CN114709873A - Small interference stability judging method for grid-connected voltage source type current converter with phase-locked loop - Google Patents

Small interference stability judging method for grid-connected voltage source type current converter with phase-locked loop Download PDF

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CN114709873A
CN114709873A CN202210439528.3A CN202210439528A CN114709873A CN 114709873 A CN114709873 A CN 114709873A CN 202210439528 A CN202210439528 A CN 202210439528A CN 114709873 A CN114709873 A CN 114709873A
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phase
voltage source
grid
axis
locked loop
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翁华
华凤林
朱维骏
张雨萌
郁丹
陆艺源
郭雨涵
李宇骏
唐人
吴君
何勇玲
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Xian Jiaotong University
Zhejiang Huayun Electric Power Engineering Design Consulting Co
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Zhejiang Huayun Electric Power Engineering Design Consulting Co
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/36—Arrangements for transfer of electric power between ac networks via a high-tension dc link
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
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Abstract

The invention discloses a method for judging the small interference stability of a grid-connected voltage source converter with a phase-locked loop, which comprises the steps of firstly establishing a mathematical model of a VSC (voltage source converter) containing a PLL (phase locked loop) connected to an infinite system through a power transmission line; then obtaining a steady state equation of the system and solving a balance point of the system; then, carrying out linearization processing on a system mathematical model, and obtaining a frequency domain equation through Laplace transformation; carrying out simplification processing to obtain a Single Input Single Output (SISO) model; and finally, deriving the essential conditions for stabilizing the grid-connected voltage source type converter with the phase-locked loop according to the classical Laus criterion, thereby obtaining simplified sufficient conditions. The invention clearly represents the analytic relationship between the grid-connected VSC small disturbance stability and the VSC controller parameters, the line parameters and the system operation mode; the method can be used for qualitatively analyzing key factors influencing the stability of the system, revealing a system instability mechanism, and guiding parameter design of the VSC controller and system operation mode formulation.

Description

Small interference stability judging method for grid-connected voltage source type current converter with phase-locked loop
Technical Field
The invention belongs to the technical field of electric power, and particularly relates to a method for judging the small interference stability of a grid-connected Voltage Source Converter (VSC) with a phase-locked loop (PLL).
Background
A grid-connected Voltage Source Converter (VSC) is widely used for renewable energy power generation and High Voltage Direct Current (HVDC) transmission, and a Phase-locked loop (PLL) is mostly used to obtain accurate Phase angle information of a Point of Common Coupling (PCC) for ensuring that a converter Voltage is synchronized with a grid Voltage. Many prior art documents indicate that the dynamic characteristics of the PLL have a negative impact on system stability.
The traditional method for researching the small interference stability of the system is mainly a modal analysis method, and a rough stable boundary of the system is described by calculating all characteristic values of the linear dynamic system near a plurality of key working points. However, system modal analysis usually relies on complex numerical modal calculations, is time consuming, and cannot physically explain how instability phenomena are triggered. In order to overcome the defects of the classical modal analysis method, an impedance model-based analysis (IMA) method is widely applied to checking the small interference stability of a system, and the core idea is to judge whether the impedance ratio of two series subsystems meets the nyquist stability standard. Recently, passivity-based methods have been used to verify system small interference stability. If the real part of the system's eigenfunction is positive at any angular frequency, the dynamic system remains stable.
Existing stability decisions rely on eigenvalue calculations or nyquist plots involving many complex and repetitive numerical calculations, and with these methods, even if system power transmission limits or controller parameter ranges that can ensure system stability are available, no analytical relationship can be established between control parameters, system operating points, and system stability.
Disclosure of Invention
The invention aims to solve the technical problem that the defects in the prior art are overcome, and provides a method for judging the small interference stability of a grid-connected voltage source type current converter with a phase-locked loop, wherein a SISO (single input single output) model between the small disturbance of the d-axis component of the reference current of a phase reactor and the small disturbance of the x-axis component of the current of the phase reactor is established by utilizing the steady-state relation between a linearized system model and variables, and the analytic stable condition of a research system is obtained based on the classical Laus criterion; the stability of the system is judged by analyzing the stable condition through simple calculation, and the unstable mechanism of the system can be well disclosed and researched.
The invention adopts the following technical scheme:
a method for judging the small interference stability of a grid-connected voltage source type current converter with a phase-locked loop comprises the following steps:
s1, establishing a mathematical model that a voltage source type converter with a phase-locked loop is connected to an infinite system through a power transmission line;
s2, obtaining a steady state equation of the infinite system according to the step S1, and calculating to obtain a steady state operating point of the infinite system;
s3, carrying out linearization processing on the VSC grid-connected system model according to the steady-state operating point obtained in the step S2, and obtaining a frequency domain equation through Laplace transformation;
s4, based on the disturbed dynamic multi-time scale characteristic of the voltage source type converter with the phase-locked loop and the control characteristic of the voltage source type converter with the phase-locked loop, simplifying the frequency domain equation of the step S3 to obtain a simplified model;
s5, obtaining a single-input single-output model according to the simplified model in the step S4;
s6, according to the single-input single-output model obtained in the step S5, deriving the essential conditions for small interference stability of the grid-connected voltage source type converter with the phase-locked loop according to the classic Laus criterion;
and S7, obtaining a grid-connected VSC stability index related to the q-axis inner loop current control time constant and the PLL time constant by obtaining a simplified stability sufficient condition by neglecting line resistance according to the sufficient condition obtained in the step S6, wherein when the grid-connected VSC stability index is larger than a set value, the grid-connected VSC has small interference stability.
Specifically, in step S1, the mathematical model of the voltage source converter with the phase-locked loop connected to the infinite system via the power transmission line is specifically:
Figure BDA0003614526510000031
Figure BDA0003614526510000032
Figure BDA0003614526510000033
Figure BDA0003614526510000034
Figure BDA0003614526510000035
Figure BDA0003614526510000036
Figure BDA0003614526510000037
Figure BDA0003614526510000038
wherein the content of the first and second substances,
Figure BDA0003614526510000039
and
Figure BDA00036145265100000310
are the components in the x-y coordinate system of the inverter and PCC point voltages respectively,
Figure BDA00036145265100000311
and
Figure BDA00036145265100000312
component R in d-q coordinate system of converter and PCC point voltagecAnd LcRespectively the resistance and the inductance of the phase reactor,
Figure BDA00036145265100000313
representing the components in the x-y coordinate system of the current through the phase reactor,
Figure BDA00036145265100000314
representing the component, ω, of the d-q coordinate system of the current through the phase reactorsIn order to synchronize the rotational speeds of the rotors,
Figure BDA00036145265100000315
and
Figure BDA00036145265100000316
respectively corresponding current control reference values, RlAnd LlIs the resistance and the inductance of the line,
Figure BDA00036145265100000317
representing the components in the x-y coordinate system of the infinite voltage source voltage with an initial phase angle of zero,
Figure BDA00036145265100000318
representing the components in the d-q coordinate system of an infinite voltage source voltage with an initial phase angle of zero,
Figure BDA00036145265100000319
and
Figure BDA00036145265100000320
proportional coefficients and integral coefficients of the d-axis and q-axis are controlled for the inner loop current respectively,
Figure BDA0003614526510000041
and
Figure BDA0003614526510000042
is the proportional coefficient and integral coefficient of the PLL, x is the state variable of the PLL control, ω is the PLL rotation speed, and θ is the angle by which the d axis leads the x axis.
Specifically, in step S2, the steady-state equation of the infinite system is specifically:
Figure BDA0003614526510000043
Figure BDA0003614526510000044
Figure BDA0003614526510000045
Figure BDA0003614526510000046
Figure BDA0003614526510000047
Figure BDA0003614526510000048
Figure BDA0003614526510000049
Figure BDA00036145265100000410
Figure BDA00036145265100000411
wherein the content of the first and second substances,
Figure BDA00036145265100000412
and
Figure BDA00036145265100000413
steady state values of the components in the x-y coordinate system of the inverter and PCC point voltages respectively,
Figure BDA00036145265100000414
is a component steady state value under the x-y coordinate system of the current flowing through the phase reactor,
Figure BDA00036145265100000415
is a component steady state value under an x-y coordinate system of infinite voltage source voltage with an initial phase angle of zero,
Figure BDA00036145265100000416
Figure BDA00036145265100000417
and
Figure BDA00036145265100000418
component steady-state values under a d-q coordinate system of the converter and the PCC point voltage respectively,
Figure BDA00036145265100000419
is a component steady-state value T under an infinite voltage source voltage d-q coordinate system with an initial phase angle of zero(0)The initial value of the rotation matrix is the initial value,
Figure BDA00036145265100000420
for the steady state values of the components in the d-q coordinate system of the current through the phase reactor,
Figure BDA00036145265100000421
is a rotation matrix derived from the steady state values,
Figure BDA00036145265100000422
and
Figure BDA00036145265100000423
respectively corresponding current control reference values.
Specifically, in step S3, the frequency domain equation of the linearization system is:
Figure BDA00036145265100000424
Figure BDA00036145265100000425
Figure BDA0003614526510000051
Figure BDA0003614526510000052
Figure BDA0003614526510000053
Figure BDA0003614526510000054
wherein the content of the first and second substances,
Figure BDA0003614526510000055
respectively the amount of change of the x-y axis component of the inverter voltage,
Figure BDA0003614526510000056
respectively the variation of the x-y axis component of the PCC point voltage, s is a complex variable, RcAnd LcRespectively the resistance and the inductance of the phase reactor,
Figure BDA0003614526510000057
respectively, the variation of the x-y axis component of the current flowing through the phase reactor, RlAnd LlRespectively the resistance and the inductance of the line, and delta theta is the variable quantity of the angle of the x axis ahead of the d axis, T(0)Is the initial value of the rotation matrix,
Figure BDA0003614526510000058
is the steady state value of the x-y axis component of the PCC point voltage,
Figure BDA0003614526510000059
in order to be the amount of variation,
Figure BDA00036145265100000510
respectively the amount of change of the d-q axis component of the inverter voltage,
Figure BDA00036145265100000511
for steady state values of the d-q axis components of the converter voltage,
Figure BDA00036145265100000512
for steady state values of the d-q axis component of the current through the phase reactor,
Figure BDA00036145265100000513
respectively the amount of change in the d-q axis component of the current flowing through the phase reactor,
Figure BDA00036145265100000514
for controlling the magnitude of the change in the reference value of the current, Ad(s)、AqAnd(s) is a matrix parameter.
Specifically, step S4 specifically includes:
and (4) regarding the output of power outer loop control of the voltage source type converter with the phase-locked loop as constant, controlling the voltage source type converter with the phase-locked loop by adopting a unit power factor, keeping the reactive power exchanged with a power grid at a PCC point as zero, setting PI parameters for d-axis and q-axis inner loop current control, neglecting the resistance of a phase reactor, and simplifying the frequency domain equation of the step S3 to obtain a simplified model.
Further, the simplified model is:
Figure BDA0003614526510000061
wherein D is11(s)、D12(s)、D21(s)、D22(s) are the matrix parameters, respectively,
Figure BDA0003614526510000062
respectively the amount of change of the x-y axis component of the current flowing through the phase reactor,
Figure BDA0003614526510000063
respectively, the amount of change in the d-q axis component of the current control reference value flowing through the phase reactor.
Further, PI parameters for controlling the d-axis and q-axis inner ring currents are specifically as follows:
Figure BDA0003614526510000064
wherein σdAnd σqAre the time constants for the d-axis and q-axis inner loop current control,
Figure BDA0003614526510000065
and
Figure BDA0003614526510000066
proportional and integral coefficients, R, for the inner loop current control d and q axes, respectivelycAnd LcRespectively the resistance and inductance of the phase reactor.
Specifically, in step S5, the single-input single-output model specifically includes:
Figure BDA0003614526510000067
wherein D is11(s)、D12(s)、D21(s)、D22(s), G(s) are matrix parameters, up(0)Is the steady state value of the PCC point voltage, theta(0)Is the steady state value of d axis leading x axis angle, s is the complex variable, sigmadAnd σqIs the time constant, ω, of the d-and q-axis inner loop current controlsFor synchronizing the rotational speeds, LlIs a line inductance, RlAs a result of the resistance of the line,
Figure BDA0003614526510000068
is the steady state value of the d-axis component of the current through the phase reactor.
Specifically, in step S6, the essential conditions for stabilizing the small disturbance of the grid-connected voltage source converter with the phase-locked loop are as follows:
Figure BDA0003614526510000069
wherein k is a Laus criterion discriminant coefficient,
Figure BDA00036145265100000610
for the integral coefficient of the PLL, r is the judgment of the Laus criterionThe right root of the equation.
Specifically, in step S7, the simplified stability sufficiency condition is:
Figure BDA0003614526510000071
wherein σPLLIs the time constant of PLL, sigma is the stability index of grid-connected VSC, theta(0)Is a steady state value, omega, of d axis leading x axis anglesIs the synchronous speed.
Compared with the prior art, the invention has at least the following beneficial effects:
the invention relates to a method for judging the small interference stability of a grid-connected voltage source type converter with a phase-locked loop, wherein a research model is that a single VSC is connected to an infinite bus model through a transmission line, a single-input single-output (SISO) transfer function is established between small disturbance of a phase reactor reference current d-axis component and small disturbance of a phase reactor current x-axis component based on a derived linearized model and the steady-state relation of each variable, a stable analytic essential condition of a system is derived by using a classical labor criterion based on the SISO model, and a simplified sufficient condition is further derived; the stability of the system can be judged through simple quantitative calculation under the proposed analysis stability condition; revealing a system instability mechanism; the analytic relation among the VSC controller parameters, the electrical distance between the VSC and the infinite system and the system running mode is reflected, and the VSC controller parameter selection is guided.
Further, with the development of new energy, a large number of power generation devices connected by a converter are connected to a power system, and according to the current research, stability analysis can be performed based on a mathematical model that the VSC including the phase-locked loop in step S1 of the present invention is connected to an infinite system through a power transmission line.
Further, in step S2, a steady state value of the system state quantity may be obtained by solving a steady state equation of the system, which lays a foundation for further linearization at the equilibrium point.
Furthermore, the time domain equation is converted into a frequency domain equation through Laplace transform, and the system performance can be indirectly analyzed without solving a differential equation.
Further, based on the dynamic multi-time scale characteristic of the VSC after being disturbed and the control characteristic of the VSC, the linearization model in the step S3 is simplified, factors which have negligible influence on stability analysis are eliminated, and analysis is greatly simplified.
Furthermore, the PI parameter setting of d-axis and q-axis inner ring current control accords with the actual condition of the power system, and model simplification is facilitated according to the quick inner ring current response characteristic of the VSC.
Further, by constructing the SISO model, the input-output stability of the system under study can be based on
Figure BDA0003614526510000081
And
Figure BDA0003614526510000082
the transfer function between the two is judged, and a foundation is laid for deducing the stability of the researched system through the Laus criterion.
Further, the essential condition for the stability of the grid-connected voltage source type converter with the phase-locked loop is directly obtained according to the classical Laus criterion of the three-order linear system, and the theory is strict.
Furthermore, the essential condition for stabilizing the VSC is obtained on the basis of the sufficient condition, and the essential condition is concise and direct and is convenient for determining key factors influencing the stability of the system.
In conclusion, the grid-connected VSC small interference stability criterion with the PLL establishes a simple analytic relationship between system stability and key factors, and can be used for qualitative and quantitative analysis of the system stability and guiding parameter design of a VSC controller and formulation of a system operation mode.
The technical solution of the present invention is further described in detail by the accompanying drawings and embodiments.
Drawings
FIG. 1 is a flow chart of the present invention;
fig. 2 is a circuit diagram of a VSC connected to an infinite system via a transmission line;
FIG. 3 is a graph of the relationship between space vector coordinates;
FIG. 4 is a block diagram of a transfer function of a phase locked loop;
fig. 5 is a graph of a dynamic response simulation result of VSCs under different reference powers.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, not all, embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
In the description of the present invention, it should be understood that the terms "comprises" and/or "comprising" indicate the presence of the stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof.
It is also to be understood that the terminology used in the description of the invention herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. As used in the specification of the present invention and the appended claims, the singular forms "a," "an," and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise.
It should be further understood that the term "and/or" as used in this specification and the appended claims refers to any and all possible combinations of one or more of the associated listed items, and including such combinations, e.g., a and/or B, may mean: a exists alone, A and B exist simultaneously, and B exists alone. In addition, the character "/" herein generally indicates that the former and latter related objects are in an "or" relationship.
It should be understood that although the terms first, second, third, etc. may be used to describe preset ranges, etc. in embodiments of the present invention, these preset ranges should not be limited to these terms. These terms are only used to distinguish preset ranges from each other. For example, the first preset range may also be referred to as a second preset range, and similarly, the second preset range may also be referred to as the first preset range, without departing from the scope of the embodiments of the present invention.
The word "if" as used herein may be interpreted as "at … …" or "when … …" or "in response to a determination" or "in response to a detection", depending on the context. Similarly, the phrases "if determined" or "if detected (a stated condition or event)" may be interpreted as "when determined" or "in response to a determination" or "when detected (a stated condition or event)" or "in response to a detection (a stated condition or event)", depending on the context.
Various structural schematics according to the disclosed embodiments of the invention are shown in the drawings. The figures are not drawn to scale, wherein certain details are exaggerated and possibly omitted for clarity of presentation. The shapes of various regions, layers and their relative sizes and positional relationships shown in the drawings are merely exemplary, and deviations may occur in practice due to manufacturing tolerances or technical limitations, and a person skilled in the art may additionally design regions/layers having different shapes, sizes, relative positions, according to actual needs.
The invention provides a method for judging the small interference stability of a grid-connected voltage source type converter with a phase-locked loop, and provides sufficient conditions and simplified sufficient conditions for the small interference stability of the voltage source type converter with the phase-locked loop. Firstly, establishing a mathematical model of VSC (voltage source converter) containing PLL (phase locked loop) connected to an infinite system through a power transmission line; then obtaining a steady state equation of the system and solving a balance point of the system according to a control target; then, simplifying the system mathematical model; further obtaining a SISO model; then, deriving a necessary condition for stabilizing the VSC with the PLL according to a classic Laus criterion; finally, a simplified stability sufficient condition is obtained by neglecting line resistance, a grid-connected VSC stability index related to a q-axis inner loop current control time constant and a PLL time constant is obtained, and when the index is larger than a certain specific value, the small interference stability of the grid-connected VSC can be guaranteed.
Referring to fig. 1, the method for determining the small interference stability of a grid-connected voltage source converter with a phase-locked loop according to the present invention includes the following steps:
s1, establishing a Voltage Source Converter (VSC) with a Phase Locked Loop (PLL) and accessing the VSC to a mathematical model of an infinite system through a power transmission line;
referring to fig. 2, a network equation of the VSC connected to the infinite system via the transmission line in the d-q coordinate system is:
Figure BDA0003614526510000101
referring to FIG. 3, the x-y reference frame converted to angular velocity rotation is transformed by constant power Park to obtain
Figure BDA0003614526510000102
Figure BDA0003614526510000103
Wherein the content of the first and second substances,
Figure BDA0003614526510000104
(2) the variables in (1) and (3) are further derived into a d-q rotating system
Figure BDA0003614526510000111
Wherein the content of the first and second substances,
Figure BDA0003614526510000112
the control equation for the phase reactor current control is as follows:
Figure BDA0003614526510000113
referring to fig. 4, the dynamic equation of the PLL is as follows:
Figure BDA0003614526510000114
Figure BDA0003614526510000115
wherein the content of the first and second substances,
Figure BDA0003614526510000116
and
Figure BDA0003614526510000117
are the components in the x-y coordinate system of the inverter and PCC point voltages respectively,
Figure BDA0003614526510000118
and
Figure BDA0003614526510000119
component R in d-q coordinate system of converter and PCC point voltagecAnd LcRespectively the resistance and the inductance of the phase reactor,
Figure BDA00036145265100001110
representing the components in the x-y coordinate system of the current through the phase reactor,
Figure BDA00036145265100001111
representing the components in the d-q coordinate system of the current through the phase reactor,
Figure BDA00036145265100001112
and
Figure BDA00036145265100001113
respectively corresponding current control reference values, RlAnd LlIs the resistance and the inductance of the line,
Figure BDA00036145265100001114
representing the components in the x-y coordinate system of the infinite voltage source voltage with an initial phase angle of zero,
Figure BDA00036145265100001115
representing the components of an infinite voltage source voltage d-q coordinate system with an initial phase angle of zero, the d-q coordinate system and the x-y coordinate system being at angular velocities ω and ω, respectivelysRotating counterclockwise, the d axis leads the x axis by theta degrees,
Figure BDA00036145265100001116
and
Figure BDA00036145265100001117
proportional coefficients and integral coefficients of the d-axis and q-axis are controlled for the inner loop current respectively,
Figure BDA00036145265100001118
and
Figure BDA00036145265100001119
are the proportional and integral coefficients of the PLL, and x is the state variable controlled by the PLL.
S2, obtaining a steady state equation of the infinite system according to the step S1, and calculating to obtain a balance point (steady state operation point) of the infinite system;
steady state values of the variables were obtained from the expressions (2) to (7).
The system steady state equation is described as follows:
Figure BDA0003614526510000121
Figure BDA0003614526510000122
Figure BDA0003614526510000123
wherein the content of the first and second substances,
Figure BDA0003614526510000124
Figure BDA0003614526510000125
Figure BDA0003614526510000126
equations (8) and (9) are left-multiplied by T(0)To obtain
Figure BDA0003614526510000127
Figure BDA0003614526510000128
Where the subscript (0) of a variable indicates its steady state or equilibrium value.
(8) The steady state relationships between variables are described in (14), which is very helpful to simplify the SISO model of the system in the next step.
S3, carrying out linearization processing on the VSC grid-connected system model according to the balance point obtained in the step S2, and obtaining a frequency domain equation through Laplace transformation;
linearizing (2) to (7) around the equilibrium point, and performing laplace transform on the linearized equation to obtain a frequency domain equation as follows:
Figure BDA0003614526510000131
Figure BDA0003614526510000132
Figure BDA0003614526510000133
Figure BDA0003614526510000134
Figure BDA0003614526510000135
Figure BDA0003614526510000136
wherein the content of the first and second substances,
Figure BDA0003614526510000137
Figure BDA0003614526510000138
s4, simplifying the frequency domain equation in the step S3 based on the disturbed dynamic multi-time scale characteristic of the VSC and the control characteristic of the VSC to obtain a simplified model;
for simplifying the analysis, the VSC grid-connected system under study is assumed:
1) since the response speed of the VSC external power supply control is typically much slower than the response speed of the internal current control loop and PLL, the output of the VSC's power outer loop control is considered constant in the stability analysis;
2) the VSC adopts classical unit power factor control, reactive power exchanged with a power grid at a PCC point is kept to be zero, and the PCC point is a common connection point of the VSC and an alternating current system;
3) PI parameters for controlling the d-axis and q-axis inner loop currents are set according to the following rules;
Figure BDA0003614526510000141
wherein σdAnd σqThe time constants of the d-axis and q-axis inner loop current control reflect the response speed of the VSC inner loop current control.
4) Neglecting the phase reactor resistance;
the steady state active and reactive power at the PCC point is denoted as Pc(0)And Qc(0)；
Figure BDA0003614526510000142
Combining (10), (14) and (24) at the designation Pc(0)And Qc(0)U, bp(0)And theta(0)Solving the following nonlinear equation yields:
Figure BDA0003614526510000143
Figure BDA0003614526510000144
and
Figure BDA0003614526510000145
calculated by (24).
Under unity power factor control, Qc(0)0, the following expression is obtained from (12) and (24):
Figure BDA0003614526510000146
combining (24) and (25) to obtain,
Figure BDA0003614526510000147
based on (10), (14), and (27), the following equation is obtained.
Figure BDA0003614526510000151
Figure BDA0003614526510000152
Figure BDA0003614526510000153
In summary, the simplified model is specifically:
Figure BDA0003614526510000154
Figure BDA0003614526510000155
wherein σdAnd σqAre the time constants for the d-axis and q-axis inner loop current control,
Figure BDA0003614526510000156
Figure BDA0003614526510000157
s5, obtaining a Single Input Single Output (SISO) model according to the simplified model in the step S4;
combining (17), (21) and (22),
Figure BDA0003614526510000158
Figure BDA0003614526510000159
substituting (17) to (19) into (20) based on (26), and eliminating
Figure BDA0003614526510000161
And
Figure BDA0003614526510000162
to obtain
Figure BDA0003614526510000163
Based on (23), using the steady state relationship in (13), substituting (15) into (33), eliminating
Figure BDA0003614526510000164
And
Figure BDA0003614526510000165
(33) the method is simplified as follows:
Figure BDA0003614526510000166
substitution of (16) into (31) the Erase variable
Figure BDA0003614526510000167
And
Figure BDA0003614526510000168
then (31) is substituted into (34) to eliminate the variable delta theta, then
Figure BDA0003614526510000169
And
Figure BDA00036145265100001610
the transfer function between is formulated as follows:
Figure BDA00036145265100001611
Figure BDA00036145265100001612
according to (26) and (35), inGiven the
Figure BDA00036145265100001613
Can be based on
Figure BDA00036145265100001614
And
Figure BDA00036145265100001615
the transfer function between them to determine the input/output stability of the system under study.
The single-input single-output (SISO) model is specifically:
Figure BDA0003614526510000171
substituting (28), (29), and (32) into (36), and writing the denominator of (36) as:
D(s)＝(1+sσd)Dr(s) (37)
Figure BDA0003614526510000172
wherein σdAnd σqAre the time constants for the d-axis and q-axis inner loop current control,
Figure BDA0003614526510000173
Figure BDA0003614526510000174
the stability of the system is determined by determining (37) the sign of the root. Assuming that the d-q axis inner loop current control is stable, i.e. sigmadAnd σqIs positive. Regardless of the positive root (fixed modality) in (37), system stability is determined only by the sign of the root in (38).
S6, according to the single-input single-output (SISO) model obtained in the step S5, deriving a sufficient condition for stabilizing a grid-connected Voltage Source Converter (VSC) with a phase-locked loop (PLL) according to a classical Laus criterion;
according to the classic Laus criterion of a three-order linear system, the essential condition for system stability is that the following three inequality constraints are met:
σq>0 (39)
Figure BDA0003614526510000175
Figure BDA0003614526510000181
obviously, (39) naturally holds, and (40) holds if (42) is satisfied.
k>0 (42)
By setting the appropriate sigmaqLet (42) hold at any operating point.
Therefore, the stability of the VSC grid-connected system is completely determined by (41).
Equation (41) is written as:
Figure BDA0003614526510000182
to pair
Figure BDA0003614526510000183
Differentiating to obtain:
Figure BDA0003614526510000184
equation (44) shows the function
Figure BDA0003614526510000185
Is monotonically increasing; to satisfy the constraint of inequality (43) to ensure stable operation of the VSC,
Figure BDA0003614526510000186
greater than the right root of the function (noted
Figure BDA0003614526510000187
) I.e. by
Figure BDA0003614526510000188
In summary, the essential conditions for stabilizing the grid-connected voltage source type converter with the phase-locked loop are as follows:
Figure BDA0003614526510000189
wherein the content of the first and second substances,
Figure BDA00036145265100001810
Figure BDA0003614526510000191
Figure BDA0003614526510000192
and S7, obtaining a grid-connected VSC stability index related to the q-axis inner loop current control time constant and the PLL time constant by neglecting the line resistance according to the sufficient conditions obtained in the step S6, and ensuring the small interference stability of the grid-connected VSC when the index is larger than a certain specific value.
Will generally be σqA few milliseconds is set to ensure a fast inner loop current response of the VSC. Thus, for a VSC-coupled generator integrated into a high voltage power transmission system (e.g. 220kV), the following inequality is fulfilled:
Figure BDA0003614526510000193
based on (47), the following expression is obtained
Figure BDA0003614526510000194
Figure BDA0003614526510000195
Based on (48) and (49), obtaining
Figure BDA0003614526510000196
Based on (45), (46) and (50) to obtain
Figure BDA0003614526510000197
Thus, sufficient conditions to obtain simplified VSC stabilization are as follows:
Figure BDA0003614526510000198
wherein, σ is definedPLLIs the time constant of the PLL.
For the renewable energy sources connected to the power grid through the high-voltage transmission line, compared with line reactance, the line resistance is omitted, and the simplified stability sufficiency conditions are as follows:
Figure BDA0003614526510000201
wherein σPLLIs the time constant of the PLL and is,
Figure BDA0003614526510000202
and sigma is a stability index of the grid-connected VSC.
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. The components of the embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations. Thus, the following detailed description of the embodiments of the present invention, presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be obtained by a person skilled in the art without making any creative effort based on the embodiments in the present invention, belong to the protection scope of the present invention.
The characteristic values of three types of VSC models are shown in the following table, wherein the full-order model is described by (2) to (7), the SISO model is described by (36), and the analytic model is based on the model (38) with the line resistance omitted.
TABLE 1
Figure BDA0003614526510000203
Figure BDA0003614526510000211
In the full-order model, λ5And λ6Both close to-10.47, corresponding to the two eigenvalues eliminated in the SISO model proposed by the invention and in the analytical model based on (22), respectively; lambda [ alpha ]4～λ6Only with the control parameters of the VSC, independent of the operating point; lambda [ alpha ]1And λ2Is a pair of dominant eigenvalues and the stability of the system is only determined by λ1And λ2The sign of the real part of (a). When the power generation amount of the renewable energy source is increased and the power generation amount is 140MW, lambda is1And λ2The real part of (a) is positive. Lambda of SISO model and full order model1And λ2Almost the same, which indicates that the SISO model ensures higher computational accuracy.
In addition, in the proposed analytical model in which the line resistance is neglected, λ1And λ2Real part assemblyThe real part of the model is larger than that of the full-order model, so that the analytic model provided by the invention can generate an unstable phenomenon earlier than the full-order model along with the increase of renewable power generation. This demonstrates well the conservation of the simplified sufficiency conditions.
Referring to fig. 5, the dynamic response of VSCs at different reference powers is described. As shown in fig. 5(a) and (b), as the amount of renewable energy generation increases, the active power of the VSC and the amplitude of the voltage at the PCC point gradually increase, but the oscillation frequency is the same, indicating that the oscillation frequency of the dynamic system under study is almost independent of the system operating point and almost completely determined by the PI parameter of the PLL.
As shown in fig. 5(c), when the renewable power generation amount suddenly increases to 120MW, the active power from VSC in the analytic model will exhibit divergent oscillations, and the full-order model can be stable at this time, which verifies the conservatism of the analytic model ignoring the line resistance.
As shown in FIG. 5(d), σPLLThe oscillation of active power can be effectively inhibited. In addition, the oscillation frequency is dependent on
Figure BDA0003614526510000212
The value decreases.
As shown in fig. 5(e), with LlIncrease of VSC, and at L, the active power amplitude of the VSC increaseslStarting at 1pu appears as a divergent oscillation, which indicates that an increase in electrical distance severely degrades the small disturbance stability of the VSC.
In conclusion, the method for judging the small interference stability of the grid-connected voltage source type converter with the phase-locked loop has the advantages that the given criterion theory of the small interference stability of the VSC with the PLL is rigorous, concise and intuitive, and the concise analytic relation between the system stability and the system working point, the electrical distance and the control parameters of the VSC is established, so that the method can be used for guiding the parameter design of the VSC controller and the system operation mode formulation.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The above-mentioned contents are only for illustrating the technical idea of the present invention, and the protection scope of the present invention is not limited thereby, and any modification made on the basis of the technical idea of the present invention falls within the protection scope of the claims of the present invention.

Claims (10)

1. The method for judging the small interference stability of the grid-connected voltage source type current converter with the phase-locked loop is characterized by comprising the following steps of:
s1, establishing a mathematical model that a voltage source type converter with a phase-locked loop is connected to an infinite system through a power transmission line;
s2, obtaining a steady state equation of the infinite system according to the step S1, and calculating to obtain a steady state operation point of the infinite system;
s3, carrying out linearization processing on the VSC grid-connected system model according to the steady-state operating point obtained in the step S2, and obtaining a frequency domain equation through Laplace transformation;
s4, based on the disturbed dynamic multi-time scale characteristic of the voltage source type converter with the phase-locked loop and the control characteristic of the voltage source type converter with the phase-locked loop, simplifying the frequency domain equation of the step S3 to obtain a simplified model;
s5, obtaining a single-input single-output model according to the simplified model in the step S4;
s6, according to the single-input single-output model obtained in the step S5, deriving a necessary condition for stabilizing small interference of the grid-connected voltage source converter with the phase-locked loop according to a classical Laus criterion;
and S7, obtaining a grid-connected VSC stability index related to the q-axis inner loop current control time constant and the PLL time constant by neglecting the line resistance according to the sufficient conditions obtained in the step S6, wherein when the grid-connected VSC stability index is larger than a set value, the grid-connected VSC has small interference stability.
2. The method for judging the small interference stability of the grid-connected voltage source converter with the phase-locked loop according to claim 1, wherein in the step S1, the mathematical model that the voltage source converter with the phase-locked loop is connected to an infinite system through a power transmission line specifically comprises the following steps:
Figure FDA0003614526500000021
Figure FDA0003614526500000022
Figure FDA0003614526500000023
Figure FDA0003614526500000024
Figure FDA0003614526500000025
Figure FDA0003614526500000026
Figure FDA0003614526500000027
Figure FDA0003614526500000028
wherein the content of the first and second substances,
Figure FDA0003614526500000029
and
Figure FDA00036145265000000210
are the components in the x-y coordinate system of the inverter and PCC point voltages respectively,
Figure FDA00036145265000000211
and
Figure FDA00036145265000000212
component R in d-q coordinate system of converter and PCC point voltagecAnd LcRespectively the resistance and the inductance of the phase reactor,
Figure FDA00036145265000000213
representing the components in the x-y coordinate system of the current through the phase reactor,
Figure FDA00036145265000000214
representing the component, ω, of the d-q coordinate system of the current through the phase reactorsIn order to synchronize the rotational speeds of the rotors,
Figure FDA00036145265000000215
and
Figure FDA00036145265000000216
respectively corresponding current control reference values, RlAnd LlIs the resistance and the inductance of the line,
Figure FDA00036145265000000217
representing the components in the x-y coordinate system of the infinite voltage source voltage with an initial phase angle of zero,
Figure FDA00036145265000000218
representing the components in the d-q coordinate system of an infinite voltage source voltage with an initial phase angle of zero,
Figure FDA00036145265000000219
and
Figure FDA00036145265000000220
proportional coefficients and integral coefficients of the d-axis and q-axis are controlled for the inner loop current respectively,
Figure FDA00036145265000000221
and
Figure FDA00036145265000000222
is proportional coefficient and integral coefficient of PLL, x is state variable controlled by PLL, omega is rotation speed of PLL, theta is angle of d axis before x axis.
3. The method for judging the small interference stability of the grid-connected voltage source converter with the phase-locked loop according to claim 1, wherein in the step S2, the steady-state equation of the infinite system is specifically as follows:
Figure FDA0003614526500000031
Figure FDA0003614526500000032
Figure FDA0003614526500000033
Figure FDA0003614526500000034
Figure FDA0003614526500000035
Figure FDA0003614526500000036
Figure FDA0003614526500000037
Figure FDA0003614526500000038
Figure FDA0003614526500000039
wherein the content of the first and second substances,
Figure FDA00036145265000000310
and
Figure FDA00036145265000000311
steady state values of the components in the x-y coordinate system of the inverter and PCC point voltages respectively,
Figure FDA00036145265000000312
is a component steady state value under the x-y coordinate system of the current flowing through the phase reactor,
Figure FDA00036145265000000313
is a component steady state value under an x-y coordinate system of infinite voltage source voltage with an initial phase angle of zero,
Figure FDA00036145265000000314
Figure FDA00036145265000000315
and
Figure FDA00036145265000000316
component steady-state values under a d-q coordinate system of the converter and the PCC point voltage respectively,
Figure FDA00036145265000000317
is a component steady-state value T under an infinite voltage source voltage d-q coordinate system with an initial phase angle of zero(0)The initial value of the rotation matrix is the initial value,
Figure FDA00036145265000000318
for the steady state values of the components in the d-q coordinate system of the current through the phase reactor,
Figure FDA00036145265000000319
is a rotation matrix derived from the steady state values,
Figure FDA00036145265000000320
and
Figure FDA00036145265000000321
respectively corresponding current control reference values.
4. The method for determining the small interference stability of the grid-connected voltage source converter with the phase-locked loop according to claim 1, wherein in the step S3, the frequency domain equation of the linearization system is as follows:
Figure FDA00036145265000000322
Figure FDA00036145265000000323
Figure FDA00036145265000000324
Figure FDA0003614526500000041
Figure FDA0003614526500000042
Figure FDA0003614526500000043
wherein the content of the first and second substances,
Figure FDA0003614526500000044
respectively the amount of change of the x-y axis component of the inverter voltage,
Figure FDA0003614526500000045
respectively the variation of the x-y axis component of the PCC point voltage, s is a complex variable, RcAnd LcRespectively the resistance and the inductance of the phase reactor,
Figure FDA0003614526500000046
respectively, the variation of the x-y axis component of the current flowing through the phase reactor, RlAnd LlRespectively the resistance and the inductance of the line, and delta theta is the variable quantity of the angle of the x axis ahead of the d axis, T(0)Is the initial value of the rotation matrix,
Figure FDA0003614526500000047
is the steady state value of the x-y axis component of the PCC point voltage,
Figure FDA0003614526500000048
in order to be the amount of variation,
Figure FDA0003614526500000049
respectively the amount of change of the d-q axis component of the inverter voltage,
Figure FDA00036145265000000410
for steady state values of the d-q axis components of the converter voltage,
Figure FDA00036145265000000411
for steady state values of the d-q axis component of the current through the phase reactor,
Figure FDA00036145265000000412
are respectively provided withFor the amount of change in the d-q axis component of the current flowing through the phase reactor,
Figure FDA00036145265000000413
for controlling the magnitude of the change in the reference value of the current, Ad(s)、AqAnd(s) is a matrix parameter.
5. The method for judging the small interference stability of the grid-connected voltage source converter with the phase-locked loop according to claim 1, wherein the step S4 specifically comprises the following steps:
and (4) regarding the output of the power outer ring control of the voltage source type converter with the phase-locked loop as constant, controlling the voltage source type converter with the phase-locked loop by adopting a unit power factor, keeping the reactive power exchanged with a power grid at a PCC point to be zero, setting PI (proportional integral) parameters of the d-axis and q-axis inner ring current control, neglecting the resistance of a phase reactor, and simplifying the frequency domain equation of the step S3 to obtain a simplified model.
6. The method for judging the small interference stability of the grid-connected voltage source converter with the phase-locked loop according to claim 5, wherein the simplified model is as follows:
Figure FDA0003614526500000051
wherein D is11(s)、D12(s)、D21(s)、D22(s) are the matrix parameters, respectively,
Figure FDA0003614526500000052
respectively the amount of change of the x-y axis component of the current flowing through the phase reactor,
Figure FDA0003614526500000053
respectively, the amount of change in the d-q axis component of the current control reference value flowing through the phase reactor.
7. The method for judging the small interference stability of the grid-connected voltage source converter with the phase-locked loop according to claim 5, wherein the PI parameters for controlling the d-axis inner loop current and the q-axis inner loop current are specifically as follows:
Figure FDA0003614526500000054
wherein σdAnd σqAre the time constants for the d-axis and q-axis inner loop current control,
Figure FDA0003614526500000055
and
Figure FDA0003614526500000056
proportional and integral coefficients, R, for the inner loop current control d and q axes, respectivelycAnd LcRespectively the resistance and inductance of the phase reactor.
8. The method for determining the small interference stability of the grid-connected voltage source converter with the phase-locked loop according to claim 1, wherein in the step S5, the single-input single-output model specifically comprises:
Figure FDA0003614526500000057
wherein D is11(s)、D12(s)、D21(s)、D22(s), G(s) are matrix parameters, up(0)Is the steady state value of the PCC point voltage, theta(0)Is the steady state value of d axis leading x axis angle, s is the complex variable, sigmadAnd σqIs the time constant, ω, of the d-and q-axis inner loop current controlsFor synchronizing the rotational speeds, LlIs a line inductance, RlIn order to be the resistance of the line,
Figure FDA0003614526500000058
is the steady state value of the d-axis component of the current through the phase reactor.
9. The method for determining the small interference stability of the grid-connected voltage source converter with the phase-locked loop according to claim 1, wherein in step S6, the essential conditions for the small interference stability of the grid-connected voltage source converter with the phase-locked loop are as follows:
Figure FDA0003614526500000059
wherein k is a Laus criterion discriminant coefficient,
Figure FDA00036145265000000510
and r is the right root of the Laus criterion discriminant equation, which is the integral coefficient of the PLL.
10. The method for determining the small disturbance stability of the grid-connected voltage source converter with the phase-locked loop according to claim 1, wherein in step S7, a simplified stability sufficient bar ω is providedsThe parts are as follows:
Figure FDA0003614526500000061
wherein σPLLIs the time constant of PLL, sigma is the stability index of grid-connected VSC, theta(0)Is a steady state value, omega, of d axis leading x axis anglesIs the synchronous speed.
CN202210439528.3A 2022-04-25 2022-04-25 Small interference stability judging method for grid-connected voltage source type current converter with phase-locked loop Pending CN114709873A (en)

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