CN113552430B - Method and device for judging transient stability of converter based on critical index - Google Patents
Method and device for judging transient stability of converter based on critical index Download PDFInfo
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Abstract
The invention discloses a method and a device for judging transient stability of a converter based on a critical index, wherein the method comprises the following steps: selecting an indicator related to transient stability of the converter as a function of one or more variables related to the converter; substituting one or more variables into the function to obtain the current value of the index; comparing the current value of the index with the critical value of the index; and judging the transient stability of the converter according to the comparison result. The device comprises: the system comprises an index establishing unit, an index current value calculating unit, a comparing unit and a result judging unit, wherein the index establishing unit, the index current value calculating unit, the comparing unit and the result judging unit are used for realizing the method. The method and the device for judging the transient stability of the converter based on the critical index have the characteristics of simple criterion, high accuracy, strong universality for different fault types and high applicability for different converter control modes.
Description
Technical Field
The invention relates to the technical field of power electronics, in particular to a method and a device for judging transient stability of a converter based on a critical index.
Background
The proportion of new energy power generation represented by wind-solar power sources in a power system rises year by year, and a three-phase voltage source converter is an interface between the asynchronous machine power sources and an alternating current power grid; on the other hand, with the rapid development of dc transmission and micro-grids, such converters play an increasingly important role in power systems. This requires that the converter is able to provide support to the grid as much as possible after a transient in the grid, reducing power shortage, and not be able to get off the grid, shutting down as ever.
During transients, the converter will face two problems, namely fault ride-through and transient stability. The fault ride-through can ensure that the converter is not over-voltage or over-current during the fault as much as possible, and simultaneously provides support for a fault power grid; the transient stability is the guarantee of fault ride-through, and if the converter is unstable after transient, the converter can lose control and cannot execute fault ride-through, and meanwhile serious accidents such as power oscillation, direct-current voltage breakdown and the like can also occur.
Transient instability of the converter occurs in low voltage ride through research of the fan at the earliest, and when the voltage of the alternating current power grid is low, the phase-locked loop of the wind turbine generator grid side converter can lose lock. Phase-locked loop loss of lock is an important cause of converter instability under large disturbances. Research in the last ten years can analyze the destabilization mechanism of the phase-locked loop under large disturbance clearly, but no mature method can accurately and effectively judge the transient stability of the phase-locked loop at present because the phase-locked loop has a nonlinear link. Considering the similarity of the dynamic equation of the phase-locked loop and the motion equation of the rotor of the synchronous machine, the transient stability of the phase-locked loop is researched by a literature by means of an equal area method, the energy function and the fault limit cutting time when the proportional gain of the PI controller of the phase-locked loop is not considered are deduced, and a quantitative method for judging the transient stability of the phase-locked loop is provided accordingly. However, more intensive studies have found that the neglected proportional gain is in some cases equivalent to a considerable damping, and in other cases equivalent to a negative damping, resulting in the current decision method being practically unreliable, with the result being sometimes conservative and sometimes too optimistic.
On the other hand, a class of converters without phase-locked loops has been proposed in recent years, and is called a networking-type control converter, because it simulates the synchronization of a synchronous machine with a power grid, wherein the most representative converter adopts virtual synchronous control. Needless to say, the transient destabilization mechanism of this converter is similar to that of a synchronous machine, but it can be quite conservative if the transient stability determination is still made using the equal area method. The reason for this is that the design damping coefficient is far greater than the inertia coefficient, just contrary to synchronous machines, because the power of the converter cannot be frequently fluctuated in parameter design. Therefore, no better transient stability determination method for a virtual synchronous control converter has been proposed so far.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a method and a device for judging the transient stability of a converter based on a critical index, which can obtain the judging result of the transient stability of the converter by calculating one or more index values in the converter and comparing the index values with the critical index, and has the characteristics of simple criterion, high accuracy, strong universality for different fault types and high applicability for different converter control modes.
In order to solve the technical problems, the invention is realized by the following technical scheme:
the invention provides a method for judging transient stability of a converter based on a critical index, which comprises the following steps:
s11: selecting an indicator related to transient stability of a converter, the indicator being a function of one or more variables related to the converter;
s12: substituting the one or more variables in the S11 into the function to obtain the current value of the index;
s13: comparing the current value of the index in the step S12 with a critical value of the index;
s14: and judging the transient stability of the converter according to the comparison result of the S13.
Preferably, the converter is a three-phase voltage source converter, and works in a rectifying or inverting state; and/or the number of the groups of groups,
the converter includes: and the output of the angle generating unit is an angle which is used as the reference voltage or the reference current of the alternating current side of the converter.
Preferably, the variables include: three-phase voltages of the AC side grid-connected point of the converter; and/or the number of the groups of groups,
an output angle of the angle generating unit; further, the method comprises the steps of,
the index comprises: positive sequence component amplitude of three-phase voltage of an alternating current side power grid of the converter; and/or the number of the groups of groups,
an energy function of the angle generating unit.
Preferably, the threshold value of the index includes: critical positive sequence voltage amplitude; and/or critical energy.
The critical positive sequence voltage amplitude is a bifurcation point;
the bifurcation point represents an abnormal bifurcation occurring under the critical positive sequence voltage amplitude when manifold shapes of two unstable balance points adjacent to the stable balance point are changed along with the change of the positive sequence voltage amplitude in a dynamic system of a phase-locked loop of the converter.
Preferably, the construction method of the energy function comprises the following steps:
s61: the angle generating unit and the closed loop thereof are written in the form of a second-order dynamic equation:
s62: neglecting f 1 Delta-containing term in (1), ignoring f 2 If not, skipping, thereby yielding a new dynamic equation:
s63: constructing an energy function:
V(δ,x)＝F 1 (x)–F 2 (δ)+V 0
wherein F is 1 (x) Is f 1 (x) Is the primary function of F 2 (delta) is f 2 Primitive function of (delta), V 0 Is any real number.
Preferably, if the angle generating unit of the converter is a phase locked loop, a first variable δ of the energy function is a difference between an output angle of the phase locked loop and a voltage angle of an ac side grid of the converter, and a second variable x is an integrator state of a PI controller of the phase locked loop;
if the angle generating unit is a virtual synchronous control, the first variable delta of the energy function is the difference between the output angle of the virtual synchronous control and the voltage angle of the ac side grid of the converter, and the second variable x is the difference between the internal frequency of the virtual synchronous control and the compensation frequency.
Preferably, the method for calculating the critical energy is as follows: critical energy equal to V (delta) c 0), wherein delta c In the dynamic system of the phase-locked loop, the output angle of the phase-locked loop corresponding to the unstable balance point closest to the stable balance point is the difference between the output angle of the phase-locked loop and the voltage angle of the alternating-current side power grid of the converter.
Preferably, the transient stability determination result in S14 is: the converter is transient stable or the converter is at risk of transient instability.
Preferably, the index includes a plurality of;
firstly, judging the transient stability of the converter by using one of the indexes, and continuously judging the transient stability of the converter by using the other index when the judging result is that the converter is at risk of transient instability, thereby proceeding.
The invention also provides a device for judging the transient stability of the converter based on the critical index, which is used for realizing the method for judging the transient stability of the converter based on the critical index, and comprises the following steps: the device comprises an index establishing unit, an index current value calculating unit, a comparing unit and a result judging unit; wherein,,
the index establishing unit is used for selecting an index related to transient stability of the converter, wherein the index is a function of one or more variables related to the converter;
the index current value calculation unit is used for substituting the one or more variables in the index establishment unit into the function to obtain the current value of the index;
the comparison unit is used for comparing the current value of the index in the index current value calculation unit with the critical value of the index;
the result judging unit is used for judging the transient stability of the converter according to the comparison result of the comparing unit.
Compared with the prior art, the invention has the following advantages:
(1) According to the method and the device for judging the transient stability of the converter based on the critical index, provided by the invention, only the corresponding variable size in the index is required to be acquired in real time, the specific form of the fault is not required to be concerned, the time cost and the algorithm difficulty caused by fault identification are reduced, and the method and the device are suitable for almost all alternating current fault types;
(2) According to the method and the device for judging the transient stability of the converter based on the critical index, provided by the invention, the method for obtaining the index is simply and quickly realized by substituting the method into a formula for calculation and comparing to obtain a judging result, and can be used for on-line judgment;
(3) The method and the device for judging the transient stability of the converter based on the critical index can be expanded in stages, can overcome the conservation of the current judging method as much as possible when the converter is judged in a combined mode according to a certain order, and have higher accuracy on the judging result of the transient stability of the converter;
(4) The method and the device for judging the transient stability of the converter based on the critical index are suitable for the converter with the phase-locked loop, are suitable for the virtual synchronous control converter without the phase-locked loop, the former is the main stream of the converter in the current power system, and the latter is the most important one of the converters without the phase-locked loop, so that the method and the device have the advantages of strong universality and wide application range.
Of course, it is not necessary for any one product to practice the invention to achieve all of the advantages set forth above at the same time.
Drawings
Embodiments of the present invention are further described below with reference to the accompanying drawings:
FIG. 1 is a flow chart of a method for determining transient stability of a converter based on a threshold according to an embodiment of the invention;
FIG. 2 is a flow chart of a method for determining transient stability of a converter based on a threshold according to a preferred embodiment of the invention;
FIG. 3 is a schematic diagram illustrating a converter and a grid-connected system thereof according to an embodiment of the present invention;
FIG. 4 is a method for obtaining critical positive sequence voltage amplitude according to a preferred embodiment of the present invention;
FIG. 5a is a schematic diagram illustrating a stable domain of a dynamic equation of a phase locked loop before a different-dormitory bifurcation occurs in a phase plane according to an embodiment of the present invention;
FIG. 5b is a stable domain of a dynamic equation of a phase locked loop after the phase plane is branched off;
fig. 5c shows the stability domain of the phase-locked loop dynamic equation according to an embodiment of the present invention estimated by using the energy function on the phase plane.
Detailed Description
The following describes in detail the examples of the present invention, which are implemented on the premise of the technical solution of the present invention, and detailed embodiments and specific operation procedures are given, but the scope of protection of the present invention is not limited to the following examples.
Fig. 1 is a flowchart of a method for determining transient stability of a converter based on a threshold according to an embodiment of the invention.
Referring to fig. 1, the method for determining transient stability of a converter according to the present embodiment includes the following steps:
s11: selecting an indicator related to transient stability of the converter as a function of one or more variables related to the converter;
s12: substituting one or more variables in S11 into the function to obtain the current value of the index;
s13: comparing the current value of the index in S12 with the critical value of the index;
s14: and judging the transient stability of the converter according to the comparison result of the S13.
In a preferred embodiment, the converter is a three-phase voltage source converter, operating in a rectifying or inverting state; and/or the converter comprises: and an angle generation unit that outputs an angle as an angle for a reference voltage or a reference current on the ac side of the inverter. Further, the variables include: three-phase voltage of the AC side grid-connected point of the converter; and/or an output angle of the angle generating unit. Further, the index includes: positive sequence component amplitude of three-phase voltage of ac side grid of converter; and/or an energy function of the angle generating unit. Further, the threshold values of the index include: critical positive sequence voltage amplitude; and/or critical energy.
In one embodiment, a three-phase voltage source type converter with a phase locked loop is described as an example.
Referring to fig. 3, the converter and the grid-connected system of the present embodiment include: a three-phase voltage source type converter, a power grid equivalent circuit and a converter control part. The ac side of the converter is provided with a filter circuit, and then is connected with an ac power grid through an ac side grid connection point. The alternating current power grid adopts a Thevenin equivalent circuit, and the equivalent voltage phasor is U g The line impedance is Z g . For the control part, the angle generating unit of the converter in the figure is a phase-locked loop, and the input of the phase-locked loop is the voltage U of the AC side grid-connected point s The output is the angle theta controlled by the converter, and the output of the integrator of the phase-locked loop PI controller is x; the current controller adopts vector control and controls the output current I of the converter under the coordinate system of theta s Always follow its reference value I s,ref 。
Before introducing the above determination method, it is first necessary to write out the dynamic equation of the phase-locked loop:
wherein: delta = theta-theta g The difference between the output angle of the phase-locked loop and the voltage angle of the alternating current power grid;
for current injection factor, k p ＝k p,pll U g And k is equal to i ＝k i,pll U g The actual proportional gain and the actual integral gain of the phase-locked loop PI controller, respectively. Normalizing the obtained product:
the method meets the following conditions:
then, a threshold voltage at which the system is subject to the anisotropic bifurcation is obtained. The dynamic equation of the phase-locked loop is observed, the system is not difficult to find that the system has only two parameters m and gamma, and the numerical relation of the two parameters can be obtained by utilizing a computer solving method when the different-dormitory bifurcation occurs.
Referring to fig. 4, γ=γ c (m) is a functional image of m and γ when the heterosink bifurcation occurs. On the other hand, the relation between m and gamma and the positive sequence voltage amplitude of the power grid is as follows:
wherein: m is m 0 Is the current injection factor at rated voltage, gamma 0 Is the damping coefficient at rated voltage, U g * The per unit value of the ac mains positive sequence voltage may be less than 1 in the event of a fault. Thus, with the change of the ac grid positive sequence voltage, m and γ always satisfy:
this relation is also plotted in fig. 4 and taken to be γ=γ c And (3) the intersection points (m ', gamma') of the (m) are obtained, and the corresponding critical positive sequence voltage amplitude can be obtained by solving the positive sequence voltage amplitude of the power grid corresponding to the intersection points.
Assuming that the power grid has failed at this time, the positive sequence voltage amplitude of the power grid can be extracted in some way, and the positive sequence voltage amplitude is compared with the critical positive sequence voltage amplitude obtained in the previous step. If the voltage amplitude is larger than the critical positive sequence voltage amplitude, judging that the transient state of the converter is stable, and ending the judging process at the moment; otherwise, judging that the converter has the risk of transient instability
In a preferred embodiment, the index includes a plurality of indices; firstly, judging the transient stability of the converter by using one index, and continuously judging the transient stability of the converter by using the other index when the judging result is that the converter has the risk of transient instability, thereby circulating. In one embodiment, if the converter is at risk of transient instability using critical positive sequence voltage magnitude determination, it may be selected whether to continue using other criteria for determination. Such as an energy function, may be used to make further decisions. Constructing an energy function for a dynamic equation of the phase-locked loop, wherein:
neglecting f 1 Delta-containing term in (1), ignoring f 2 The x-containing term in (2) can be obtained:
f is calculated 1 (x) And f 2 (delta) primitive functions. Next, it is not difficult to construct an energy function:
it is easy to verify that its derivative remains half-negative throughout, i.e. meets the requirements of the energy function. Next, the equilibrium point position of the phase-locked loop dynamic equation is found. Let m be>0, the abscissa delta of the unstable equilibrium point nearest to the stable equilibrium point c Equal to pi-arcsin m; let m be<0, the abscissa delta of the unstable equilibrium point nearest to the stable equilibrium point c Equal to-pi-arcsin m. From this, the critical energy V (delta) c ,0)。
Next, the state of the converter at this time is substituted into an expression of the energy function to obtain a current energy function value, and the value is compared with the critical energy obtained in the previous step. If the energy is less than or equal to the critical energy, determining that the converter is transient stable; otherwise, the risk of transient instability of the converter is determined.
Referring to fig. 5, in order to further illustrate the principle of the above-mentioned determination method, the stability domain of the normalized phase-locked loop dynamic equation on the phase plane is drawn. Wherein, fig. 5a is a stable domain before the occurrence of the heterogenous bifurcation, fig. 5b is a stable domain after the occurrence of the heterogenous bifurcation, fig. 5c is a stable domain range estimated by using an energy function, which is a set of states in which the energy function value is smaller than the critical energy. At the moment of transient occurrence, the state x of the integrator of the PI controller of the phase-locked loop will not change abruptly and its stable value is usually zero, so after transient occurrence, x 2 Still at x 1 On the shaft. If the voltage drop is not sufficient to cause a sink bifurcation to occur at this point, then the phase locked loop state must be within the stable domain, i.e. the converter must be transient stable, according to fig. 5 a. If the voltage drop is deeper and lower than the critical positive sequence voltage amplitude, the stable domain range is reduced to become the shape of fig. 5b, and the phase-locked loop state is possibly out of the stable domain range, so that further determination is needed. Since the derivative of the energy function with respect to time is semi-negative, the stability domain range estimated from the energy function is smaller than the actual stability domain range, i.e. the stability domain range of fig. 5b comprises the stability domain range of fig. 5 c. Thus, as long as the energy function value of the phase-locked loop after transient state is less than or equal to the critical energyThe converter must be transient stable. Otherwise, there is a risk of instability. At this time, since the stable domain range after the heterogenous bifurcation and the stability and the range estimated by using the energy function are already very close, the decision result of the second time is basically the same as the actual result, and the decision result which is too optimistic does not appear.
In summary, the method reduces the conservation of transient stability estimation by using the energy function when the voltage drop degree is not large by respectively discussing the conditions before and after the branching of the different dormitories.
In an embodiment, a device for determining transient stability of a converter based on a critical index is further provided, which is configured to implement the method for determining transient stability of a converter based on a critical index, including: the device comprises an index establishing unit, an index current value calculating unit, a comparing unit and a result judging unit; wherein,,
the index establishing unit is used for selecting an index related to transient stability of the converter, wherein the index is a function of one or more variables related to the converter;
the index current value calculation unit is used for substituting the one or more variables in the index establishment unit into a function to obtain the current value of the index;
the comparison unit is used for comparing the current value of the index in the index current value calculation unit with the critical value of the index;
the result judging unit is used for judging the transient stability of the converter according to the comparison result of the comparing unit.
It should be noted that, the steps in the method provided by the present invention may be implemented by using corresponding modules, units, etc. in the apparatus, and those skilled in the art may refer to a technical solution of the apparatus to implement the step flow of the method, that is, the embodiment of the apparatus may be understood as a preferred example for implementing the method, which is not described herein.
It will be appreciated by those skilled in the art that the apparatus provided by the present invention and its various units may be implemented as logic gates, switches, application specific integrated circuits, programmable logic controllers, embedded microcontrollers, etc. by simply programming the logic of the method steps, except for implementing the apparatus provided by the present invention as pure computer readable program code. Therefore, the apparatus provided by the present invention and the units thereof can be regarded as a hardware component, and the apparatus for realizing various functions included therein can also be regarded as a structure in the hardware component; means for achieving the various functions may also be considered as being either a software module that implements the method or a structure within a hardware component.
The embodiments disclosed herein were chosen and described in detail in order to best explain the principles of the invention and the practical application, and to thereby not limit the invention. Any modifications or variations within the scope of the description that would be apparent to a person skilled in the art are intended to be included within the scope of the invention.
Claims (4)
1. The method for judging the transient stability of the converter based on the critical index is characterized by comprising the following steps of:
s11: selecting an indicator related to transient stability of a converter, the indicator being a function of one or more variables related to the converter;
s12: substituting the one or more variables in the S11 into the function to obtain the current value of the index;
s13: comparing the current value of the index in the step S12 with a critical value of the index;
s14: judging the transient stability of the converter according to the comparison result of the S13;
the converter is a three-phase voltage source type converter and works in a rectifying or inverting state; and, the converter includes: an angle generation unit, the output of the angle generation unit is an angle, and the angle is used as the angle of the reference voltage or the reference current of the alternating current side of the converter;
the variables include: three-phase voltages of the AC side grid-connected point of the converter; and an output angle of the angle generating unit; further, the index includes: positive sequence component amplitude of three-phase voltage of an alternating current side power grid of the converter; and, an energy function of the angle generating unit;
the critical values of the index include: critical positive sequence voltage amplitude and critical energy;
the critical positive sequence voltage amplitude is a bifurcation point;
the bifurcation point represents an abnormal bifurcation occurring under the critical positive sequence voltage amplitude when manifold shapes of two unstable balance points adjacent to the stable balance point are changed along with the change of the positive sequence voltage amplitude in a dynamic system of a phase-locked loop of the converter;
the construction method of the energy function comprises the following steps:
s61: the angle generating unit and the closed loop thereof are written in the form of a second-order dynamic equation:
s62: neglecting f 1 Delta-containing term in (1), ignoring f 2 If not, skipping, thereby yielding a new dynamic equation:
s63: constructing an energy function:
V(δ,x)＝F 1 (x)–F 2 (δ)+V 0
wherein F is 1 (x) Is f 1 (x) Is the primary function of F 2 (delta) is f 2 Primitive function of (delta), V 0 Is any real number;
if the angle generating unit of the converter is a phase-locked loop, a first variable delta of the energy function is a difference between an output angle of the phase-locked loop and a voltage angle of an alternating-current side power grid of the converter, and a second variable x is an integrator state of a PI controller of the phase-locked loop;
if the angle generating unit is a virtual synchronous control, a first variable delta of the energy function is the difference between the output angle of the virtual synchronous control and the voltage angle of the alternating-current side power grid of the converter, and a second variable x is the difference between the internal frequency of the virtual synchronous control and the compensation frequency;
the method for calculating the critical energy comprises the following steps: critical energy equal to V (delta) c 0), wherein delta c In the dynamic system of the phase-locked loop, the output angle of the phase-locked loop corresponding to the unstable balance point closest to the stable balance point is the difference between the output angle of the phase-locked loop and the voltage angle of the alternating-current side power grid of the converter.
2. The method for determining the transient stability of the converter based on the critical index according to claim 1, wherein the transient stability determination result in S14 is: the converter is transient stable or the converter is at risk of transient instability.
3. The method for determining the transient stability of a converter based on a critical index according to claim 2, wherein the index includes a plurality of indexes;
firstly, judging the transient stability of the converter by using one of the indexes, and continuously judging the transient stability of the converter by using the other index when the judging result is that the converter is at risk of transient instability, thereby proceeding.
4. A critical indicator-based converter transient stability determination apparatus for implementing the critical indicator-based converter transient stability determination method according to any of claims 1 to 3, comprising: the device comprises an index establishing unit, an index current value calculating unit, a comparing unit and a result judging unit; wherein,,
the index establishing unit is used for selecting an index related to transient stability of the converter, wherein the index is a function of one or more variables related to the converter;
the index current value calculation unit is used for substituting the one or more variables in the index establishment unit into the function to obtain the current value of the index;
the comparison unit is used for comparing the current value of the index in the index current value calculation unit with the critical value of the index;
the result judging unit is used for judging the transient stability of the converter according to the comparison result of the comparing unit.
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|---|---|---|---|---|
| US5483462A (en) * | 1990-05-07 | 1996-01-09 | Cornell Research Foundation, Inc. | On-line method for determining power system transient stability |
| CN109659930B (en) * | 2018-12-15 | 2022-07-22 | 南京理工大学 | VSG-IIDG-containing power system transient stability analysis method based on energy function |
| CN109740229A (en) * | 2018-12-26 | 2019-05-10 | 湖南大学 | The judgment method of virtual machine transient rotor angle stability |
| CN110504706B (en) * | 2019-07-22 | 2021-05-04 | 中国农业大学 | Transient stability prediction method and device for virtual synchronous generator grid connection |
| CN110311375B (en) * | 2019-07-29 | 2022-11-29 | 东北大学 | Micro-grid transient stability control method containing multiple virtual synchronous machines |
| CN111030112B (en) * | 2020-01-02 | 2021-10-26 | 北京交通大学 | Method for judging transient stability of alternating current-direct current hybrid power system containing flexible direct current |
| CN111969647B (en) * | 2020-07-24 | 2022-08-02 | 南方电网科学研究院有限责任公司 | Converter transient instability stabilization control method and device based on state resetting |
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