CN108988320B - Method for analyzing influence of response characteristic of dynamic element of power system on transient voltage stability - Google Patents

Method for analyzing influence of response characteristic of dynamic element of power system on transient voltage stability Download PDF

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CN108988320B
CN108988320B CN201810682902.6A CN201810682902A CN108988320B CN 108988320 B CN108988320 B CN 108988320B CN 201810682902 A CN201810682902 A CN 201810682902A CN 108988320 B CN108988320 B CN 108988320B
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CN108988320A (en
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杜兆斌
张文倩
黄昌树
夏成军
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South China University of Technology SCUT
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
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Abstract

The invention discloses a method for analyzing the influence of the response characteristic of a dynamic element of a power system on the stability of transient voltage. In order to study the main influence of the generator, the high voltage direct current transmission system (HVDC) and the induction motor on the transient voltage stability, a new analysis method is proposed to study the influence of the main dynamic elements on the transient voltage stability from the viewpoint of the generalized branch potential energy. According to the change rule and stability margin information of transient potential energy distribution in the network after the fault, an evaluation index is established by taking the reactive power recovery characteristics of each dynamic element after the fault as a basic variable, and then the transient voltage instability mechanism of the power grid is analyzed. Finally, a three-machine nine-node alternating current and direct current system is adopted to carry out simulation test on an MATLAB and PSAT software platform, and the result shows the feasibility and the effectiveness of the method.

Description

Method for analyzing influence of response characteristic of dynamic element of power system on transient voltage stability
Technical Field
The invention relates to the technical field of analysis of transient voltage stability influence of a power grid, in particular to analysis of influence of dynamic elements such as high-voltage direct-current power transmission, a generator and an induction motor on transient voltage stability of the power grid, and further analysis of a transient voltage instability mechanism after a power system fault.
Background
With the increasing of the number of direct current feed-in returns of receiving-end power grids represented by long triangles and bead triangles and the increasing of the proportion of direct current power feed-in, the power grid in China is not a pure alternating current power grid any more, but becomes a large-scale national-scale alternating current-direct current interconnected power grid, and the complexity degree is increased gradually. Large area power failure accidents due to voltage instability or voltage collapse continue to occur. Home and abroad electric power researchers have to pay more and more attention to the problem of voltage stability. Compared with a traditional alternating current system, the high-voltage direct current system with the thyristor as the core has many new dynamic characteristics, the influence of the reactive power recovery characteristic after the fault on the voltage stability is more prominent, and the voltage stability of the system is more influenced along with the gradual increase of the direct current feed-in proportion. How to better evaluate the influence of a series of dynamic elements including the direct current converter on the stability after the fault and guide the method for optimizing the stability performance have practical significance. In the traditional research idea, a time domain simulation method is often used, and the influence of the dynamic component on the transient stability of the system is analyzed by changing system parameters, but the time consumption is long. The direct method gradually steps into the field of view of the public with the advantage that it can be used to analyze stability and provide stability margins, where the energy function becomes an important tool. In an alternating current-direct current hybrid system, the reactive power recovery characteristic of a direct current receiving end converter system is also the voltage instability of the whole system caused by the instability of an induction motor, and the specific reasons are difficult to distinguish. This problem is associated with less work. And how to construct the corresponding evaluation index to distinguish the influence of different dynamic elements is a difficult problem.
Disclosure of Invention
With the increase of the complexity of the power network, after the system fails, the dynamic recovery characteristics of various power devices will have different influences on the transient voltage stability of the power system. The excessive concentration of transient energy of the system after the fault is the main reason of the instability of the system, and the change of the power of the generator is reflected in various local potential changes according to the parameters and characteristics of each part of the system. Inspired by the above thought and the transient voltage analysis skill, the invention provides an evaluation method for evaluating the influence of dynamic elements of different systems on the transient voltage stability. The invention provides a new analysis method for researching the influence of main dynamic elements such as a generator, a high voltage direct current transmission system (HVDC), an induction motor and the like on the transient voltage stability from the viewpoint of the generalized branch potential energy. According to the change rule and stability margin information of transient potential energy distribution in the network after the fault, an evaluation index is established by taking the reactive dynamic recovery characteristics of each electrical device after the fault as a basic variable, and then the transient voltage instability mechanism of the power grid is analyzed. The method can quantitatively balance the action of each dynamic element, analyze the mechanism of system voltage instability and guide the optimization strategy of the transient voltage stability of the system.
The purpose of the invention can be achieved by adopting the following technical scheme:
a method for analyzing the influence of the response characteristic of a dynamic element of a power system on the stability of transient voltage comprises the following steps:
s1, establishing a power system mathematical model, and constructing an energy function expression capable of reflecting the power system mathematical model based on the Lyapunov theory;
and S2, judging the transient voltage stability. The transient voltage stability is judged by adopting a constant energy surface constructed by the bifurcation condition of the power system and a heuristic voltage instability type dominant unstable balance point, but the method is not limited to the method. The method comprises the following steps:
s201, constructing an energy function;
s202, solving a dominant unstable balance point;
s203, solving the critical energy Ucr;
s204, solving the energy U at the fault clearing moment;
s205, judging the size of the energy U at the fault clearing moment and the critical energy Ucr, and if the energy U at the fault clearing moment is larger than the critical energy Ucr, judging that the transient voltage of the system is unstable; otherwise, continuing to the next step;
s206, judging whether a singular surface is encountered, if so, judging that the transient voltage of the system is unstable, and otherwise, judging that the system is stable.
S3, extracting parts related to dynamic elements according to the energy function expression constructed in the step S1, and establishing potential energy component functions of the dynamic elements, wherein the dynamic elements include but are not limited to a generator, a high-voltage direct-current power transmission system and an induction motor;
s4, during the fault, the power system injects a large amount of energy into the power grid, the rotating speed of the generator is increased to increase kinetic energy, after the fault is cleared, the total energy is conserved, and the kinetic energy is gradually converted into potential energy of each dynamic element and the power transmission line along the power network. As the oscillation of the kinetic energy changes, the potential energy of the individual dynamic elements increases gradually and is also accompanied by a certain oscillation. The dynamic element with the largest potential energy amplification is subjected to larger energy impact, and accordingly local energy overshoot is easier to form, so that collapse is easier to occur at the dynamic element, and therefore the vulnerable area of the power grid can be simply analyzed by utilizing the potential energy increment of the first half cycle wave of the potential energy oscillation curve where the maximum potential energy of each dynamic element is located after a fault.
Setting the time when the potential energy component of the equipment reaches the maximum value (or the maximum value) after the fault as T2, and setting the potential energy component corresponding to the time as U2In this cycle, the minimum time before the maximum value is reached is T1, and the potential energy component at the corresponding time is U1Then this periodThe difference of medium potential energy is delta U ═ U2-U1。
The evaluation index I: sigma1＝ΔU/ΔQ
And the evaluation index II: sigma2＝V(T2)/ΔU
And the delta Q is the reactive power variation of the equipment under the influence of the dynamic recovery characteristic after the fault in the corresponding time period. V (T2) is the corresponding incoming bus voltage magnitude for the device at time T2. Sigma1The larger the value is, the larger the potential energy increase caused by the reactive dynamic change of the equipment in the period is, namely the larger the energy impact is, the more easily the amplitude which can be borne by the network is exceeded, and then the stability condition is easy to be damaged at the position, and finally the system is crashed; sigma2The smaller the value of (b) is, that is to say, the moment when the device recovers after a fault and the energy impact is large, the voltage value of the bus node connected to the device is still lower, that is to say, the device is more likely to become a critical branch. Therefore, the evaluation of the influence of different system dynamic elements on the transient voltage stability can be realized.
Further, the mathematical model of the power system has N generator nodes, N load nodes, 2 bus nodes of the dc system converter station, and only 1 balance node, and includes:
the fourth-order generator model is expressed as follows:
Figure GDA0002537586010000041
the three-order induction motor model is expressed as follows:
Figure GDA0002537586010000042
the energy function expression of the mathematical model of the power system is as follows:
U＝UAC+UL1+UL2i+Ug+UR+UI+Ud+UDC
wherein:
Figure GDA0002537586010000043
Figure GDA0002537586010000051
Figure GDA0002537586010000052
Figure GDA0002537586010000053
Figure GDA0002537586010000054
and has the following components:
E＝[E1,…,En]T，Ei＝[E′qiEfdi]；T＝blockdiag[T1,…,Tn]，
Figure GDA0002537586010000055
Figure GDA0002537586010000056
wherein, subscripts i and j represent network bus node labels, i ═ 1, 2, …, N + 3; j is 1, 2, …, N + 3.
Where ρ isiIs to make Bi -1TiPositively determined parameters, and for any non-zero matrix vector, all have xTBi -1Tix>0，i＝1，2，…，n。C＝[C1,…,Cn]T，Ci＝[0l]；
Figure GDA0002537586010000057
Figure GDA0002537586010000058
UDC＝-VIVRBIRcos(θI-θR)；
Figure GDA0002537586010000059
In the above formula, when i is 1, 2, …, n, ω isiIs the rotational speed of the generator,ifor generator rotor angle, MiIs the generator inertia time constant, PmiFor generator mechanical power, DiIs damping coefficient, E'qiIs q-axis transient potential, XdiIs the transient reactance of the generator, X'diIs the sub-transient reactance of the generator, T'doiIs d-axis transient time constant, EfdiFor excitation potential, PeiFor the electromagnetic power of the generator, muiFor feedback of gain factor, T, to excitation controllerviFor controlling the time constant, k, of excitationiIs a linear coefficient, l, related to the voltage of an accessed bus in a first-order mathematical model of the excitation voltageiA control constant for connecting the bus i and making the excitation of the generator positive; r subscript represents a rectifier side variable, I subscript represents an inverter side variable, VRAnd VIThe amplitude of the AC bus voltage is T 'when i ═ N +1, N +2, …, N + N + 3'diAs stator open-circuit time constant, MiIs an induction motor inertia time constant, E'LiIs internal potential amplitude, X'iIs a transient reactance, XiIn order to be a synchronous reactance,ifor the power angle of the induction motor, siFor induction motor slip, TmiFor induction of electromagnetic torque of motors, TeiIs a mechanical torque; u shapeACFor exchanging network potential energy, UL1For static load potential energy, UL2iFor accessing i-node induction motor load potential energy, UgFor all the generators of the system, URPotential energy of DC rectification side and AC network interface, UIPotential energy of DC inversion side and AC network interface, UDCFor potential energy between nodes of a DC network, UdFor exchanging DC powerPotential energy component of composition, ViAnd VjThe voltage amplitudes, theta, of the bus-bar indices i and j, respectivelyiAnd thetajThe phase angles of the voltages, Q, of the bus-bars i and j, respectivelyL1iReactive power, P, of static load connected to bus-bar numbered iL1iThe active power of the static load connected to the bus with the reference number i.
Compared with the prior art, the invention has the following advantages and effects:
the method is used for analyzing the transient voltage instability influence factors of the system by taking the reactive dynamic characteristics of the dynamic elements as the interest variables from the perspective of energy and domains based on the distribution and propagation characteristics of energy in the power system. The invention provides a simple evaluation index, transient voltage, reactive power and energy are combined, the influence of each dynamic element on the transient voltage stability is comprehensively analyzed from the perspective of a system, and voltage optimization measures can be further guided and selected on the basis.
Drawings
FIG. 1 is a schematic flow chart of a method for analyzing the influence of the response characteristic of a dynamic element of a power system on the stability of transient voltage disclosed in the present invention;
FIG. 2 is a schematic diagram of a three-machine nine-node system including DC;
FIG. 3 is a graph of the voltage at the 1.18s partial bus node at the fault clearing time;
FIG. 4 is a graph of the change in DC potential of the induction motor after 1.178s clearing the fault;
FIG. 5 is a graph of the change in potential energy of the generator after 1.178s clearing the fault;
FIG. 6 is a power angle diagram of the generator at 1.178s fault clearing;
FIG. 7 is a graph of induction motor slip for a 1.18s post fault instability condition.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Examples
As shown in fig. 1, a flowchart of a method for analyzing an influence of a response characteristic of a dynamic element of a power system on transient voltage stability is shown, where the method for analyzing an influence of a response characteristic of a dynamic element of a power system on transient voltage stability includes the following steps:
and S1, establishing a power system mathematical model, and constructing an energy function expression capable of reflecting the power system mathematical model based on the Lyapunov theory. The resulting energy function expression is shown below:
U＝UAC+UL1+UL2i+Ug+UR+UI+Ud+UDC
wherein:
Figure GDA0002537586010000081
Figure GDA0002537586010000082
Figure GDA0002537586010000083
Figure GDA0002537586010000084
and has the following components:
E＝[E1,…,En]T，Ei＝[E′qiEfdi]；T＝blockdiag[T1,…,Tn]，
Figure GDA0002537586010000085
Figure GDA0002537586010000086
Figure GDA0002537586010000087
where ρ isiIs to make Bi -1TiPositively determined parameters, and for any non-zero matrix vector, all have
xTBi -1Tix>0，i＝1，2，3；
C＝[C1,…,Cn]T，Ci＝[0 l]；
Figure GDA0002537586010000088
Figure GDA0002537586010000089
Figure GDA00025375860100000810
In the present embodiment, when i and j are 1, 2, 3, …, 9, i is 1, 2, 3, i is the bus of the generator, i is 6, i is the load bus of the induction motor, and the subscripts i and j represent the network bus node numbers. When i is 1, 2, 3, ωiIs the rotational speed of the generator,ias a generatorRotor angle, MiIs the generator inertia time constant, PmiFor generator mechanical power, DiIs damping coefficient, E'qiIs q-axis transient potential, XdiIs the transient reactance of the generator, X'diIs the sub-transient reactance of the generator, T'doiIs d-axis transient time constant, EfdiFor excitation potential, PeiFor the electromagnetic power of the generator, muiFor feedback of gain factor, T, to excitation controllerviFor controlling the time constant, k, of excitationiIs a linear coefficient, l, related to the voltage of an accessed bus in a first-order mathematical model of the excitation voltageiA control constant for connecting the bus i and making the excitation of the generator positive; r subscript represents a rectifier side variable, I subscript represents an inverter side variable, VRAnd VIThe amplitude of the AC bus voltage; when i is 6, T'diAs stator open-circuit time constant, MiIs an induction motor inertia time constant, E'LiIs internal potential amplitude, X'iIs a transient reactance, XiIn order to be a synchronous reactance,ifor the power angle of the induction motor, siFor induction motor slip, TmiFor induction of electromagnetic torque of motors, TeiIs a mechanical torque; u shapeACFor exchanging network potential energy, UL1For static load potential energy, UL2iFor accessing i-node induction motor load potential energy, UgFor all the generators of the system, URPotential energy of DC rectification side and AC network interface, UIPotential energy of DC inversion side and AC network interface, UDCFor potential energy between nodes of a DC network, UdPotential energy component formed for DC power exchange, ViAnd VjThe voltage amplitudes, theta, of the bus-bar indices i and j, respectivelyiAnd thetajThe phase angles of the voltages, Q, of the bus-bars i and j, respectivelyL1iReactive power, P, of static load connected to bus-bar numbered iL1iThe active power of the static load connected to the bus with the reference number i.
Step S2, transient voltage stability determination. The transient voltage stability is judged by adopting a power system bifurcation condition and a constant energy surface of a voltage instability type dominant unstable balance point structure obtained based on a heuristic method, but the method is not limited to the method.
In this embodiment, a three-phase short-circuit fault is set when the bus 5 is at the time of 1s, the time of 1.18s is cleared, the PSAT is interrupted during time domain simulation, that is, as shown in fig. 3, under the fault, the transient operation trajectory touches a singular surface after the fault, which causes that the time domain simulation under a differential algebraic equation set (DAE) model cannot be operated, at this time, the transient energy value after the fault is cleared is 0.36, which is smaller than the critical energy obtained by leading an unstable equilibrium point, but under the fault, the transient operation trajectory touches the singular surface after the fault, which causes that the time domain simulation under the DAE model cannot be operated, and since the singular bifurcation phenomenon is closely related to the transient voltage instability, the present embodiment is also considered to have the transient voltage instability.
And step S3, extracting parts related to dynamic elements according to the energy function expression constructed in the step S1, and establishing a potential energy component function of each dynamic element, wherein the dynamic elements comprise but are not limited to a generator, a high-voltage direct-current power transmission system and an induction motor.
The potential energy component function of each dynamic element obtained in step S1 is expressed as follows:
potential energy of the generator:
Figure GDA0002537586010000101
potential energy component of induction motor:
Figure GDA0002537586010000102
potential energy component of the direct current transmission system:
Figure GDA0002537586010000103
the variables are characterized by the symbols in step S1. And obtaining the potential energy component values and the change curves of each time step according to the time domain simulation result.
Step S4, during the fault, the power system injects a large amount of energy into the power grid, the rotating speed of the generator is increased to increase kinetic energy, after the fault is cleared, the total energy is conserved, and the kinetic energy is gradually converted into potential energy of each dynamic element and the power transmission line along the power network. As the oscillation of the kinetic energy changes, the potential energy of the individual dynamic elements increases gradually and is also accompanied by a certain oscillation. The dynamic element with the largest potential energy amplification is subjected to larger energy impact, and accordingly local energy overshoot is easier to form, so that collapse is easier to occur at the dynamic element, and therefore the vulnerable area of the power grid can be simply analyzed by utilizing the potential energy increment of the first half cycle wave of the potential energy oscillation curve where the maximum potential energy of each dynamic element is located after a fault.
Setting the time when the potential energy component of the equipment reaches the maximum value (or the maximum value) after the fault as T2, and setting the potential energy component corresponding to the time as U2In this cycle, the minimum time before the maximum value is reached is T1, and the potential energy component at the corresponding time is U1Then the potential energy difference in this period is Δ U ═ U2-U1。
The evaluation index I: sigma1＝ΔU/ΔQ
And the evaluation index II: sigma2＝V(T2)/ΔU
And the delta Q is the reactive power variation of the equipment under the influence of the dynamic recovery characteristic after the fault in the corresponding time period. V (T2) is that the device is at T2The time corresponds to the amplitude of the incoming bus voltage. Sigma1The larger the value is, the higher the increase speed of the potential energy caused by the reactive dynamic change of the equipment in the period is, the larger the increase is, namely, the more energy impact can be borne, the more easily the amplitude can be borne by the network at the position can be exceeded, and then the stability condition is more easily damaged at the position, and finally the system is crashed; sigma2The smaller the value of (b) is, that is to say, the moment when the device recovers after a fault and the energy impact is large, the voltage value of the bus node connected to the device is still lower, that is to say, the device is more likely to become a critical branch.
Based on the system of fig. 2, the three-phase short-circuit fault is set when the bus 5 is at 1s, and the fault is cleared at 1.05s, 1.1s, 1.14s and 1.178s respectively.
Comparing the same fault clearing time, the potential energy oscillation amplification curve after the fault (taking fig. 4 and fig. 5 as examples) can obviously find that: in the period of reaching the maximum potential energy of the direct current system and the No. 2 generator, the oscillation amplitude from the minimum value to the maximum value is maximum, then the load of the induction motor is applied, and finally the No. 1 generator and the No. 3 generator are applied. Meanwhile, it can be found that as the electrical distance from the fault point increases, the time of the maximum amplitude of potential energy oscillation of each electrical device under the energy impact gradually increases, which also reflects the propagation characteristic of energy in the network and the situation that transient voltage instability may occur in a multi-pendulum manner.
TABLE 1 index σ1
Figure GDA0002537586010000121
TABLE 2 index two sigma2
Figure GDA0002537586010000122
In Table 1, the index one σ of the DC system1The corresponding value is much higher than the other devices, followed by the number 2 generator and induction motor load, while the number 3 generator, which is the farthest electrical distance from the fault point, is the smallest. The method is characterized in that under the action of the recovery characteristics of each electrical device, when the direct current receiving end converter system is subjected to maximum energy impact due to dynamic reactive change, the potential energy oscillation amplitude and the amplification speed of the direct current system are easy to increase, namely, local energy is easy to be too large at the position, the local energy exceeds the bearing capacity of the position to cause system stability damage, and then the transient voltage breakdown of the system is accelerated. Therefore, the reactive power recovery characteristic of the direct current receiving end converter system is dominant in the transient voltage instability of the system.
With the increase of the fault clearing time, the induction motor load and the No. 2 generator index one sigma1Gradually increases in absolute value of (a) and σ of the direct current system1The value becomes smaller by a small margin. Therefore, the longer the fault clearing time is, the larger the voltage drop amplitude of each node of the system during the fault is, and the load characteristic of the induction motor is stable to the transient voltageThe influence of sex is gradually increased. In the three generators, when the No. 2 generator is impacted by energy, under the action of direct current recovery characteristics, load characteristics of an induction motor and transmission characteristics of a power transmission network, the influence of reactive dynamic change formed for supporting network node voltage on self potential energy oscillation amplitude and frequency is higher than that of the other two generators, which shows that after a fault is cleared, the No. 2 generator is easy to have overlarge local energy change, and if transient voltage instability occurs, the No. 2 generator is expected to have power angle instability earlier than the other two generators. Because the connected No. 2 bus is connected with the direct current system, and in the table 2, the indexes of No. 2 generator, high-voltage direct current system and induction motor load are two sigma2The corresponding values are much lower than for generator No. 1 and generator No. 3, so generator No. 2, the dc system, the induction motor load form the voltage weak point of the power system.
In addition, as is apparent from the data in table 1 and the above two tables, as the fault clearing time increases, the larger the voltage drop amplitude during the fault is, the larger the energy value injected into the system during the fault is, the larger the energy impact on each dynamic element of the system after the fault is, the larger the local energy value accumulated at the load of the number 2 generator, the dc system and the induction motor is, and the lower the transient voltage stability is.
Under a stable condition (fig. 6 is an example), the relative power angle swing amplitude of the No. 2 generator far exceeds that of the other two units, and the power angle is advanced. When transient voltage instability occurs, although the PSAT cannot continue simulation due to the limitation of the DAE model when encountering a singular surface, fig. 7 shows that the slip of the induction motor reaches a peak value and has a tendency to decrease when 1.2s occurs, that is, the load rotor of the induction motor starts to accelerate, which indicates that when encountering a singular surface, the voltage of the whole system is collapsed instead of the voltage of the induction motor due to the load voltage instability of the induction motor caused by the stalling caused by the abnormal acceleration of the induction motor, and therefore, the dominance of the reactive power recovery characteristic of the dc-receiving-end converter system on the transient voltage instability of the system is also laterally illustrated.
In summary, in order to study the main influence of the generator, the high voltage direct current transmission system (HVDC) and the motor on the transient voltage stability, the invention provides a new analysis method to study the influence of the main dynamic elements on the transient voltage stability from the viewpoint of the generalized branch potential. According to the change rule and stability margin information of transient potential energy distribution in the network after the fault, an evaluation index is established by taking the reactive dynamic recovery characteristics of each electrical device after the fault as a basic variable, and then the transient voltage instability mechanism of the power grid is analyzed. The result of the time domain simulation is basically consistent with the analysis result of the method, and the effectiveness of the method is verified.
The above embodiments are preferred embodiments of the present invention, but the present invention is not limited to the above embodiments, and any other changes, modifications, substitutions, combinations, and simplifications which do not depart from the spirit and principle of the present invention should be construed as equivalents thereof, and all such changes, modifications, substitutions, combinations, and simplifications are intended to be included in the scope of the present invention.

Claims (4)

1. A method for analyzing the influence of the response characteristic of a dynamic element of a power system on the stability of transient voltage is characterized by comprising the following steps:
s1, establishing a power system mathematical model, and constructing an energy function expression capable of reflecting the power system mathematical model based on the Lyapunov theory;
s2, transient voltage stability judgment, namely judging the transient voltage stability through the bifurcation condition of the power system and a constant energy surface of a voltage instability type dominant instability balance point structure obtained based on a heuristic method;
s3, extracting parts related to dynamic elements according to the energy function expression constructed in the step S1, and establishing potential energy component functions of the dynamic elements, wherein the dynamic elements comprise a generator, a high-voltage direct-current power transmission system and an induction motor;
s4, during a fault, the power system injects a large amount of energy into the power grid, the rotation speed of the generator increases to cause the increase of kinetic energy, after the fault is cleared, the total energy is conserved, the kinetic energy is gradually converted into the potential energy of each dynamic element and the power transmission line along the power network, the potential energy of each dynamic element is gradually increased along with the oscillation change of the kinetic energy and is accompanied with certain oscillation, the dynamic element with the largest potential energy increment is subjected to larger energy impact, and the fragile area of the power grid is analyzed by utilizing the potential energy increment of the first half periodic wave of the potential energy oscillation curve of the maximum potential energy of each dynamic element.
2. The method for analyzing influence of response characteristics of dynamic elements of an electric power system on transient voltage stability according to claim 1, wherein the step S2 comprises the following steps:
s201, constructing an energy function;
s202, solving a dominant unstable balance point;
s203, solving the critical energy Ucr;
s204, solving the energy U at the fault clearing moment;
s205, judging the size of the energy U at the fault clearing moment and the critical energy Ucr, and if the energy U at the fault clearing moment is larger than the critical energy Ucr, judging that the transient voltage of the system is unstable; otherwise, continuing to the next step;
s206, judging whether a singular surface is encountered, if so, judging that the transient voltage of the system is unstable, and otherwise, judging that the system is stable.
3. The method for analyzing influence of response characteristics of dynamic elements of an electric power system on transient voltage stability according to claim 1, wherein in step S4, the vulnerable area of the power grid is analyzed by the potential energy increment of the first half periodic wave of the potential energy oscillation curve where the maximum value of the potential energy of each dynamic element is located, and the influence of the dynamic elements of different systems on transient voltage stability is evaluated by the following evaluation indexes, specifically as follows:
setting the time when the potential energy component of the equipment reaches the maximum value or the maximum value after the fault as T2, and setting the potential energy component corresponding to the time as U2In this potential energy fluctuation cycle, the minimum time before reaching the maximum value is T1, and the potential energy component at the corresponding time is U1Then the potential energy difference in the potential energy fluctuation period is delta U ═ U2-U1The evaluation index is defined as follows:
the evaluation index I: sigma1＝ΔU/ΔQ
And the evaluation index II: sigma2＝V(T2)/ΔU
And in the corresponding time period, the delta Q is the reactive power variation of the equipment under the influence of the dynamic recovery characteristic after the fault, and V (T2) is the corresponding access bus voltage amplitude of the equipment at the time T2.
4. The method according to claim 1, wherein the mathematical model of the power system has N generator nodes, N load nodes, 2 bus nodes of the dc system converter station, and only 1 balance node, and comprises:
the fourth-order generator model has the expression:
Figure FDA0002537586000000031
the three-order induction motor model has the expression:
Figure FDA0002537586000000032
the energy function expression of the mathematical model of the power system is as follows:
U＝UAC+UL1+UL2i+Ug+UR+UI+Ud+UDC
wherein:
Figure FDA0002537586000000033
Figure FDA0002537586000000034
Figure FDA0002537586000000035
Figure FDA0002537586000000036
and has the following components:
E＝[E1,…,En]T，Ei＝[E′qiEfdi]；T＝blockdiag[T1,…,Tn]，
Figure FDA0002537586000000037
A＝blockdiag[A1,…,An]，
Figure FDA0002537586000000041
B＝blockdiag[B1,…,Bn]，
Figure FDA0002537586000000042
Figure FDA0002537586000000043
where the subscripts i and j represent the network bus node designation, i 1, 2, …, N +3, j 1, 2, …, N +3, ρiIs to make Bi -1TiPositively determined parameters, and for any non-zero matrix vector, all have xTBi -1Tix>0，i＝1，2…，n；
C＝[C1,…,Cn]T，Ci＝[0l]；
Figure FDA0002537586000000044
Figure FDA0002537586000000045
UDC＝-VIVRBIRcos(θI-θR)；
Figure FDA0002537586000000046
In the above formula, when i is 1, 2, …, n, ω isiIs the rotational speed of the generator,ifor generator rotor angle, MiIs the generator inertia time constant, PmiFor generator mechanical power, DiIs damping coefficient, E'qiIs q-axis transient potential, XdiIs the transient reactance of the generator, X'diIs the sub-transient reactance of the generator, T'doiIs d-axis transient time constant, EfdiFor excitation potential, PeiFor the electromagnetic power of the generator, muiFor feedback of gain factor, T, to excitation controllerviFor controlling the time constant, k, of excitationiIs a linear coefficient, l, related to the voltage of an accessed bus in a first-order mathematical model of the excitation voltageiA control constant for connecting the bus i and making the excitation of the generator positive; r subscript represents a rectifier side variable, I subscript represents an inverter side variable, VRAnd VIThe amplitude of the AC bus voltage is T 'when i ═ N +1, N +2, …, N + N + 3'diAs stator open-circuit time constant, MiIs an induction motor inertia time constant, E'LiIs internal potential amplitude, X'iIs a transient reactance, XiIn order to be a synchronous reactance,ifor the power angle of the induction motor, siFor induction motor slip, TmiFor induction of electromagnetic torque of motors, TeiIs a mechanical torque; u shapeACFor exchanging network potential energy, UL1For static load potential energy, UL2iFor accessing i-node induction motor load potential energy, UgFor all generator energy of the system, URPotential energy of DC rectification side and AC network interface, UIPotential energy of DC inversion side and AC network interface, UDCFor potential energy between nodes of a DC network, UdPotential energy component formed for DC power exchange, ViAnd VjThe voltage amplitudes, theta, of the bus-bar indices i and j, respectivelyiAnd thetajThe phase angles of the voltages, Q, of the bus-bars i and j, respectivelyL1iReactive power, P, of static load connected to bus-bar numbered iL1iThe active power of the static load connected to the bus with the reference number i.
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