CN107611996B - Multi-frequency oscillation out-of-step oscillation center positioning and migration tracking system and method thereof - Google Patents

Multi-frequency oscillation out-of-step oscillation center positioning and migration tracking system and method thereof Download PDF

Info

Publication number
CN107611996B
CN107611996B CN201710839674.4A CN201710839674A CN107611996B CN 107611996 B CN107611996 B CN 107611996B CN 201710839674 A CN201710839674 A CN 201710839674A CN 107611996 B CN107611996 B CN 107611996B
Authority
CN
China
Prior art keywords
oscillation
center
voltage
oscillation center
point
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN201710839674.4A
Other languages
Chinese (zh)
Other versions
CN107611996A (en
Inventor
马静
邓卓俊
李沛
刘静
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
North China Electric Power University
Original Assignee
North China Electric Power University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by North China Electric Power University filed Critical North China Electric Power University
Priority to CN201710839674.4A priority Critical patent/CN107611996B/en
Publication of CN107611996A publication Critical patent/CN107611996A/en
Application granted granted Critical
Publication of CN107611996B publication Critical patent/CN107611996B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Landscapes

  • Supply And Distribution Of Alternating Current (AREA)

Abstract

The invention belongs to the technical field of stability analysis of power systems, and particularly relates to a multi-frequency oscillation out-of-step oscillation center positioning and migration tracking system and a method thereof based on a position function, wherein three side power supplies are connected to one point through three lines to construct a three-machine equivalent system model; obtaining a voltage vector expression of any point under the simultaneous action of the three-side power supply according to the superposition theorem; setting an oscillation center position function according to the line impedance ratio; rewriting a voltage vector expression of any point into a mode value and phase form, expanding the mode value and phase form into a quadratic function, calculating a partial derivative, and then obtaining an expression of the oscillation center position of any side according to a trigonometric function relation and a mean value inequality; analyzing the influence of three factors of a system relative power angle, impedance structure parameters and system power supply voltage amplitude on an oscillation center, obtaining the condition of the occurrence of the step-out center on each side, and determining the position of the step-out center after obtaining a criterion according to the trigonometric function relation of voltage vectors.

Description

Multi-frequency oscillation out-of-step oscillation center positioning and migration tracking system and method thereof
Technical Field
The invention belongs to the technical field of stability analysis of power systems, and particularly relates to a multi-frequency oscillation out-of-step oscillation center positioning and migration tracking system and method based on a position function.
Background
With the development of ultrahigh voltage interconnected power grids and the access of a large amount of new energy in China, the scale of a power system is gradually enlarged, the operation mode of the system is changeable, and the possibility that the system is disturbed to oscillate and cause a large-scale power failure accident is also increased sharply. Meanwhile, the system oscillation presents the characteristics of complex cause, variable modes and the like, and the oscillation center may not be on a certain fixed line but may dynamically migrate on different lines, thereby bringing a serious challenge to the oscillation identification of the safety and stability device of the power system.
At present, the analysis and research of the oscillation characteristics at home and abroad are mostly based on two-machine system models, and the analysis methods mainly comprise three types: based on voltage current or impedance trajectory variation characteristics, based on frequency distribution characteristics, and based on energy or power, etc. However, in a multi-frequency oscillation scene, the analysis method based on the two-machine model is not applicable any more, and the oscillation characteristics obtained based on the two-machine model are difficult to describe the actual situation of multi-frequency oscillation. Out-of-step oscillation center positioning methods in multi-frequency oscillation scenes are rarely reported.
Disclosure of Invention
In order to solve the technical problems, the invention provides a multi-frequency oscillation out-of-step oscillation center positioning and migration tracking system and a method thereof based on a position function.
The system comprises a system information acquisition module, an oscillation center position migration tracking module, an out-of-step center positioning module and an out-of-step oscillation center position output module which are sequentially connected; the system information acquisition module is used for acquiring system structural parameters, power angles, rotating speeds and voltage amplitudes of generators on all sides of the system and sending acquired data to the step-out center positioning module; the oscillation center position migration tracking module calculates the oscillation center position of each side of the system by using the information acquired by the information acquisition module, so that the tracking and analysis of the drift path of the oscillation center of the multi-frequency oscillation system are realized; the step-out center positioning module is used for positioning the position of a step-out center in the system according to the provided step-out center positioning criterion; and the step-out oscillation center position output module is used for outputting a step-out center position and an oscillation center drift path.
The method comprises the following steps:
step 1: three side power supplies are connected to one point through three lines to construct a three-machine equivalent system model;
step 2: obtaining a voltage vector expression of any point under the simultaneous action of the three-side power supply according to the superposition theorem;
and step 3: setting an oscillation center position function according to the line impedance ratio; rewriting a voltage vector expression of any point into a mode value and phase form, expanding the mode value and phase form into a quadratic function, calculating a partial derivative, and then obtaining an expression of the oscillation center position of any side according to a trigonometric function relation and a mean value inequality;
and 4, step 4: analyzing the influence of three factors of a system relative power angle, impedance structure parameters and system power supply voltage amplitude on an oscillation center, obtaining the condition of the occurrence of the step-out center on each side, and determining the position of the step-out center after obtaining a criterion according to the trigonometric function relation of voltage vectors.
The voltage vector expression is represented by taking the side A as the following table:
Figure BDA0001409466430000021
in the formula (I), the compound is shown in the specification,
Figure BDA0001409466430000022
is the voltage vector at any point p in the a-side line,
Figure BDA0001409466430000023
is the equivalent potential of an A-side system, p is the distance from any point rho to a bus A, and delta12And delta13Respectively equal potential of B side system
Figure BDA0001409466430000024
Equivalent potential of A side system
Figure BDA0001409466430000025
Equivalent potential of C-side system
Figure BDA00014094664300000211
Equivalent potential of A side system
Figure BDA0001409466430000026
The phase angle difference between the two phases is small,
Figure BDA0001409466430000027
is the voltage amplitude ratio of the equivalent potential of the B-side system to the equivalent potential of the A-side system,
Figure BDA0001409466430000028
the voltage amplitude ratio of the equivalent potential of the C-side system to the equivalent potential of the A-side system, the intermediate variable
Figure BDA0001409466430000029
Intermediate variables
Figure BDA00014094664300000210
ZAΣ＝ZA+ZAO，ZBΣ＝ZB+ZBO，ZCΣ＝ZC+ZCO，ZAΣ、ZBΣ、ZCΣRespectively represents the comprehensive impedance of the system at the A side, the B side and the C side,ZA、ZB、ZCrespectively represent the equivalent power source impedance of the system at the A side, the B side and the C side, ZAO、ZBO、ZCOEqual value impedance of A, B, C three-side lines.
The expression of the oscillation center position on any side is expressed with side a as, for example:
Figure BDA0001409466430000031
i may take A, B, C, fi(delta) represents the A, B, C side oscillation center position function, taking i as an example of A,
Figure BDA0001409466430000032
S2and S1The quadratic and the first order coefficient respectively of the voltage magnitude factor of the system for the position p,
Figure BDA0001409466430000033
the conditions for the occurrence of the out-of-step center on each side are as follows:
Figure BDA0001409466430000034
wherein the coefficient k may be [0, + ∞ [ ]]Any value in the range between (a) and (b),
Figure BDA0001409466430000035
three lines are connected with the voltage phasor of the point O,
Figure BDA0001409466430000036
intermediate variables
Figure BDA0001409466430000037
The criterion comprises a main criterion 1, a main criterion 2 and an auxiliary criterion, wherein the main criterion 1 is as follows:
Figure BDA0001409466430000038
wherein epsilon is a protection action judgment threshold; the main criterion 2 is:
Figure BDA0001409466430000039
the auxiliary criterion is:
Figure BDA00014094664300000310
wherein k is the ratio of the voltage at the point O to the electromotive force amplitude of the generator at each side; when the main criterion 1 and the main criterion 2 meet one of the two criteria, the next calculation can be carried out; if the out-of-step center falls within the A-side system, it is also necessary to consider k ∈ [0, + ∞]I.e. by
Figure BDA00014094664300000311
If the main criterion and the auxiliary criterion are met simultaneously, the step-out center is in the A-side system, and the position of the step-out center is as follows:
Figure BDA0001409466430000041
in the formula, p0Representing the ratio of the impedance distance between the step-out center and the A-side system to the comprehensive impedance of the A-side system, and finally obtaining the position function of the step-out center:
Figure BDA0001409466430000042
。
the invention has the beneficial effects that: aiming at the technical problem that multi-frequency oscillation is difficult to describe based on oscillation characteristics obtained by a two-machine model in a multi-frequency oscillation scene, a multi-frequency oscillation step-out oscillation center positioning and migration tracking system based on a position function, a multi-frequency oscillation step-out oscillation center positioning and migration tracking method and a multi-frequency oscillation step-out oscillation center positioning and migration tracking method are provided, an expression of voltage and current in the multi-frequency oscillation scene is obtained, then a step-out center position function and an oscillation center position function are constructed according to the definition of an oscillation center and a step-out center, positioning criteria of the step-out center in the multi-frequency oscillation scene are obtained. The simulation result of the equivalent model of the multi-machine system verifies the correctness and effectiveness of the criterion and the tracking of the oscillation center of the method.
Drawings
Fig. 1 is a structural diagram of a system for locating and migrating tracking a center of a multi-frequency oscillation out-of-step oscillation based on a position function according to the present invention.
Fig. 2 is a schematic diagram of a three-machine system model in an embodiment of the invention.
Fig. 3 is a voltage phasor diagram when an a-side step-out center occurs in the embodiment of the present invention.
FIG. 4 is a graph of the amplitude and position of the oscillation center voltage over time in an embodiment of the present invention.
Fig. 5 is a graph showing the variation of the amplitude and position of the oscillation center voltage with time in different oscillation modes according to the embodiment of the present invention.
Fig. 6 is a graph showing the change of the amplitude and position of the oscillation center voltage with time when the impedance parameter is changed according to the embodiment of the present invention.
Fig. 7 is a graph showing the change of the amplitude and position of the oscillation center voltage with time when the impedance parameter is changed according to the embodiment of the present invention.
Fig. 8 is a graph showing the change in the position of the oscillation center voltage in the case of different potential amplitude ratios in the embodiment of the present invention.
Detailed Description
The embodiments are described in detail below with reference to the accompanying drawings.
Fig. 1 is a structural diagram of a multi-frequency oscillation out-of-step oscillation center positioning and migration tracking system based on a position function, which includes a system information acquisition module, an oscillation center position migration tracking module, an out-of-step center positioning module and an out-of-step oscillation center position output module that are connected in sequence.
Fig. 2 is a schematic diagram of a model of a three-machine system, in fig. 2,
Figure BDA0001409466430000055
equal potential of the system is respectively bus R, bus S and bus T, delta1、δ2、δ3Respectively corresponding equivalent power angle, ZA、ZB、ZCRespectively corresponding equivalent power supply impedances. ZAO、ZBOAnd ZCOEqual impedances of the lines RO, SO, TO, respectively. In the analysis process, the bus flow direction line is taken as the positive direction of the current, the impedance value is unchanged within the frequency range, and the impedance angles of the upper-level element and the lower-level element of the system are equal.
The current of any point in the system can be calculated by using a superposition theorem, and the current flowing on the line is the sum of the currents flowing when the three power supplies act independently. Taking side a as an example, consider only the case where side a power supply 1 is acting alone:
Figure BDA0001409466430000051
in the formula: zAΣ＝ZA+ZAO，ZBΣ＝ZB+ZBO，ZCΣ＝ZC+ZCOThe impedance values represent the combined impedance of the a-side, B-side, and C-side systems, respectively.
Similarly, the expression of the a-side current when only the B-side power supply 2 alone is considered and when the C-side power supply 3 alone is considered can be obtained as:
Figure BDA0001409466430000052
when three power supplies in the system act simultaneously, the current expression of the A side obtained by applying the superposition theorem is as follows:
Figure BDA0001409466430000053
from equation (3), the voltage at any point in the system can be calculated. Taking side A as an example, let us say that any point ρ on the line AO, the distance from the point to the bus A
Figure BDA0001409466430000054
Wherein ZAρThe equivalent impedance value from the system A to the rho point, the voltage expression of the point is as follows:
Figure BDA0001409466430000061
in the formula: p is more than or equal to 0 and less than or equal to 1,
Figure BDA0001409466430000062
is the voltage phasor at point p.
The formula (3) may be substituted for the formula (4):
Figure BDA0001409466430000063
in formula (5), the
Figure BDA0001409466430000064
With the a-side equivalent power supply potential as a reference, equation (5) can be rewritten as:
Figure BDA0001409466430000065
in the formula, delta12And delta13Are respectively an electric potential
Figure BDA0001409466430000066
And electric potential
Figure BDA0001409466430000067
Electric potential
Figure BDA0001409466430000068
And electric potential
Figure BDA0001409466430000069
The phase angle difference between them, i.e.: delta12＝δ2-δ1，δ13＝δ3-δ1，
Figure BDA00014094664300000610
Is the voltage amplitude ratio of the equivalent potential of the B-side system to the equivalent potential of the A-side system,
Figure BDA00014094664300000611
the voltage amplitude ratio of the equivalent potential of the C-side system to the equivalent potential of the A-side system is obtained.
Tracking of the migration of the oscillation center:
the oscillation center is the point where the voltage amplitude drops to the lowest in the system under a certain oscillation mode. But since the determination of the center of oscillation serves the automation in the system, for a certain system-side protection or disconnection device, the meaning of the center of oscillation should be further defined as a voltage sag condition within the device's perceptible range. Therefore, the system side oscillation center is defined as the lowest voltage point in the comprehensive impedance range of the system on the side under a certain oscillation mode. Let the oscillation centers on the A, B, C sides in FIG. 2 be D respectivelyA、DB、DCThe corresponding oscillation center position function can be defined as:
Figure BDA00014094664300000612
in the formula:
Figure BDA00014094664300000613
the impedance values of the A-side, B-side and C-side systems to the oscillation center of the side, fA(δ)、fB(δ)、fC(δ) is a function of the position of the oscillation center on the A side, a function of the position of the oscillation center on the B side, and a function of the position of the oscillation center on the C side, respectively.
In order to facilitate the analysis of the voltage amplitude of each point, the square of the voltage amplitude of any point rho point on the A side is defined as a voltage amplitude factor SF on the A sideAThen its voltage expression (6) can be rewritten into the form of modulus and phase as follows:
Figure BDA0001409466430000071
in the formula:
Figure BDA0001409466430000072
is a voltage amplitude coefficient of a rho point,
Figure BDA0001409466430000073
is the equivalent initial phase angle of the phase-locked loop,
Figure BDA0001409466430000074
an expression for the voltage magnitude factor can be obtained from equation (6):
Figure BDA0001409466430000075
as can be seen from formula (9), SFAIs a function of the power angle difference, the voltage amplitude ratio and the position parameter p of the other side equivalent power supply relative to the A side power supply.
Expanding equation (9) as a quadratic function with respect to p can result:
SFA＝S2p2-S1p+1 (10)
in the formula: s2And S1The quadratic coefficient and the first order coefficient of the voltage amplitude factor of the system for the position p are respectively expressed as follows:
Figure BDA0001409466430000076
finding SF in the formula (10)APartial derivatives with respect to the position parameter p:
Figure BDA0001409466430000077
in the formula (I), the compound is shown in the specification,
Figure BDA0001409466430000078
indicating that the partial derivative is taken of the parameter.
Derived from trigonometric relationships and mean inequalities, S2It is always true that 0 or more is used. Therefore, when
Figure BDA0001409466430000079
When is SFAThere is a minimum value, the voltage is lowest. At this time corresponding p1ANamely an A-side oscillation center position expression:
Figure BDA00014094664300000710
from the above analysis, at a certain time, in a certain oscillation mode, there exists only one voltage lowest point in one side system, namely: the side (the cross section) oscillation center has uniqueness. p is a radical of1A>1, the lowest voltage point of the line is positioned at the point O, and the oscillation center of the system is not positioned on the line; p is a radical of1A<At 0, the oscillation center is positioned at the back side of the system, and the oscillation center of the system is not positioned on the line; 0<p1A<1 the centre of oscillation of the line is located inside the line. Accordingly, the functional expression of the oscillation center position of each side can be written as follows:
Figure BDA0001409466430000081
in the formula, i can be represented by A, B, C and represents A, B, C side oscillation center position function expressions respectively.
The magnitude of the oscillation center voltage is an important basis for judging the stability degree of the system, and an expression of the oscillation center voltage factor can be obtained by substituting p ═ f (delta) into formula (14):
Figure BDA0001409466430000082
from the expressions (13) to (14) of the oscillation center position, the oscillation center position is determined by the relative power angle of the system, the impedance structure parameter and the amplitude ratio of the power supply voltage of the system. The influence of the three factors on the oscillation center is analyzed respectively, and the system potential amplitude is assumed to be equal, namely k12＝k13The first two factors are analyzed for 1, and then the case of unequal amplitude is analyzed. Considering the potential amplitudes to be equal, the oscillation center position expression is:
Figure BDA0001409466430000083
positioning the step-out center:
the step-out center is: in a certain oscillation mode, the voltage drops to the point of zero in the system at a certain moment. In an equivalent two-machine system with uniform impedance, the step-out center occurs when the system potential phase angle differs by 180 °. Because the currents of all points in the A-side system are equal in oscillation, if a step-out center appears in the A-side system, the phase angle between the potential of the A-side system and the voltage of the O point is 180 degrees. The same applies to the other sides. The conditions under which the out-of-step center occurs on each side can be found by combining formula (2):
Figure BDA0001409466430000084
wherein k may be [0, + ∞ [ ]]Any value in the range between (a) and (b),
Figure BDA0001409466430000085
the O point voltage phasor can be obtained from the equation (6)
Figure BDA0001409466430000091
The expression of (a) is:
Figure BDA0001409466430000092
in the formula (I), the compound is shown in the specification,
Figure BDA0001409466430000093
when the potential of any side in the system meets the criterion in the formula (17), the step-out center exists in the side system. However, since tracking and positioning of the step-out center are difficult to achieve by this equation, taking side a as an example, when the step-out center occurs, equation (18) can be rewritten as follows:
Figure BDA0001409466430000094
voltage phasor at the time of equation (17) being satisfied
Figure BDA0001409466430000095
And phasor
Figure BDA0001409466430000096
The phase difference is 180 deg., and the voltage phasor diagram at this time is shown in fig. 3, in which the phasors
Figure BDA0001409466430000097
Respectively represent
Figure BDA0001409466430000098
The sum of the three is
Figure BDA0001409466430000099
Phasors
Figure BDA00014094664300000910
Is phasor
Figure BDA00014094664300000911
Phasors
Figure BDA00014094664300000912
And (4) summing. Also, considering the magnitude of the a-side system potential as 1, from figure 3,
Figure BDA00014094664300000913
∠DOB＝π-δ12and ∠ ODB ═ δ13- π. According to the trigonometric function relationship, the conditions for the occurrence of the step-out center are as follows:
Figure BDA00014094664300000914
wherein epsilon is a protection action judgment threshold. The formula (20) is the main criterion 1. When δ is equal to12And delta13When the values of (d) are integer multiples of pi, the denominators on both sides of the equation in equation (20) are zero and cannot be calculated, or the values on both sides are infinite. In this case, the three system potentials are in a straight line, and need to be described in two cases:
a) if delta12And delta13If the value of (a) is not an integer multiple of 2 pi, then there must be at least one side potential
Figure BDA00014094664300000917
Conversely, there is at least one out-of-sync center in the system. In particular, when delta12And delta13Are all odd multiples of pi and k13kAB+k12kAC<kBCWhen the temperature of the water is higher than the set temperature,
Figure BDA00014094664300000915
simultaneously with
Figure BDA00014094664300000916
In the opposite direction, the two out-of-step centers exist in the system on both the B side and the C side, namely the two out-of-step centers exist in the system. At this time, since the boundary value defined by equation (16) is greater than 1, neither the oscillation center nor the step-out center occurs in the a-side system.
b) If delta12And delta13The values of (2) are integral multiples of 2 pi, and the formula (3) shows that the current in the system is zero and no step-out center exists. At this time, the out-of-step centering is not necessary.
In summary, the main criterion 2 needs to be considered as follows:
Figure BDA0001409466430000101
and if the main criterion 1 and the main criterion 2 meet one of the two criteria, the next calculation can be carried out. If the out-of-step center falls within the A-side system, it is also necessary to consider k ∈ [0, + ∞]I.e. by
Figure BDA0001409466430000102
Therefore, the auxiliary criterion is added as follows:
Figure BDA0001409466430000103
wherein k is the ratio of the voltage at the point O to the electromotive force amplitude of the generator at each side. If the main criterion and the auxiliary criterion are met simultaneously, the step-out center is in the A-side system, and the position of the step-out center is as follows:
Figure BDA0001409466430000104
in the formula, p0And the ratio of the impedance distance from the step-out center to the A-side system to the comprehensive impedance of the A-side system is represented.
By substituting the expression of k in equation (22) into equation (23), the function of the position of the step-out center can be obtained:
Figure BDA0001409466430000105
as can be seen from equation (24), there may be a plurality of step-out centers in the system, and the step-out centers migrate at different positions in the system as the power angle changes. The moment when the out-of-sync center exists can be seen approximately as the wobble of the combination of the two systems relative to the other system. However, since the power angle is continuously changed, the situation of short-time recombination of different systems is presented, and the combination rule is determined by the magnitude and sign of the relative angular velocity. Tracking and monitoring of the out-of-step center can be achieved according to equation (24), and similar deductions can be made on the other two sides. It is noted that the out-of-step center is the oscillation center at a particular time, and therefore, the boundary of the oscillation center is also the boundary of the out-of-step center migration, and in accordance with the oscillation center situation, there is only one out-of-step center in the system at most at a certain time.
In order to verify whether the method provided by the invention is correct under the conditions of different oscillation modes, different impedance parameters and different voltage amplitude ratios, a model shown in figure 2 is built by utilizing PSCAD, and in a basic simulation model, the potential amplitudes of three side power supplies are considered to be equal (k is considered to be equal)12＝1，k13＝1)，
Figure BDA0001409466430000106
And
Figure BDA0001409466430000107
respectively at Δ ω123 °/s and Δ ω13Around a relative angular velocity of 5 °/s
Figure BDA0001409466430000108
Rotation, the system impedance parameters are: zAΣ＝100∠86.5°Ω，ZBΣ＝60∠86.5°Ω，ZCΣ＝50∠86.5°Ω。
In the oscillation process, the oscillation center position and the oscillation center voltage amplitude of each side are shown in fig. 4, in which curve 1 represents the value of the oscillation center position function of each side and curve 2 represents the oscillation center voltage amplitude. As can be seen from fig. 4, the oscillation centers of the respective sides move toward the inside of the line from the point O and return after reaching the minimum value, and for example, the oscillation center of the side a returns after reaching the minimum value 0.6364.
The oscillation center of each side is shifted from the point O to the inside of the circuit, returns to the point O after reaching the farthest position, and then shifts to other sides. During the oscillation center migration, there may be an overlap, namely: when the oscillation center of one line moves from inside the line to point O, the oscillation center of the other line has already started to move from point O to inside the line thereof. At this time, the oscillation center of the system takes the point with the smaller voltage, and under the oscillation scene described in this section, the oscillation center of the system sequentially drifts from L1 to L2 and L3. In fig. 4(b) and (C), during the period from t to t being 92.93s to t being 96.25s, the system-side oscillation center is located in the C-side system, and in this oscillation scenario, the voltage at the O point is seriously decreased due to the step-out center occurring in the C-side system, which may affect both the line protection and the demodulation devices on both sides, so that a problem may occur when only the system oscillation center is adopted for identification, and it is necessary to use the system-side oscillation centers for determination.
Taking side A as an example, the analysis result of the step-out center positioning criterion is analyzed. In the formula (20), the criterion of satisfying formula (a) in the main criterion 1 or the main criterion 2 is taken as a criterion to perform a preliminary screening, and the determination result and the oscillation center position information are shown in table 1. Comparing the voltage curves in fig. 5(a), it can be seen that the step-out center can be accurately located by the locating method. And the out-of-sync center may move in different locations on the same side system, or in different side systems.
TABLE 1
t δ12 δ13 Main criterion 1 Main criterion 2 Additional criteria Function of position
43.76s 131.277° 218.795° √ × √ 0.7379
180s 180° 180° × √ √ 0.6364
316.2s 228.597° 141° √ × √ 0.7379
In the case of impedance parameters and voltage amplitudes that are consistent with the basic model, consideration is given to
Figure BDA0001409466430000111
And
Figure BDA0001409466430000112
respectively at Δ ω122 °/s and Δ ω13Around a relative angular velocity of 5 °/s
Figure BDA0001409466430000113
And (4) rotating. In the oscillation process, the oscillation center position and the oscillation center voltage amplitude of each side are shown in fig. 5, in which curve 1 represents the value of the oscillation center position function of each side and curve 2 represents the oscillation center voltage amplitude. As can be seen from fig. 5, during the oscillation process, the range of the oscillation center shift is the same as that in fig. 4, but in this oscillation mode, the oscillation center first shifts back and forth on L1 and L2 once, and then moves to L3, and the oscillation center may appear on three lines.
Considering the voltage amplitude ratio and the same in the oscillation mode basic model, the A-side system parameter changes to ZAΣWhen the other side parameters are not changed, the oscillation center position and the oscillation center voltage amplitude of each side are as shown in fig. 6, in which curve 1 represents the value of the oscillation center position function of each side and curve 2 represents the oscillation center voltage amplitude, in this case, the boundary value of the a-side oscillation center transition range is 0.67045, the oscillation center transition range is reduced, and the boundary values of the B-side and C-side are 0.75641 and 0.84286, respectively, and the transition range is increased.
Considering that the voltage amplitude ratio and the oscillation mode are the same as those in the basic model, the B-side system parameter changes to ZAΣWhen the other side parameters are not changed at 30 ∠ 86.5.5 ° Ω, the oscillation center position and the oscillation center voltage amplitude of each side are as shown in fig. 7, where curve 1 represents the value of the oscillation center position function of each side and curve 2 represents the oscillation center voltage amplitude.
Considering that the system impedance parameter and the oscillation mode are the same as the basic model, k in the simulation12，k13In the case of different values, the function of the oscillation center position on each side is shown in fig. 8. As can be seen from fig. 8, the change in the potential amplitude ratio directly affects the shift range of the oscillation center. When k is121.05 and k13When the voltage amplitude ratio is equal to 1.1, the transition range of the oscillation center on the a side becomes small, and the transition law of the oscillation center coincides with the case where the voltage amplitude ratio is equal. When k is120.95 and k13When the value is 0.95, the range of the oscillation center shift increases. Specifically, when the power angle differences are all close to 0, the oscillation center passes through the inside of the a-side system to reach the back side of the a-side system, but at this time, no step-out center exists in the a-side system, and therefore, no consideration is needed. Table 2 and Table 3 show k12＝0.95,k130.95 and k12＝1.05,k13And (3) the positioning results of the out-of-step centers under the two conditions of 1.1 show that the method can accurately position the out-of-step centers under various scenes.
TABLE 2
Figure BDA0001409466430000121
Figure BDA0001409466430000131
TABLE 3
t δ12 δ13 Main criterion 1 Main criterion 2 Additional criteria Function of position
43.47s 130.407° 217.345° √ × √ 0.7277
180s 180° 180° × √ √ 0.6208
316.5s 229.497° 142.495° √ × √ 0.7125
The above embodiments are only preferred embodiments 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 also within 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 (5)

1. A multi-frequency oscillation out-of-step oscillation center positioning and migration tracking method based on a position function is characterized by comprising the following steps:
step 1: three side power supplies are connected to one point through three lines to construct a three-machine equivalent system model;
step 2: obtaining a voltage vector expression of any point under the simultaneous action of the three-side power supply according to the superposition theorem;
and step 3: setting an oscillation center position function according to the line impedance ratio; rewriting a voltage vector expression of any point into a mode value and phase form, expanding the mode value and phase form into a quadratic function, calculating a partial derivative, and then obtaining an expression of the oscillation center position of any side according to a trigonometric function relation and a mean value inequality;
and 4, step 4: analyzing the influence of three factors of a system relative power angle, impedance structure parameters and system power supply voltage amplitude on an oscillation center, obtaining the condition of the occurrence of the step-out center on each side, and determining the position of the step-out center after obtaining a criterion according to the trigonometric function relation of voltage vectors.
2. The method of claim 1, wherein the voltage vector expression is expressed with side a as follows:
Figure FDA0002322917490000011
in the formula (I), the compound is shown in the specification,
Figure FDA0002322917490000012
is the voltage vector at any point p in the a-side line,
Figure FDA0002322917490000013
is the equivalent potential of an A-side system, p is the distance from any point rho to a bus A, and delta12And delta13Respectively equal potential of B side system
Figure FDA0002322917490000014
Equivalent potential of A side system
Figure FDA0002322917490000015
Equivalent potential of C-side system
Figure FDA0002322917490000016
Equivalent potential of A side system
Figure FDA0002322917490000017
The phase angle difference between the two phases is small,
Figure FDA0002322917490000018
k12is the voltage amplitude ratio of the equivalent potential of the B-side system to the equivalent potential of the A-side system,
Figure FDA0002322917490000019
k13the voltage amplitude ratio of the equivalent potential of the C-side system to the equivalent potential of the A-side system, the intermediate variable
Figure FDA00023229174900000110
Intermediate variables
Figure FDA00023229174900000111
ZAΣ＝ZA+ZAO，ZBΣ＝ZB+ZBO，ZCΣ＝ZC+ZCO，ZAΣ、ZBΣ、ZCΣRespectively representing the combined impedance of the A-side, B-side and C-side systems, ZA、ZB、ZCRespectively represent the equivalent power source impedance of the system at the A side, the B side and the C side, ZAO、ZBO、ZCOEqual value impedance of A, B, C three-side lines.
3. The method according to claim 2, wherein the expression of the oscillation center position on any side is expressed with side a as follows:
Figure FDA0002322917490000021
i may take A, B, C, fi(delta) represents the A, B, C side oscillation center position function, taking i as an example of A,
Figure FDA0002322917490000022
S2and S1The quadratic and the first order coefficient respectively of the voltage magnitude factor of the system for the position p,
Figure FDA0002322917490000023
4. a method according to claim 3, characterized in that the conditions for the occurrence of a step-out center on each side are:
Figure FDA0002322917490000024
wherein the coefficient k may be [0, + ∞ [ ]]Any value in the range between (a) and (b),
Figure FDA0002322917490000025
three lines are connected with the voltage vector of the point O,
Figure FDA0002322917490000026
intermediate variables
Figure FDA0002322917490000027
5. The method of claim 4, wherein the criteria include main criterion 1, main criterion 2, and auxiliary criterion, and wherein main criterion 1 is:
Figure FDA0002322917490000028
wherein epsilon is a protection action judgment threshold; the main criterion 2 is:
Figure FDA0002322917490000029
the auxiliary criterion is:
Figure FDA0002322917490000031
wherein k is the ratio of the voltage at the point O to the electromotive force amplitude of the generator at each side; when the main criterion 1 and the main criterion 2 meet one of the two criteria, the next calculation can be carried out; if the out-of-step center falls within the A-side system, it is also necessary to consider k ∈ [0, + ∞]I.e. by
Figure FDA0002322917490000032
If the main criterion and the auxiliary criterion are met simultaneously, the step-out center is in the A-side system, and the position of the step-out center is as follows:
Figure FDA0002322917490000033
in the formula, p0Representing the ratio of the impedance distance between the step-out center and the A-side system to the comprehensive impedance of the A-side system, and finally obtaining the position function of the step-out center:
Figure FDA0002322917490000034
CN201710839674.4A 2017-09-15 2017-09-15 Multi-frequency oscillation out-of-step oscillation center positioning and migration tracking system and method thereof Active CN107611996B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201710839674.4A CN107611996B (en) 2017-09-15 2017-09-15 Multi-frequency oscillation out-of-step oscillation center positioning and migration tracking system and method thereof

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201710839674.4A CN107611996B (en) 2017-09-15 2017-09-15 Multi-frequency oscillation out-of-step oscillation center positioning and migration tracking system and method thereof

Publications (2)

Publication Number Publication Date
CN107611996A CN107611996A (en) 2018-01-19
CN107611996B true CN107611996B (en) 2020-04-21

Family

ID=61060842

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201710839674.4A Active CN107611996B (en) 2017-09-15 2017-09-15 Multi-frequency oscillation out-of-step oscillation center positioning and migration tracking system and method thereof

Country Status (1)

Country Link
CN (1) CN107611996B (en)

Families Citing this family (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN108400594A (en) * 2018-03-27 2018-08-14 云南电网有限责任公司 A kind of method and system of determining Power System Oscillation Center Transport
CN108736492A (en) * 2018-05-21 2018-11-02 云南电网有限责任公司 A kind of composite information out-of-step solution method and system for oscillation center migration
CN110690716B (en) * 2019-08-16 2022-09-27 中国电力科学研究院有限公司 Method and system for positioning active splitting section of power grid based on voltage trajectory information
CN110736939A (en) * 2019-11-07 2020-01-31 林心 dynamic identification system for oscillation center of power system
CN110763940A (en) * 2019-11-07 2020-02-07 林心 Method for estimating oscillation center of power system by using phasor diagram method

Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN107134776A (en) * 2017-06-27 2017-09-05 华北电力大学 The centralized positioning of multi frequency system asynchronous oscillation and displacement path tracing system and method

Patent Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN107134776A (en) * 2017-06-27 2017-09-05 华北电力大学 The centralized positioning of multi frequency system asynchronous oscillation and displacement path tracing system and method

Also Published As

Publication number Publication date
CN107611996A (en) 2018-01-19

Similar Documents

Publication Publication Date Title
CN107611996B (en) Multi-frequency oscillation out-of-step oscillation center positioning and migration tracking system and method thereof
Tebianian et al. Dynamic state estimation in power systems: Modeling, and challenges
Wang et al. Multi-area dynamic state estimation with PMU measurements by an equality constrained extended Kalman filter
Yu et al. An unscented particle filtering approach to decentralized dynamic state estimation for DFIG wind turbines in multi-area power systems
Milano A geometrical interpretation of frequency
CN107526901B (en) Power system step-out center positioning and oscillation center tracking system and method thereof
CN102403720A (en) Hyper-real-time setting method for superposed time sequences based on transient voltage safety margin
CN103902814A (en) Electric power system operation state detecting method based on dynamic partitioning
Davarikia et al. Real-time integrity indices in power grid: a synchronization coefficient based clustering approach
Guo et al. A Virtual-Flux State Observer-Based Inductance Identification Method for Model Predictive Control of Grid-Tied Inverters With a Finite Phase Angle Set-Based PLL
CN107958120B (en) System Thevenin equivalent parameter calculation method based on power series expansion
CN109617061A (en) The fast evaluation method of stability margin in the case of a kind of unbalanced fault
CN107069697A (en) Power system transient stability based on track characteristic root judges and disturbance type screening technique
US20200132772A1 (en) Dynamic state estimation of an operational state of a generator in a power system
CN112865096A (en) Power distribution network state estimation method and system considering PMU (phasor measurement Unit) measurement phase angle deviation
Bednarz et al. Compensation of the rotor faults in the vector controlled induction motor drive using parameter estimator
CN104578010A (en) Full impedance distance protection method based on FPGA
CN111208340A (en) Single-phase fundamental wave reactive current accurate detection method based on Fourier transform
CN107045489A (en) The determination method and device of critical clearing time
Daisy et al. Single phase fault location in power distribution network using combination of impedance based method and voltage sage matching algorithm
Dang et al. Fast single-phase fault location method based on community graph depth-first traversal for distribution network
JP2018091745A (en) Method, device and program for calculating instantaneous value symmetric component
Rouhani et al. A robust dynamic state estimator against exciter failures
Emami et al. Power system dynamic state estimation using particle filter
Xing et al. On-line Identification of Equivalent Inertia for DFIG Wind Turbines Based on Extended Kalman Filters

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant