence of PLL and outer loop control on current inner loop control.
A second establishing unit 803 for obtaining a simplified transfer function of inner loop control of the current based on a second assumption condition; according to the simplified transfer function, the dynamic output phase expression of the phase-locked loop is specified, and the inner loop control analysis transfer function of the voltage source type converter grid-connected current considering the dynamic influence of the phase-locked loop is established. In order to obtain the current inner loop control analysis transfer function model considering the influence of the PLL and the AC power grid intensity, the PLL output phase disturbance expression in the formula (73) needs to be specifiedElimination of Delta thetapllA closed loop is constructed from the control system to the main circuit.
From formulas (73) and ugd＝0，ugqAvailable as 0:
finishing to obtain:
fig. 5 shows a block diagram of equation (75) to visually illustrate the effect of the PLL on the inner loop current control.
The solving expression (75) can be obtained by taking the PLL influence into consideration, and the analytic expression of the grid-connected VSC current inner loop control is
Wherein,
a block diagram of a transfer function expression for analyzing a small signal in current inner loop control of a grid-connected VSC system is shown in fig. 6. From the equations (76) (78), it can be seen that the equivalent inductance Lg representing the ac network strength plays a decisive role in the PLL and current inner loop control interaction, LgThe magnitude of (c) determines the severity of the interaction between the two. When the AC power grid is an infinite system, Rg≈0，Lg≈0，Gdd＝Gqq＝0，Gdq＝GqdAnd when the value is 0, the value is B, C and 0, the PLL and the current inner loop control have no influence, and the current inner loop control has no influence on the d and q axis control. When the AC power grid strength is small, LgNot equal to 0, the interaction between PLL and current inner loop is strengthened, and I representing the magnitude of active and reactive power is known from equation (78)cd0、Icq0The larger the interaction, the more significant the interaction.
And the design unit 804 is used for analyzing the inner ring control instability mechanism of the voltage source converter grid-connected system and guiding parameter design based on the inner ring control analytic transfer function.
From the equation (80), the characteristic equation for determining the stability of the inner loop current control is
G0Consisting of three parts, GCL/ZicThe effect of the inner loop control in the ideal case is reflected without taking the PLL and the grid strength into account, the GPLL reflects the influence of the PLL, and the rest reflects the influence of the grid strength, the active current (active power), the reactive current (reactive power). Under the assumption of unity power factor:
by combining the formula (80) with the stability criterion on the Bode graph or the Nyquist graph shown in fig. 7, the influence of factors such as the power grid strength, the active power, the PLL bandwidth and the like on the inner-loop control stability can be analyzed, and the PLL bandwidth and the inner-loop control bandwidth parameter design are guided. The equivalent reactance of the power grid determines the initial position of the Bode diagram, the bandwidth of the phase-locked loop determines the position of the maximum value of the amplitude, and the bandwidth of the inner loop does not influence the maximum value of the amplitude. The parameters of the bandwidth of the phase-locked loop can be reasonably selected according to the strength of the power grid and the bandwidth of the inner loop, and the condition that the maximum value of the Bode graph amplitude is less than 0 is met is guaranteed.
The voltage source converter grid-connected system inner ring control analysis transfer function modeling system 800 according to the embodiment of the present invention corresponds to the voltage source converter grid-connected system inner ring control analysis transfer function modeling method 100 according to another embodiment of the present invention, and details thereof are not repeated herein.
The invention has been described with reference to a few embodiments. However, other embodiments of the invention than the one disclosed above are equally possible within the scope of the invention, as would be apparent to a person skilled in the art from the appended patent claims.
Generally, all terms used in the claims are to be interpreted according to their ordinary meaning in the technical field, unless explicitly defined otherwise herein. All references to "a/an/the [ device, component, etc ]" are to be interpreted openly as referring to at least one instance of said device, component, etc., unless explicitly stated otherwise. The steps of any method disclosed herein do not have to be performed in the exact order disclosed, unless explicitly stated.
Claims (16)
1. A method for modeling an inner ring control analytic transfer function of a grid-connected system of a voltage source converter comprises the following steps:
establishing a voltage source type converter grid-connected system mathematical model considering the power grid strength and the phase-locked loop dynamics based on a first assumed condition;
carrying out linearization processing on the voltage source type converter grid-connected system mathematical model;
acquiring a simplified transfer function of inner loop control of the current based on a second assumed condition; according to the simplified transfer function, the dynamic output phase expression of the phase-locked loop is specified, and an inner loop control analysis transfer function of the grid-connected current of the voltage source type converter considering the dynamic influence of the phase-locked loop is established;
and analyzing an inner ring control instability mechanism of the voltage source type converter grid-connected system and guiding parameter design based on the inner ring control analytic transfer function.
2. The method of claim 1, the first hypothetical condition being:
only the strength of the electrical connection is considered, the inner loop current feedback value can track the inner loop current reference value in real time, the filter capacitor of the common connection point is ignored, the delay in the modulation process and the sampling delay are ignored, and the loss is ignored.
3. The method of claim 1, the grid tie system mathematical model comprising:
a main circuit mathematical model, a phase-locked loop dynamic mathematical model and an inner loop control mathematical model.
4. The method of claim 3, the primary circuit mathematical model being:
the mathematical model of the main circuit part is as follows under dq coordinate system
Wherein L iseq＝Lt+Larm/2，Req＝Rt+Rarm/2，Lac＝Leq+Lg，Rac＝Req+RgS denotes a differential operator, ReqIs the equivalent resistance between the PCC bus and the converter valve side, LeqIs the equivalent inductance between the PCC bus and the converter valve side, LtIs the equivalent inductance, L, of an AC mains transformerarmIs an MMC bridge arm inductor, RtIs an equivalent resistance of an AC network transformer, LacIs equivalent inductance between the converter and the infinite system, RacIs the equivalent resistance from the converter to the infinite system, icdFor the d-axis component of the converter output current icqFor the converter output current q-axis component, ucdIs d-axis component, u, of the converter equivalent output voltagesdIs the d-axis component, ω, of the PCC bus voltage1At a nominal angular frequency, ucqFor the q-axis component of the converter equivalent output voltage, usqIs the q-axis component of the PCC bus voltage, LgIs an equivalent inductance of an AC network, RgIs the equivalent resistance of the AC network, ugdD-axis component, u, of infinite system voltagegqThe d-axis component of the infinite system voltage.
5. The method of claim 3, the phase-locked loop dynamic mathematical model being:
wherein,
wherein, thetaPLLFor dynamically outputting phase, theta, to a phase-locked looppllFor phase-locked loop output phase thetaPLLAnd omega1Difference of t, ω1t is an initial phase of 0 at a constant angular velocity ω1Phase of rotating dq coordinate system, kp_pllFor phase-locked loop dynamic proportional integral controller proportionality coefficient, Ti_pllIntegrating time constant, u, for a phase locked loop dynamic proportional integral controllersqIs the q-axis component, ω, of the PCC bus voltage1Is the rated angular velocity of dq coordinate system, s is LaplacaOperator of sj, GpllIs a proportional-integral controller for a phase-locked loop,the q-axis component of the equivalent output voltage of the converter in the dq coordinate system of the control system.
6. The method of claim 5, wherein the dynamic mathematical model of the phase-locked loop is designed to have a second-order response characteristic with a parameter calculation formula as follows:
wherein, ω ispllFor dynamically designing the bandwidth of the phase-locked loop, the damping ratio ξ is 0.707 usd0Is a steady-state value of the d-axis component of the PCC bus voltage.
7. The method of claim 3, the inner loop control mathematical model being:
wherein,
wherein,for reference values of the d-axis component of the inverter output voltage in the control system coordinate system,for controlling inverter output in the system coordinate systemA reference value of the q-axis component of the voltage,to control the value of the d-axis component of the inverter output voltage in the system coordinate system,for controlling the value of the q-axis component of the converter output voltage in the system coordinate system, omegafIs the voltage filter bandwidth, TfIs the time constant of the voltage filter, omegaCLIs the inner loop bandwidth, kp_clIs the inner loop PI controller proportionality coefficient, Ti_clProportional coefficient, integral time constant, G, of inner loop controllerfIs a PCC bus voltage filter, GCLIs an inner ring proportional-integral controller,for reference values of the d-axis component of the inverter output current in the control system coordinate system,for reference values of the q-axis component of the inverter output current in the control system coordinate system,to control the value of the d-axis component of the inverter output current in the system coordinate system,for controlling the value of the q-axis component of the converter output current in the system coordinate system, omega1At a nominal angular frequency, LeqIs the equivalent inductance between the PCC bus and the converter valve side, s is the Laplace operator, ReqIs the equivalent resistance between the PCC bus and the converter valve side.
8. The method of claim 3, the mathematical model of the modulation process being:
wherein G isd＝e-sTd，TdFor the equivalent delay of the flexible-straight control system, ucdIs d-axis component, u, of the equivalent output voltage at the AC side of the convertercqFor the q-axis component of the equivalent output voltage at the AC side of the converter, udcIs a DC side voltage, Udc0Is a steady-state value of the DC side voltage, thetapllFor phase-locked loop output phase thetaPLLAnd omega1the difference between the values of t and t,for reference values of the d-axis component of the inverter output voltage in the control system coordinate system,for reference values of q-axis components of converter output voltage in a control system coordinate system, GdIs a time delay simulation link.
9. An analytic transfer function modeling system of voltage source converter grid-connected system inner loop control, the system comprising:
the first establishing unit is used for establishing a voltage source type converter grid-connected system mathematical model considering the power grid strength and the phase-locked loop dynamic state based on a first assumed condition;
the processing unit is used for carrying out linearization processing on the voltage source type converter grid-connected system mathematical model;
a second establishing unit for acquiring a simplified transfer function of inner loop control of the current based on a second assumption condition; according to the simplified transfer function, the dynamic output phase expression of the phase-locked loop is specified, and an inner loop control analysis transfer function of the grid-connected current of the voltage source type converter considering the dynamic influence of the phase-locked loop is established;
and the design unit is used for analyzing the inner ring control instability mechanism of the voltage source type converter grid-connected system and guiding parameter design based on the inner ring control analytic transfer function.
10. The system of claim 9, the first assumption condition being:
only the strength of the electrical connection is considered, the inner loop current feedback value can track the inner loop current reference value in real time, the filter capacitor of the common connection point is ignored, the delay in the modulation process and the sampling delay are ignored, and the loss is ignored.
11. The system of claim 9, the grid tie system mathematical model comprising:
a main circuit mathematical model, a phase-locked loop dynamic mathematical model and an inner loop control mathematical model.
12. The system of claim 11, the primary circuit mathematical model being:
the mathematical model of the main circuit part is as follows under dq coordinate system
Wherein L iseq＝Lt+Larm/2，Req＝Rt+Rarm/2，Lac＝Leq+Lg，Rac＝Req+RgS denotes a differential operator, ReqIs the equivalent resistance between the PCC bus and the converter valve side, LeqIs the equivalent inductance between the PCC bus and the converter valve side, LtIs the equivalent inductance, L, of an AC mains transformerarmIs an MMC bridge arm inductor, RtIs an equivalent resistance of an AC network transformer, LacFor the purpose of changing from one to anotherEquivalent inductance between the device and the infinite system, RacIs the equivalent resistance from the converter to the infinite system, icdFor the d-axis component of the converter output current icqFor the converter output current q-axis component, ucdIs d-axis component, u, of the converter equivalent output voltagesdIs d-axis component of PCC bus voltage, omega 1 is rated angular frequency, ucqFor the q-axis component of the converter equivalent output voltage, usqIs the q-axis component of the PCC bus voltage, LgIs an equivalent inductance of an AC network, RgIs the equivalent resistance of the AC network, ugdD-axis component, u, of infinite system voltagegqThe d-axis component of the infinite system voltage.
13. The method of claim 11, the phase-locked loop dynamic mathematical model being:
wherein,
wherein, thetaPLLFor dynamically outputting phase, theta, to a phase-locked looppllFor phase-locked loop output phase thetaPLLAnd omega1Difference of t, ω1t is an initial phase of 0 at a constant angular velocity ω1Phase of rotating dq coordinate system, kp_pllFor phase-locked loop dynamic proportional integral controller proportionality coefficient, Ti_pllIntegrating time constant, u, for a phase locked loop dynamic proportional integral controllersqIs the q-axis component, ω, of the PCC bus voltage1Is the nominal angular velocity of dq coordinate system, s is the Laplace operator, GpllIs a proportional-integral controller for a phase-locked loop,the q-axis component of the equivalent output voltage of the converter in the dq coordinate system of the control system.
14. The system of claim 13, wherein the dynamic mathematical model of the phase-locked loop is designed to have a second-order response characteristic with a parameter calculation formula as follows:
wherein, ω ispllFor dynamically designing the bandwidth of the phase-locked loop, the damping ratio ξ is 0.707 usd0Is a steady-state value of the d-axis component of the PCC bus voltage.
15. The system of claim 11, the inner loop control mathematical model being:
wherein,
wherein,for reference values of the d-axis component of the inverter output voltage in the control system coordinate system,to control the reference value of the q-axis component of the inverter output voltage in the system coordinate system,to control the value of the d-axis component of the inverter output voltage in the system coordinate system,for controlling the value of the q-axis component of the converter output voltage in the system coordinate system, omegafIs the voltage filter bandwidth, TfIs the time constant of the voltage filter, omegaCLIs the inner loop bandwidth, kp_clIs the inner loop PI controller proportionality coefficient, Ti_clProportional coefficient, integral time constant, G, of inner loop controllerfIs a PCC bus voltage filter, GCLIs an inner ring proportional-integral controller,for reference values of the d-axis component of the inverter output current in the control system coordinate system,for reference values of the q-axis component of the inverter output current in the control system coordinate system,to control the value of the d-axis component of the inverter output current in the system coordinate system,for controlling the value of the q-axis component of the converter output current in the system coordinate system, omega1At a nominal angular frequency, LeqIs the equivalent inductance between the PCC bus and the converter valve side, s is the Laplace operator, ReqIs the equivalent resistance between the PCC bus and the converter valve side.
16. The system of claim 11, the mathematical model of the modulation process being:
wherein G isd＝e-sTd，TdFor the equivalent delay of the flexible-straight control system, ucdFor the AC side equivalent output of the converterD-axis component of the output voltage ucqFor the q-axis component of the equivalent output voltage at the AC side of the converter, udcIs a DC side voltage, Udc0Is a steady-state value of the DC side voltage, thetapllFor phase-locked loop output phase thetaPLLAnd omega1the difference between the values of t and t,is a reference value of the d-axis component of the inverter output voltage,reference value, G, for q-axis component of converter output voltagedIs a time delay simulation link.
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| CN114069705A (en) * | 2021-11-19 | 2022-02-18 | 西安交通大学 | Method and system for judging large disturbance stability of grid-connected voltage source type converter |
| CN114997505A (en) * | 2022-06-16 | 2022-09-02 | 华北电力大学 | Stability analysis method and system for grid-connected power supply through converter |
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| CN116595699A (en) * | 2023-07-18 | 2023-08-15 | 华北电力科学研究院有限责任公司 | Interactive processing method and device for power quality of converter and power distribution network |
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