CN113224772A - Hydropower system ultralow frequency oscillation suppression method considering switching link - Google Patents

Hydropower system ultralow frequency oscillation suppression method considering switching link Download PDF

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CN113224772A
CN113224772A CN202110433534.3A CN202110433534A CN113224772A CN 113224772 A CN113224772 A CN 113224772A CN 202110433534 A CN202110433534 A CN 202110433534A CN 113224772 A CN113224772 A CN 113224772A
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bifurcation
smooth
frequency oscillation
ultralow frequency
switching
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薛安成
刘晓博
孔贺
王永杰
王嘉伟
付潇宇
庄文彬
郭鹏程
李业成
汪云涛
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North China Electric Power University
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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
    • H02J3/24—Arrangements for preventing or reducing oscillations of power in networks
    • H02J3/241—The oscillation concerning frequency

Abstract

The patent provides a method for suppressing ultralow frequency oscillation of a hydroelectric system by considering a switching link. The method can inhibit the ultralow frequency oscillation occurring in a high water-electricity ratio system by improving the switching structure of a non-smooth power system. Firstly, analyzing the type of a non-smooth system, and researching the bifurcation characteristic of the non-smooth system by adopting a corresponding bifurcation theory; and secondly, calculating the bifurcation characteristics of balance points and the bifurcation characteristics of trajectories of various regions of the non-smooth system along with the change of sudden load parameters, and further obtaining the corresponding non-smooth bifurcation type when the system generates ultralow frequency oscillation. And finally, aiming at a switching link influencing the bifurcation characteristic, a method for suppressing the ultralow frequency oscillation by changing a switching structure is provided.

Description

Hydropower system ultralow frequency oscillation suppression method considering switching link
Technical Field
The invention belongs to the field of stability analysis and control of a power system, and particularly relates to an ultra-low frequency oscillation suppression method based on a non-smooth bifurcation theory.
Background
In recent years, ultralow frequency oscillation accidents related to a water turbine speed regulating system occur in domestic and foreign high-water-electricity-ratio power systems for many times, and the problems of long oscillation period, low frequency, large mechanical power amplitude, no obvious inter-machine oscillation and great difference from the conventional low-frequency oscillation belong to the frequency stability problem. At present, the mechanisms of ultralow frequency oscillation include negative damped oscillation, forced oscillation and switching type oscillation. The former two oscillation mechanisms consider that the water hammer effect and the unreasonable control parameter setting of the hydraulic turbine set provide negative damping for the system, so that the system can generate continuous oscillation under small disturbance. However, it is difficult to explain the oscillation problem associated with the switching element such as the dead zone and the clipping, and it is necessary to analyze the oscillation from the viewpoint of the switching type oscillation. The switching type oscillation and the local property of a system balance point may not have a corresponding relation, the oscillation participated by a nonlinear switching link can appear under the condition of positive and negative damping, meanwhile, stable frequency oscillation participated by a dead zone when no balance point exists is found in a hydroelectric system containing an enhanced dead zone, the negative damping or forced oscillation mechanism is not applicable any more, and the non-smooth bifurcation theory can be adopted for analysis. And research and analysis show that two switching type ultralow frequency oscillations appearing in the hydropower system with the enhanced dead zone respectively correspond to Hopf-like bifurcation and C-type non-smooth bifurcation. Besides the dead zone, amplitude limiting is also a typical switching link in a power system, and has an important influence on the system stability. For example, an ultralow frequency oscillation accident is caused by amplitude limiting saturation of a speed regulating system in a certain actual high-water-electricity-ratio large power grid; the problem of subsynchronous oscillation related to amplitude limiting saturation also occurs in a new energy power system, but the corresponding specific bifurcation type is less researched at present.
From the perspective of a non-smooth system, the size of the dead zone and the amplitude limit affects the structure of the non-smooth system, and further affects the stability, oscillation and instability of the system. The patent provides a restraining method based on improving a non-smooth structure aiming at the problem of switching type ultralow frequency oscillation in a hydroelectric system containing a common dead zone and amplitude limiting at the same time.
Disclosure of Invention
The invention aims to provide a method for inhibiting switching type ultralow frequency oscillation in a hydroelectric system, which classifies non-smooth systems containing switching links aiming at the switching type oscillation with dead zones and amplitude limiting participation during negative damping of the system, analyzes the non-smooth bifurcation characteristics of the system and provides a method for inhibiting the oscillation from the aspect of improving the non-smooth structure.
The scheme is as follows:
a method for suppressing ultralow frequency oscillation of a hydroelectric system by considering a switching link is characterized by comprising the following steps:
step 1: and analyzing the type of the non-smooth system to which the hydroelectric system containing the switching link belongs.
Step 2: analyzing existence and stability of balance points of each area of the non-smooth system and system dynamics characteristics under different load disturbances, and analyzing bifurcation characteristics corresponding to oscillation by combining a non-smooth bifurcation theory.
And step 3: the influence of dead zone, amplitude limiting and other switching links on the bifurcation characteristic of the system is explored, and an ultralow frequency oscillation suppression method for reasonably improving the structure of a non-smooth system is provided.
According to the technical scheme provided by the invention, the method explores the non-smooth bifurcation characteristic of ultralow frequency oscillation in a hydroelectric system containing two switching links of a common dead zone and amplitude limiting from the perspective of actual system load disturbance, and provides a novel method for inhibiting the oscillation from the perspective of improving the system structure.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the description of the embodiments are briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on the drawings without creative efforts.
Fig. 1 is a flow chart of a method for suppressing ultralow frequency oscillation of a hydroelectric system in consideration of a switching link according to an embodiment of the present invention;
fig. 2 is a speed control system of a single hydroelectric generating set according to the embodiment of the present invention.
Fig. 3 shows a primary frequency modulation dead zone and an amplitude limiting unit according to an embodiment of the present invention.
FIG. 4 is a diagram of Hopf-like bifurcation with limited amplitude according to an embodiment of the present invention.
FIG. 5 is a diagram illustrating Hopf-like bifurcation of an infinite amplitude according to an embodiment of the present invention.
FIG. 6 is a plot of the regional characteristics of the system dynamics at different dead zones for an example embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention are 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 only a part of the embodiments of the present invention, and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments of the present invention without making any creative effort, shall fall within the protection scope of the present invention.
The embodiments of the present invention will be further described in detail with reference to the accompanying drawings, and the specific analysis process is as follows:
step 1: and analyzing the type of the non-smooth system to which the hydroelectric system containing the switching link belongs.
Non-smooth systems can be classified into piecewise smooth continuous systems, Filipov systems (piecewise smooth discontinuous systems), and non-smooth impulse systems. Specifically, a segmented smooth continuous system refers to a system in which the vector field is continuous but the Jacobian matrix is discontinuous, such as an elastic collision model; the Filipov system refers to a system in which the vector field is discontinuous and the Jacobian matrix is also discontinuous, such as a dry friction system; non-smooth pulsed systems refer to systems excited by pulses whose system trajectory is not continuous. Figure 5 shows that the single machine hydroelectric system with limited amplitude and common dead zone is a segmented smooth continuous system, so that the non-smooth bifurcation theory in the segmented smooth continuous system can be adopted for analyzing.
Step 2: analyzing existence and stability of balance points of each area of the non-smooth system and system dynamics characteristics under different load disturbances, and analyzing bifurcation characteristics corresponding to oscillation by combining a non-smooth bifurcation theory.
The water turbine speed regulating system comprises a regulating system, an electro-hydraulic servo system and a water turbine. The main control part for regulating the system comprises a frequency dead zone link, a PID control module, an amplitude limiting link and the like. The regulating system collects the frequency deviation signal of the generator set, amplifies the frequency deviation signal after passing through a primary frequency modulation dead zone and an amplitude limiting link, and outputs a gate regulating signal P together with the power opening deviation signal through PID control regulationCV. The electro-hydraulic servo system corresponds to an actuating mechanism in the speed regulator and adjusts a door signal PCVAmplified and converted into a water turbine guide vane opening signal P through links such as electro-hydraulic conversionGV. The water turbine is based on the opening signal P of the guide vaneGVIn the actual operation process, the opening or closing of the guide vane of the water turbine can generate reverse adjustment opposite to the control target in a short time due to the water hammer effect, so that if the guide vane of the water turbine is opened and closed frequently, adverse effects can be brought to the dynamic stability of the system, and the adjustment of the output mechanical power Pm becomes a key factor causing the instability of the system.
The differential equation corresponding to the single hydroelectric generating set speed regulating system model is as follows:
Figure BDA0003027957430000031
variable ω ═ x4The general dead zone output expression with amplitude limiting is as follows:
Figure BDA0003027957430000032
wherein, Kw、Kp、KIBp is the frequency deviation amplification factor in the regulating system, the amplification factor of proportional and integral links in a PID control module and a permanent state slip coefficient respectively; kP1And TyThe amplification factor and the servomotor time constant of the electro-hydraulic servo system are respectively. T isWIs the water hammer effect time constant of the water turbine. OmegarefFor setting frequencyA reference value; y isrefSetting a reference value for the gate regulating signal; pLIs the system load; kLThe effect coefficient is adjusted for the load.
The balance points in the five regions of the non-smooth system A, B, C, D, E are solved for according to the balance point definition.
1) For the region a, formula (1) is substituted with F (ω) ul to find an equilibrium point:
Figure BDA0003027957430000033
to make the balance point omega*In region A, PLThe requirements are satisfied:
Figure BDA0003027957430000034
2) for region B, F (ω) is made ωref- ω - ε is substituted for formula (1) to find the equilibrium point:
Figure BDA0003027957430000035
to make the balance point omega*In region B, PLThe requirements are satisfied: p2＜PL＜P1
Wherein, P2＝Yref+KLε
3) For the region C, formula (1) is substituted with F (ω) of 0 to find an equilibrium point:
Figure BDA0003027957430000036
to make the balance point omega*In region C, PLThe requirements are satisfied: p3＜PL＜P2
Wherein, P3＝Yref-KLε
4) For region D, F (ω) is made ωrefEquilibrium is found by substituting- ω + ε for formula (1)Point:
Figure BDA0003027957430000041
to make the balance point omega*In region D, PLThe requirements are satisfied: p4＜PL＜P3
Wherein the content of the first and second substances,
Figure BDA0003027957430000042
5) in the region E, formula (1) is substituted with F (ω) dl to find an equilibrium point:
Figure BDA0003027957430000043
to make the balance point omega*In region E, PLThe requirements are satisfied: pL＜P4
Typical parameters of a speed regulating system are adopted: omegaref＝1，Yref＝1，KP＝5，KI＝1，KP1＝40，bp＝0.03，T＝13.86，TJ＝10，KL＝1.5，TW＝1.6，KW1.1, 0.0008, 0.01 for ul and-0.01 for dl. No special explanation is provided, and each variable in the text adopts a per unit value.
The following can be obtained: p1＝1.3829、P2＝1.0012、P1＝0.9988、P1＝0.6171
When the initial load of the system is the rated load (P)L1), the system has a stable equilibrium point (x) only inside the dead zone region1，x2，x3，x4) And (1, 1, 1, 1), linearizing the differential equation system at the balance point, and solving a Jacobian matrix characteristic value to judge the stability of the balance point.
1) For region A, C, E, F (ω) is a constant, Jacobian matrix J thereof1Comprises the following steps:
Figure BDA0003027957430000044
the corresponding 4 feature roots are: lambda [ alpha ]1＝-bpKI，λ2＝-KP1/Ty，λ3＝-2/TW，λ4＝-KL/TJ. The four characteristic roots are negative real numbers, so the equilibrium point in region A, C, E is a stable node.
2) For region B, D, F (ω) is a variable, corresponding Jacobian matrix J2Comprises the following steps:
Figure BDA0003027957430000051
substituting typical parameters yields characteristic values as:
λ1＝-4.1424；λ2＝0.0191+0.6860i；λ3＝0.0191-0.6860i；λ4＝-0.2117+0.0000i
wherein λ is2And λ3The real part is the positive conjugate complex root, indicating that the equilibrium point in region B, D is an unstable focus.
The dynamics of the trajectory are explored by solving the numerical solution of the differential equation. Different initial load values (representing different load disturbances) are selected, and the track bifurcation characteristics are summarized as follows:
1) when P is present2<PL<P1The trajectory converges to a stable equilibrium point within the dead zone region (region C);
2) when P is present1<PL<P3Or P4<PL<P2Then, the trajectory forms a non-smooth limit loop that crosses the dead zone or clipping boundary;
3) when P is presentL>P3Or PL<P4When this occurs, the system trajectory converges to a stable equilibrium point in the clipping region (region a/E).
In summary, when the load is disturbed PLWhen changing from the initial value of 1 to P1 or P2, the system will accompany the stable node to cross the dead zone boundaryAn unsmooth limit ring crossing the boundary appears in the unstable focus, and the ultralow frequency oscillation phenomenon caused by Hopf-like bifurcation correspondingly occurs, and specific bifurcation characteristics are shown in figure 4.
And step 3: the influence of dead zone, amplitude limiting and other switching links on the bifurcation characteristic of the system is explored, and an ultralow frequency oscillation suppression method for reasonably improving the structure of a non-smooth system is provided.
And respectively exploring the influence of the amplitude limit of the primary frequency modulation and the size of the dead zone on the bifurcation characteristic of the system.
1) Influence of clipping element on bifurcation property:
when infinite loop time is saved, ul is + ∞, dl is infinity, a single-machine system becomes a non-smooth system consisting of three regions, and the existence and stability of balance points of each region under different load disturbances can be obtained in the same way as follows:
when P is2<PL<P1Meanwhile, stable nodes exist in the dead zone region (region C);
when PL>P1Or PL<P2There is an unstable focus within the adjustment region (region B, D).
The bifurcation characteristic of the system trajectory is as follows:
when P is2<PL<P1The trajectory converges to a stable equilibrium point within the dead zone region (region C);
② when
Figure BDA0003027957430000052
Or
Figure BDA0003027957430000053
Then, the trajectory forms a non-smooth limit loop that crosses the dead zone boundary;
③ when
Figure BDA0003027957430000054
Or
Figure BDA0003027957430000055
In time, the system trajectory oscillates and diverges, corresponding to a system instability.
Therefore, even without clipping, the ultra-low frequency oscillation phenomenon is caused along with Hopf-like bifurcation, and when the load disturbance is large, the system oscillates and diverges because of no stable balance point. The arrangement of the amplitude limiting can enable a non-smooth system to have a new switching area containing a stable balance point, so that the system can avoid frequency oscillation under extreme load disturbance, and safe operation is facilitated.
2) Dead zone size effect on bifurcation characteristics
The dead zone is used as an important switching link and has a large influence on the stability of an actual power system, so that the influence of the size of the dead zone (switching link parameter) on the Hopf bifurcation-like characteristic of simplifying a single-machine system balance point and a fault post-trajectory in the presence of amplitude limiting is mainly analyzed.
TABLE 1 Balanced Point bifurcation behavior under different dead zones with clipping
Figure BDA0003027957430000061
SEP (B/D/E): stable nodes are arranged in the region B/D/E; UEP (a/C): there is an unstable focus in region A/C.
Table 1 shows that: when the dead zone value is not 0, the divergence point deviates from the rated load parameter 1 more as the dead zone value increases; but the parameter domain interval length with unstable equilibrium point in the region B/D remains unchanged.
TABLE 2 bifurcation characteristics of post-fault trajectories under different dead bands
Figure BDA0003027957430000062
C-LC: convergence to a stable limit cycle; C-SEP: converge to SEP.
Table 2 shows that: when the dead zone value is not 0, the system is operated from the initial stable operation to the bifurcation point corresponding to the occurrence of switching type oscillation, and deviates from the rated load parameter 1 along with the increase of the dead zone. In particular, the system is less affected by the dead zone size from the point of divergence of the oscillation to converge to a stable equilibrium point in the region a/E after clipping is set.
Further, according to the dynamic zone characteristics of the finite-amplitude single-machine system in fig. 6, it can be known that: increasing the dead zone of the speed regulator enlarges the disturbance load parameter security domain interval, namely, increases the load disturbance critical value causing switching type frequency oscillation, therefore, adjusting the size of the dead zone can be used as one measure for inhibiting the oscillation.
In conclusion, compared with an oscillation suppression measure provided by a negative damping or forced oscillation mechanism, the method fully considers the influence of a nonlinear switching link on the dynamic characteristics of the system, is simpler and more convenient in the aspect of improving the system structure, and has a certain engineering application value.
It is noted that those skilled in the art will recognize that embodiments of the present invention are not described in detail herein.
The above description is only for the preferred 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 (4)

1. A method for suppressing ultralow frequency oscillation of a hydroelectric system by considering a switching link is characterized by comprising the following steps:
step 1, analyzing the type of a non-smooth system to which a hydroelectric system containing a switching link belongs;
step 2, analyzing existence and stability of balance points of each area of the non-smooth system and system dynamics characteristics under different load disturbances, and analyzing bifurcation characteristics corresponding to oscillation by combining a non-smooth bifurcation theory;
and 3, analyzing the influence of dead zones, amplitude limiting and other switching links on the bifurcation characteristics of the system, and providing an ultralow frequency oscillation suppression method for reasonably improving the structure of the unsmooth system.
2. The method for suppressing the ultralow frequency oscillation of the hydroelectric system considering the switching link according to claim 1, wherein: in the step 1, the classification standard of the non-smooth system is combined, the system is classified according to the switching link in the power system, and the bifurcation characteristic of the system is analyzed by adopting a corresponding non-smooth bifurcation theory.
3. The method for suppressing the ultralow frequency oscillation of the hydroelectric system considering the switching link according to claim 1, wherein: in the step 2, by analyzing the non-smooth bifurcation characteristics of the balance point and the trajectory of the system along with the change of the sudden change load parameters, the Hopf-like bifurcation of the non-smooth system corresponding to the ultra-low frequency oscillation of the hydroelectric system containing the common dead zone and the amplitude limiting is obtained, and the specific bifurcation point is obtained to be used as the basis for subsequently inhibiting the Hopf-like oscillation.
4. The method for suppressing the ultralow frequency oscillation of the hydroelectric system considering the switching link according to claim 1, wherein: in the step 3, according to the influence of the amplitude limit and the size of the dead zone on the non-smooth bifurcation characteristic, the switching area with a stable balance point is increased by setting the amplitude limit, so that the safe operation of the system under extreme disturbance is facilitated; and increasing the dead zone to avoid switching type ultralow frequency oscillation caused by non-smooth bifurcation, which are practical methods for improving the non-smooth system structure to inhibit switching type ultralow frequency oscillation.
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US20130197705A1 (en) * 2012-01-31 2013-08-01 General Electric Company Power system stabilization
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CN107086589A (en) * 2017-06-23 2017-08-22 云南电网有限责任公司 A kind of governor parameter optimization method for suppressing Hydropower Unit ultra-low frequency oscillation based on critical parameters
CN109412180A (en) * 2018-11-23 2019-03-01 中国南方电网有限责任公司 Ultra-low frequency oscillation control method under Hydropower Unit Asynchronous Interconnection scene

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