CN106505563B - Toughness evaluation method for grid-connected converter under power grid fault - Google Patents

Toughness evaluation method for grid-connected converter under power grid fault Download PDF

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CN106505563B
CN106505563B CN201611097809.6A CN201611097809A CN106505563B CN 106505563 B CN106505563 B CN 106505563B CN 201611097809 A CN201611097809 A CN 201611097809A CN 106505563 B CN106505563 B CN 106505563B
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toughness
current
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CN106505563A (en
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黄萌
彭宇
刘浴霜
彭东东
孙建军
查晓明
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Wuhan University WHU
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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
    • 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
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]

Abstract

The invention provides a method for evaluating toughness indexes of a grid-connected converter under the condition of power grid faults, which comprises the following steps: a: establishing an expected accident set of the power system, judging the type of the fault, and designing a converter model meeting the performance index requirement; b: analyzing the response of the converter under the power grid fault, and respectively calculating a transmission curve of a current loop and a voltage loop stability criterion; c: calculating toughness boundary conditions of the converter about key parameters under power grid disturbance, so as to judge whether the converter can tolerate the fault type, and evaluating the toughness of the converter; d: when the converter has no fault tolerance capability, the initial design can be returned to repeatedly modify the converter parameters, and finally, a design scheme meeting the fault tolerance of the power grid can be obtained. On the basis that the converter meets the performance index requirement, the fault tolerance of the grid-connected converter is evaluated, a practical grid-connected converter toughness evaluation method is formed, and the grid-connected converter toughness evaluation method can be optimally designed.

Description

Toughness evaluation method for grid-connected converter under power grid fault
Technical Field
The invention relates to a method for evaluating a grid-connected converter, in particular to a method for evaluating the toughness of the grid-connected converter under the condition of power grid failure.
Background
With the wide application of alternating current and direct current hybrid systems such as new energy power generation, micro-grids and high-voltage direct current transmission, a power electronic converter device serving as a power exchange interface is gradually used in the field of power systems more and more due to the effects of stabilizing direct current bus voltage and reducing alternating current harmonic content. Among them, the three-phase Voltage Source Converter (VSC) has the advantages of high stability and controllable power factor, is widely used, and is a very representative interface converter device.
Because the grid-connected converter comprises a semiconductor switch with weak current processing capacity and the converter device control link and faults in the alternating current and direct current hybrid system have diversity, the response of the grid-connected converter to the grid faults is greatly different from that of the traditional motor, and different response behaviors can be generated by the difference of fault types, grid structures or fault positions. In addition, due to the nonlinearity introduced by Sinusoidal Pulse Width Modulation (SPWM) and a control loop in the converter, the system is easy to enter an abnormal working state.
However, in practical engineering applications, the grid-side fault usually affects the stable operation of the VSC to a large extent, and thus the grid has very strict requirements on the operation of the interface converter. Corresponding grid-connected guide rules are established for the grid-connected converter to be connected into a power grid in all countries in the world, however, the grid-connected guide rules do not provide any index requirements for the capability of the grid-connected converter to bear impact. In the existing literature, the research on the converter is mostly to research the steady state of the VSC under an ideal power grid and improve the system control method under a fault, so that few researches pay attention to the operation behavior of the VSC under the fault impact of the power grid. The method is characterized in that the stability of a converter small signal is analyzed under small disturbance, and a three-phase VSC system is analyzed by a large signal to study the nonlinear bifurcation phenomenon of the VSC, but the operation behavior of a grid-connected power electronic device during a grid fault period is not focused on, and an effective criterion cannot be provided from a design point of view to evaluate and design the capacity of the grid-connected converter for bearing grid fault impact.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a method for evaluating the toughness (responsiveness) of a grid-connected converter under the condition of a power grid fault. The method comprises the steps of taking the fault tolerance capability of a converter as a toughness evaluation index, judging whether the converter can ensure that power electronic devices are not damaged under the condition of sudden fault, and maintaining the operation of a system; the control loop of the converter is not affected by impact, and the normal working state is quickly recovered after the fault is over; still further, support is provided for the system to return to steady state.
A method for evaluating toughness of a grid-connected converter under a power grid fault is characterized by comprising the following steps:
step A, establishing an expected accident set of the power system, judging the type of the fault, and designing a converter model meeting the performance index requirements, wherein the method specifically comprises the following steps:
step A1: dividing a power grid expected accident set oriented to safety evaluation of a power electronic device, and judging the specific type of a fault, wherein the specific type of the fault is judged by firstly dividing power grid faults into overcurrent faults, overvoltage faults, frequency fluctuation faults, phase jump faults and zero sequence or negative sequence current mutation faults according to the influence of various typical faults on a working point of a converter, then dividing the power grid faults into transient faults and slowly changing faults in detail according to a working point change rule, and finally dividing the faults into instantaneous faults and permanent faults according to whether the faults can be automatically recovered or not;
step A2: under the condition of meeting the performance index requirements, determining key parameters of the converter, and preliminarily designing a reasonable three-phase voltage source type grid-connected converter model;
step B, analyzing the response of the converter under the power grid fault, and respectively calculating a transmission curve of a current loop and a voltage loop stability criterion, wherein the method specifically comprises the following steps:
step B1: showing a state equation after dq decoupling of the system, carrying out current inner loop analysis on the system, and calculating a current loop transmission curve so as to determine the voltage and current levels of the IGBT switching device; then when the equivalent resistance R of the inductorsWhen smaller, the system will output current ioBefore saturation, the system enters a nonlinear stage, the modulation ratio m of the system can be regarded as infinite, and the voltage v is controlleddAnd vqUp to its upper limit Vg,maxAt this time, the inner loop current idReach its critical value:
Figure GDA0002389152970000031
for any id,ref>id,criticalThe system is in an over-modulation state, the power factor of which is no longer unityA power factor;
inner loop current i in overmodulationdAbout id,refIs denoted as i in the description of the inventiond＝hd(id,ref) From this, the equation for the inner loop current with respect to the current reference value can be derived:
Figure GDA0002389152970000032
the d-axis current i can be plotted by the equation (2)dAnd a reference current id,refThe transfer relationship curve of (1);
step B2: according to a control block diagram of the system, voltage outer-loop analysis is carried out on the system, and voltage loop stability criterion is obtained, specifically, firstly, according to the control block diagram of the grid-connected system, a current reference value is given by the following equation:
id,ref＝gv(ev)＝kpev+ki∫evdt (3)
wherein e isv＝Vdc,ref-vdc；
The state equation of the voltage loop can be obtained by combining the system state equation and equation (5):
Figure GDA0002389152970000033
the characteristic equation of the outer ring voltage obtained after the linearization processing and the arrangement of the equation is as follows:
Figure GDA0002389152970000034
solving the voltage ring characteristic equation to obtain a root track of an outer ring voltage characteristic equation, and judging whether a system is stable according to whether a characteristic root is positioned on a right semi-plane in the root track, wherein the root track is a voltage ring stability criterion;
step C, calculating toughness boundary conditions of the converter about key parameters under power grid disturbance, so as to judge whether the converter can tolerate the fault type, and evaluating the toughness of the converter;
step D, after the evaluation of the toughness of the converter under the initial parameters in the step C, if the converter does not meet the toughness boundary conditions under the initial parameters, namely the converter does not have the fault tolerance capability, repeatedly modifying the voltage loop gain, the current loop gain and the direct current side capacitance parameters of the converter when returning to the initial converter model designed in the step A2, so that the voltage loop gain, the current loop gain and the direct current side capacitance parameters of the converter all meet the toughness boundary conditions of the converter, and a design scheme meeting the tolerance of the power grid fault is obtained;
b2: and according to a control block diagram of the system, carrying out voltage outer loop analysis on the system, and obtaining a voltage loop stability criterion.
According to the method, firstly, the toughness of the converter is defined as the fault tolerance capability of the converter, the transient response of the converter under the power grid fault is combined, and the toughness boundary condition of disturbance is analyzed and calculated by utilizing a current transmission curve and the stability of a voltage ring, so that the toughness of the converter is evaluated, and the evaluation result can be further applied to the design of a grid-connected converter device. Compared with the prior art, the method has the advantages that,
in the method for evaluating toughness of the grid-connected converter under the power grid fault, in the step C, derivation analysis of a converter toughness evaluation analytic equation and drawing of a converter toughness boundary curve are performed;
after the fault occurs, the energy equation and the energy loss expression on the capacitor and the full response equation on the capacitor can be listed according to the energy consumption on the capacitor, and the v in the fault time can be obtaineddcTransformation function v over timedc(t)；
The transformation function of the reference current with time in the fault time period can be obtained by combining the formula (5):
id,ref(t)＝gv(ev)＝gv(Vdc,ref-vdc(t)) (6)
therefore, an analytic equation for evaluating the toughness of the converter can be given:
Figure GDA0002389152970000041
wherein u is greater than 0, which indicates that the toughness of the converter can bear the fault; u <0, which indicates that the toughness of the converter can not bear the fault; and a converter toughness boundary curve taking a converter toughness key parameter as a coordinate system can be made through a converter toughness evaluation analytic equation.
The invention has the following advantages and beneficial effects: 1. and deducing a converter toughness evaluation analytic equation to judge the fault tolerance capability of the converter, providing a more visual basis for the stability analysis of the grid-connected converter system, and providing an important reference for improving the system stability. 2. The evaluation result can be applied to the design of the grid-connected converter device, and the toughness evaluation method can give certain guidance to the design of the grid-connected converter.
Drawings
Fig. 1 is a schematic flow diagram of toughness evaluation and design of a grid-connected converter under a power grid fault.
Fig. 2 is a topological structure diagram of a three-phase voltage source type converter of the invention.
Fig. 3 is a grid-connected converter double-loop control diagram.
FIG. 4 shows d-axis current i of the converter according to the present inventiondAnd a reference current id,refThe transmission curve of (1).
FIG. 5a shows the voltage loop gain kvpAnd the DC side capacitor C is used as a coordinate system to change the power loss equivalent resistance RsThe converter toughness boundary curve of (1).
FIG. 5b shows the voltage loop gain kvpAnd the DC side capacitor C is used as a coordinate system to change the load RLThe converter toughness boundary curve of (1).
FIG. 5c shows the voltage loop gain kvpAnd a load RLAnd changing a converter toughness boundary curve of the direct current side capacitor C as a coordinate system.
FIG. 5d shows the voltage loop gain kvpAnd a load RLFor coordinate system, changing power loss equivalent resistance RsThe toughness boundary curve diagram 5e of the converter is that the DC bus voltage C and the negative voltageR carriesLAnd as a coordinate system, varying the voltage loop gain kvpThe converter toughness boundary curve of (1).
FIG. 5f shows the DC bus voltage C and the load RLAnd as a coordinate system, changing the power loss equivalent resistance RsThe converter toughness boundary curve of (1).
Fig. 6 is a power grid simulation system including a three-phase voltage source type converter built in the invention.
Detailed Description
The technical solution of the present invention will be clearly and completely described below with reference to the accompanying drawings.
Fig. 1 is a schematic flow chart showing toughness evaluation and design of a grid-connected converter under a power grid fault, and the method comprises the following steps:
a: establishing an expected accident set of the power system, judging the fault type, and designing a converter model meeting the performance index requirements, wherein the step A specifically comprises the following steps:
a1: dividing a power grid expected accident set facing the safety assessment of the power electronic device: the method comprises the steps of dividing power grid faults into overcurrent faults, overvoltage faults, frequency fluctuation faults, phase jump faults and zero sequence or negative sequence current sudden change faults according to the influence of various typical faults on working points of a converter, dividing the power grid faults into transient faults and slowly changing faults in detail according to the change rule of the working points, and dividing the faults into instantaneous faults and permanent faults according to whether the faults can be automatically recovered or not, so that the specific types of the faults are judged. The power grid forecast accident division oriented to the safety evaluation of the power electronic device is shown in table 1;
TABLE 1 grid forecast Accident partitioning for Power electronic device Security assessment
Figure GDA0002389152970000061
A2: under the condition of meeting the performance index requirements, determining key parameters of the converter, and preliminarily designing a reasonable three-phase voltage source type grid-connected converter model;
b: analyzing the response of the converter under the power grid fault, and respectively calculating a transmission curve of a current loop and a voltage loop stability criterion, wherein the step B specifically comprises the following steps:
b1: and (4) showing a state equation after the dq decoupling of the system, carrying out current inner loop analysis on the system, and calculating a current loop transmission curve so as to determine the voltage and current levels of the IGBT switching device.
Firstly, according to the topology structure diagram of the three-phase voltage source converter shown in fig. 2, a mathematical model of the three-phase voltage source converter in an abc three-phase coordinate system can be obtained by using a switch average model:
Figure GDA0002389152970000062
Figure GDA0002389152970000063
according to the synchronous rotating coordinate function, the VSC is converted into a dq rotating coordinate system, and the state equation is as follows:
Figure GDA0002389152970000064
Figure GDA0002389152970000065
Figure GDA0002389152970000071
when the inductance equivalent resistance RsWhen smaller, the system will output current ioBefore saturation, the system enters a nonlinear stage, the modulation ratio m of the system can be regarded as infinite, and the voltage v is controlleddAnd vqReaching its upper limit:
Figure GDA0002389152970000072
at this time, the inner loop current idReach its critical value:
Figure GDA0002389152970000073
for any id,ref>id,criticalThe system is in an over-modulation state, where the power factor is no longer unity. Thus, to find the current loop transfer curve, the expression of the inner loop current with respect to the reference current needs to be considered in segments.
When the converter enters a stable working state, the error amount of the control loop accounts for the leading part of the control voltage, and the following steps are carried out:
Figure GDA0002389152970000074
as can be deduced from the equations (13) and (15), when the modulation ratio m > 1 is determined in the dq synchronous rotation coordinate system, the control voltage v isd,qSaturation value to be reached:
Figure GDA0002389152970000075
Figure GDA0002389152970000076
the differential value is set to zero according to the equations (10) and (11) of the system state equation, and the control voltage v can be obtainedd,qThe saturation value of (c) also satisfies the formula:
vd,saturated＝ωlLiq-Rsid+vd(17)
vq,saturated＝-ωlLid-Rsiq+vq(18)
then the combined type (16) - (19) can obtain the inner ring current i under the overmodulation stated、iqAbout id,refIs described in (1). Because its expression is complicated, it is abbreviated here as equation id＝hd(id,ref) And iq＝hq(id,ref) From which an inner ring can be obtainedEquation for current with respect to current reference:
Figure GDA0002389152970000077
Figure GDA0002389152970000081
from the power balance equation, the current transmission equation under steady state can be obtained, and in order to simplify the equation, the system loss only considers the inductance equivalent resistance part:
Pload＝Pinput-Ploss(20)
Figure GDA0002389152970000082
the d-axis current i can be plotted by the equation (2)dAnd a reference current id,refThe transfer relationship of (2) is as shown in fig. 4. According to the transfer relation curve, the reference current i is related tod,refIncrease of d-axis current idAnd then increases and reaches a maximum value, which is then inversely proportional to the reference current. D-axis current i can be calculated by differentiating the formula (2)dMaximum value:
id,max＝hd(h'd(id,ref)＝0) (22)
from the d-axis current maximum, the ac current maximum amplitude can be known, and then the voltage and current levels of the IGBT switching devices that can withstand the fault can be determined.
B2: according to the double-loop control block diagram of the system, as shown in fig. 3, voltage outer loop analysis is performed on the system, and voltage loop stability criteria are obtained.
According to a control block diagram of a grid-connected system, a current reference value is given by the following equation:
id,ref＝gv(ev) (25)
ev＝Vdc,ref-vdc(26)
gv(ev)＝kpev+ki∫evdt (27)
the state equation of the voltage loop can be obtained by combining the equations (10) (2) (21) (25):
Figure GDA0002389152970000083
and (3) carrying out linearization processing on the equation to obtain a small signal model:
Figure GDA0002389152970000084
wherein v isdcCan be approximated by Vdc,refAccording to the formula
Figure GDA0002389152970000085
It is possible to obtain:
Figure GDA0002389152970000091
the characteristic equation for the outer loop voltage is:
Figure GDA0002389152970000092
solving the voltage ring characteristic equation can obtain the root track of the outer ring voltage characteristic equation, and judging whether the system is stable according to whether a characteristic root is positioned on the right semi-plane in the root track.
C: and calculating toughness boundary conditions of the converter about key parameters under the power grid disturbance, so as to judge whether the converter can tolerate the fault type and evaluate the toughness of the converter.
Firstly, according to an energy equation and an energy loss expression on the capacitor and a full response equation on the capacitor, v in fault time can be obtaineddcConverting a function along with time, then, deriving a converter toughness evaluation analytical equation, and determining a disturbed toughness boundary condition through the positive and negative properties of a converter toughness evaluation analytical expression, therebyAnd judging whether the converter can bear the fault or not by the self toughness performance.
After the fault occurs, the voltage v on the grid-connected sidesdThe reduction in active power results in a loss of active power that cannot meet the power demand of the load, and energy is dissipated in the capacitor to compensate for the loss. The energy equation on the capacitance can be listed as:
Figure GDA0002389152970000093
wherein Vdc0Representing the time t when the fault occurs0Amplitude of the DC voltage at a time, Vdc1Representing the end of the fault t1Amplitude of the direct voltage at time, ElossAccumulation of fault time for active power loss.
According to the fault process analysis, the voltage v on the grid-connected side can be knownsdIt will fall to near 0V in a very short time, and for the sake of simplicity, it can be regarded as t0Instantaneously dropping to 0V, the energy loss can be expressed as:
Eloss＝vsdid(t1-t0) (26)
wherein the grid side voltage vsdAnd t when d-axis currents are all faults0The voltage, current, i.e. the amplitude at which the value is steady state, at the moment.
According to the full response equation on the capacitance, there are:
Figure GDA0002389152970000094
the simultaneous equations (32) - (34) can be used to derive the time of failure vdcA transformation function over time.
Then the transformation function of the reference current over time during the fault period can be derived from equation (25):
id,ref(t)＝gv(ev)＝gv(Vdc,ref-vdc(t)) (6)
therefore, an analytic equation for evaluating the toughness of the converter can be given:
Figure GDA0002389152970000101
wherein u is>0, the toughness of the converter can bear the fault; and u<And 0, indicating that the toughness of the converter can not bear the fault. Through a converter toughness evaluation analytical equation, when the fault depth is 60% and the fault duration is 50ms, the voltage loop gain k can be usedvpLoad RLPower loss equivalent resistance RsAnd the toughness critical parameters of the converter, such as the dc bus voltage C, are toughness boundary curves of the converter in a coordinate system, as shown in fig. 5a to 5 f.
D: when the converter has no fault tolerance capability, the initial design can be returned to repeatedly modify the converter parameters, and finally, a design scheme meeting the fault tolerance of the power grid can be obtained.
To further illustrate the correctness of the toughness evaluation method of the current transformer, in an MATLAB/simulink simulation platform, a transformer, a power supply and an impedance module build a three-phase alternating current power grid system shown in fig. 6, wherein the system comprises a public power grid (equivalently, a voltage source), a transmission line (comprising line impedance), a circuit breaker, a non-ideal transformer, buses of each level, a three-phase voltage source current transformer to be researched, other local loads (equivalently, constant power loads) and the like, wherein the three-phase voltage source current transformer shown in fig. 2 is built by adopting a general bridge circuit, and voltage and current double-loop control shown in fig. 3 is built. The three-phase voltage source type converter parameters are shown in table 2.
TABLE 2 three-phase voltage source type converter parameters
Figure GDA0002389152970000102
The response of the system is simulated and verified by cycle-by-cycle simulation, the variation trend of the toughness of the converter can be analyzed by the simulation waveform by changing the toughness key parameter of the converter, and the influence of the parameter change on the toughness of the converter is shown in table 3. The fault tolerance degrees of the converter are different when different design parameters are adopted, and the results in the table 3 are consistent with the toughness boundary curve result of the converter drawn by the toughness evaluation analytic equation of the converter, so that the correctness of the toughness evaluation method of the grid-connected converter under the grid fault is verified.
TABLE 3 Effect of parameter changes on converter toughness
Figure GDA0002389152970000111
The toughness evaluation of the grid-connected converter under the power grid fault can be further applied to the design process of the converter, if the converter which is initially designed does not meet the requirement of the impact resistance of the converter, designers can return to the initial design to modify data, and finally a design scheme of the grid-connected converter meeting the requirement of the power grid fault can be provided through the design iteration process.
The above description is only an embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (1)

1. A method for evaluating toughness of a grid-connected converter under a power grid fault is characterized by comprising the following steps:
a: establishing an expected accident set of the power system, judging the fault type, and designing a converter model meeting the performance index requirements, wherein the step A specifically comprises the following steps:
a1: dividing a power grid expected accident set facing the safety assessment of the power electronic device: firstly, dividing power grid faults into overcurrent faults, overvoltage faults, frequency fluctuation faults, phase jump faults and zero sequence or negative sequence current sudden change faults according to the influence of various typical faults on working points of a converter, dividing the faults into transient faults and slowly-changing faults in detail according to the change rule of the working points, and finally dividing the faults into instantaneous faults and permanent faults according to whether the faults can be automatically recovered or not so as to judge the specific types of the faults; the power grid forecast accident division oriented to the safety evaluation of the power electronic device is shown in table 1;
TABLE 1 grid forecast Accident partitioning for Power electronic device Security assessment
Figure FDA0002389152960000011
A2: under the condition of meeting the performance index requirements, determining key parameters of the converter, and preliminarily designing a reasonable three-phase voltage source type grid-connected converter model;
b: analyzing the response of the converter under the power grid fault, and respectively calculating a transmission curve of a current loop and a voltage loop stability criterion, wherein the step B specifically comprises the following steps:
b1: showing a state equation after the dq decoupling of the system, carrying out current inner loop analysis on the system, and calculating a current loop transmission curve so as to determine the voltage and current levels of the IGBT switching device;
firstly, according to a topological structure diagram of the three-phase voltage source converter, a switch average model is adopted, so that a mathematical model of the three-phase voltage source converter under an abc three-phase coordinate system can be obtained:
Figure FDA0002389152960000012
Figure FDA0002389152960000013
according to the synchronous rotating coordinate function, the VSC is converted into a dq rotating coordinate system, and the state equation is as follows:
Figure FDA0002389152960000021
Figure FDA0002389152960000022
Figure FDA0002389152960000023
when the inductance equivalent resistance RsWhen smaller, the system will output current ioBefore saturation, the system enters a nonlinear stage, the modulation ratio m of the system can be regarded as infinite, and the voltage v is controlleddAnd vqReaching its upper limit:
Figure FDA0002389152960000024
at this time, the inner loop current idReach its critical value:
Figure FDA0002389152960000025
for any id,ref>id,criticalThe system is in an overmodulation state, and the power factor of the system is no longer the unit power factor; therefore, in order to obtain a current loop transmission curve, the expression of the inner loop current with respect to the reference current needs to be considered in a segmented manner;
when the converter enters a stable working state, the error amount of the control loop accounts for the leading part of the control voltage, and the following steps are carried out:
Figure FDA0002389152960000026
as can be deduced from the equations (6) and (8), when the system modulation ratio m > 1 is determined in the dq synchronous rotation coordinate system, the control voltage v isd,qSaturation value to be reached:
Figure FDA0002389152960000027
Figure FDA0002389152960000028
and according to the formulas (3) and (4) of the system state equation, making the system state equation be microThe value is zero, and the control voltage v can be obtainedd,qThe saturation value of (c) also satisfies the formula:
vd,saturated＝ωlLiq-Rsid+vd(11)
vq,saturated＝-ωlLid-Rsiq+vq(12)
then the combined type (9) - (12) can obtain the inner ring current i under the overmodulation stated、iqAbout id,refThe expression of (1); because its expression is complicated, it is abbreviated here as equation id＝hd(id,ref) And iq＝hq(id,ref) From this, the equation for the inner loop current with respect to the current reference value can be derived:
Figure FDA0002389152960000031
Figure FDA0002389152960000032
from the power balance equation, the current transmission equation under steady state can be obtained, and in order to simplify the equation, the system loss only considers the inductance equivalent resistance part:
Pload＝Pinput-Ploss(15)
Figure FDA0002389152960000033
the d-axis current i can be plotted from equation (13)dAnd a reference current id,refAccording to the transfer relation curve of (1), the transfer relation curve is known to follow the reference current id,refIncrease of d-axis current idThen increases and reaches a maximum value, and then is inversely proportional to the reference current; d-axis current i can be calculated by taking the derivative of the formula (13)dMaximum value:
id,max＝hd(h'd(id,ref)＝0) (17)
according to the maximum value of the d-axis current, the maximum amplitude of the alternating current can be known, and then the voltage and current grade of the IGBT switching device capable of bearing the fault can be determined;
b2: according to a double-loop control block diagram of the system, voltage outer loop analysis is carried out on the system, and voltage loop stability criteria are obtained;
according to a control block diagram of a grid-connected system, a current reference value is given by the following equation:
id,ref＝gv(ev) (18)
ev＝Vdc,ref-vdc(19)
gv(ev)＝kpev+ki∫evdt (20)
the state equation of the voltage loop can be obtained by combining the equations (3), (13), (14) and (18):
Figure FDA0002389152960000034
and (3) carrying out linearization processing on the equation to obtain a small signal model:
Figure FDA0002389152960000041
wherein v isdcCan be approximated by Vdc,refAccording to the formula
Figure FDA0002389152960000042
It is possible to obtain:
Figure FDA0002389152960000043
the characteristic equation for the outer loop voltage is:
Figure FDA0002389152960000044
solving the voltage ring characteristic equation to obtain a root track of an outer ring voltage characteristic equation, and judging whether the system is stable according to whether a characteristic root is positioned on a right semi-plane or not in the root track;
c: calculating toughness boundary conditions of the converter about key parameters under power grid disturbance, so as to judge whether the converter can tolerate the fault type, and evaluating the toughness of the converter;
firstly, according to an energy equation and an energy loss expression on the capacitor and a full response equation on the capacitor, v in fault time can be obtaineddcA converter toughness evaluation analytical equation is then deduced according to a transformation function of time, and then the toughness boundary condition of disturbance is determined according to the positive and negative properties of a converter toughness evaluation analytical expression, so that whether the converter can bear the fault or not is judged;
after the fault occurs, the voltage v on the grid-connected sidesdThe reduction of (2) causes active power loss, the power requirement of the load cannot be met, and the energy on the capacitor is consumed to supplement the loss; the energy equation on the capacitance can be listed as:
Figure FDA0002389152960000045
wherein Vdc0Representing the time t when the fault occurs0Amplitude of the DC voltage at a time, Vdc1Representing the end of the fault t1Amplitude of the direct voltage at time, ElossAccumulation of fault time for active power loss;
according to the fault process analysis, the voltage v on the grid-connected side can be knownsdIt will fall to near 0V in a very short time, and for the sake of simplicity, it can be regarded as t0Instantaneously dropping to 0V, the energy loss can be expressed as:
Eloss＝vsdid(t1-t0) (26)
wherein the grid side voltage vsdAnd t when d-axis currents are all faults0The voltage and current at the moment, namely the amplitude values of the voltage and the current at the steady state;
according to the full response equation on the capacitance, there are:
Figure FDA0002389152960000051
the simultaneous equations (25) - (27) can be used to derive the time of failure vdcA transformation function over time;
then the transformation function of the reference current over time during the fault period can be derived from equation (18):
id,ref(t)＝gv(ev)＝gv(Vdc,ref-vdc(t)) (28)
therefore, an analytic equation for evaluating the toughness of the converter can be given:
Figure FDA0002389152960000052
wherein u is>0, the toughness of the converter can bear the fault; and u<0, indicating that the toughness of the converter can not bear the fault; through the toughness evaluation analytical equation of the converter, the method can be used for working out the condition that the fault depth is 60 percent, the fault duration is 50ms, and the voltage loop gain k is includedvpLoad RLPower loss equivalent resistance RsThe converter toughness key parameter of the direct-current bus voltage C is a converter toughness boundary curve of a coordinate system;
d: when the converter has no fault tolerance capability, the initial design can be returned to repeatedly modify the converter parameters, and a design scheme meeting the fault tolerance of the power grid can be finally obtained;
in order to further explain the correctness of the toughness evaluation method of the converter, in an MATLAB/simulink simulation platform, a transformer, a power supply and an impedance module build a three-phase alternating current network system, wherein the system comprises a public power grid, a transmission line, a circuit breaker, a non-ideal transformer, buses at all levels and a three-phase voltage source converter to be researched, a universal bridge circuit is adopted to build the three-phase voltage source converter, and voltage and current double-loop control is built; the three-phase voltage source type converter parameters are shown in table 2;
TABLE 2 three-phase voltage source type converter parameters
Figure FDA0002389152960000053
The response of the system is simulated and verified by cycle-by-cycle simulation, the variation trend of the toughness of the converter can be analyzed by a simulation waveform by changing the toughness key parameter of the converter, and the influence of the parameter change on the toughness of the converter is shown in a table 3; the fault tolerance degrees of the converter are different when different design parameters are adopted, and the results in the table 3 are consistent with the toughness boundary curve result of the converter drawn by the toughness evaluation analytic equation of the converter, so that the correctness of the toughness evaluation method of the grid-connected converter under the power grid fault is verified;
TABLE 3 Effect of parameter changes on converter toughness
Figure FDA0002389152960000061
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