CN108879671B - Voltage fluctuation analysis method and system under generalized forced oscillation - Google Patents
Voltage fluctuation analysis method and system under generalized forced oscillation Download PDFInfo
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Abstract
The invention discloses a method and a system for analyzing voltage fluctuation under generalized forced oscillation. The existing research on the generalized forced oscillation mainly focuses on the power angle oscillation problem of the power system, and relatively less focuses on the voltage oscillation problem which is also important. The technical contents adopted by the invention comprise: acquiring a time domain curve of power fluctuation and voltage fluctuation of each node in a network; calculating point by point to obtain a time domain curve of voltage fluctuation proportion components according to a power flow equation of the network and power fluctuation curves of all nodes; the time domain curve of the voltage fluctuation and the time domain curve of the voltage fluctuation proportion component are subjected to difference to obtain a resonance component time domain curve; and calculating to obtain a voltage fluctuation resonance component power spectrum and voltage oscillation mode information from the resonance component time domain curve. The invention obtains the mode information of voltage oscillation by calculating the power spectrum of the resonance component, thereby realizing the analysis of the voltage fluctuation under the generalized forced oscillation.
Description
Technical Field
The invention relates to the field of electric power system forced oscillation analysis, in particular to a voltage fluctuation analysis method and system under generalized forced oscillation.
Background
With the continuous enlargement of the scale of the interconnected power grid, the low-frequency oscillation of the power system greatly restricts the transmission capability of the power grid, and becomes a prominent problem influencing the safety and stability of the interconnected power grid. The generalized forced oscillation under the random power excitation is relatively simple in occurrence condition compared with the traditional forced oscillation, and the threat to the power system is often larger. The existing research on the generalized forced oscillation mainly focuses on the power angle oscillation problem of the power system, and relatively less focuses on the voltage oscillation problem which is also important.
In contrast to the generalized forced oscillation, which is a system oscillation caused by a continuous periodic disturbance with a single frequency, the system oscillation is actually a point-to-point excitation mode from the viewpoint of the frequency domain, as shown in fig. 1, where U and Y represent excitation and response, respectively.
However, the structure of the power system is complex, the randomness is strong, the frequency of the random excitation is far higher than that of the traditional single-frequency sinusoidal excitation, and the oscillation phenomenon caused by some random excitation cannot be completely explained by a general narrow-sense forced oscillation theory, which is mainly based on the generalized forced oscillation theory of the power system. The generalized forced oscillation is relative to the narrow-sense forced oscillation, and refers to the forced oscillation of the power system under random excitation.
For a power system under a general random excitation, since an excitation amplitude thereof is generally small, the power system at this time can be regarded as a linear system. For this linear system, the power spectrum formula is calculated from the time domain curve of the excitation or response as follows:
FT(f)＝F[fT(t)] (1)
the frequency domain transfer function is assumed to be H (f), the input random excitation can be regarded as a stationary random process, and the power spectral density function of the random process is Su(f) The output can also be considered as a stationary random process with a corresponding power spectral density function of Sy(f) Then, the input and output to the linear system are:
Sy(f)＝|H(f)|2Su(f) (3)
therefore, if Su(f) Can cover a larger part of the frequency spectrum with larger power density, the corresponding power density of the system output power spectrum in the part is also larger, and the dynamic of the corresponding mode of the part is excited, as shown in f of fig. 2o1. If the power spectrum of the input random noise is shifted and moves to a higher frequency, the excited mode is f with higher dampingo2,fo3As shown in fig. 3.
Compared with the generalized forced oscillation, the narrow-sense forced oscillation is a special case of the generalized forced oscillation, the input corresponding to the narrow-sense forced oscillation is a numerical value of a certain frequency in a power spectrum, so that the narrow-sense forced oscillation is a point-to-point excitation mode, and under the condition that the excitation intensity is kept unchanged, the output power spectrum obtained after the excitation frequency is changed and multiple times of simulation is consistent with the input power spectrum, so that the power spectrum of voltage fluctuation during the narrow-sense forced oscillation has the similar characteristic with the system transfer function power spectrum in shape.
It can be seen from fig. 2 and 3 that the generalized forced oscillation is actually a point-facing excitation mode, i.e. when the frequency spectrum of some random power fluctuations in the power system covers some weakly damped natural modes of the system, these weakly damped natural modes will be excited. Therefore, compared with the condition that the narrow sense forced oscillation generates resonance, namely the disturbance source is a single frequency and the disturbance frequency is close to the natural frequency of the system, the probability of the broad sense forced oscillation is much higher, only the disturbed power spectrum is covered to the weak damping natural mode, and the phenomenon that the network random power fluctuation can often cause the oscillation of the power grid can be explained.
According to the generalized forced oscillation theory, when the power spectrum of random power fluctuation in the power system covers some weak damping modes, the forced oscillation of the system, which is also called generalized forced oscillation, is excited. In the literature, although the research on the generalized forced oscillation has been focused on the power angle and the active oscillation in many cases, the analysis of the simulation result can find that the generalized forced oscillation is accompanied by the voltage fluctuation, and the voltage fluctuation under the generalized forced oscillation is analyzed below.
For the power grid, the random excitation intensity in the power system is generally small, and the random excitation intensity is small disturbance compared with the system, so that a linear system model can be adopted for the system in the analysis process. Faster random power fluctuations in the grid may excite the dynamics of the system under certain conditions. In addition, since the voltage fluctuation under random excitation has a strong random characteristic and its characteristic is not clear from the time domain curve of the voltage fluctuation under narrow forced oscillation, it is preferable to analyze the voltage fluctuation from the frequency domain perspective using a power spectrum.
For a power system under random power excitation, the input excitation is Δ P, and the corresponding voltage response is Δ U, and the response model is shown in fig. 4.
The transfer function is decomposed according to the response characteristic of the voltage with reference to the decomposition method of the load model as follows:
G(s)＝G(0)+Gd(s) (4)
in the above formula, Gd(s) ═ G(s) -G (0), so Gd(0) The voltage response under random power excitation can be decomposed based on the derivation as follows:
u(t)＝u0(t)+ud(t) (5)
the corresponding frequency domain expression is as follows:
ΔU0＝G(0)ΔP (6)
ΔUd＝Gd(s)ΔP (7)
the above transfer function can be expressed in the form of a frequency domain, as follows:
Hd(f)＝Gd(s)|s＝j2πf，H0＝G(0) (8)
the power spectrum calculation formulas corresponding to the voltage response components are respectively as follows:
Su0(f)＝H0 2Sp0(f) (9)
Sud(f)＝|Hd(f)|2Spd(f) (10)
wherein, Delta U0The system function corresponding to the component is H0The steady state relationship between the input and output is reflected. Thus, the voltage response corresponding to this component is primarily related to the network equation and the power excitation, and is not referred to as the proportional component. Delta UdThe transfer function corresponding to the component is Hd(f) According to the generalized forced oscillation theory, if the power spectrum of the power fluctuation covers Hd(f) The weakly damped oscillation mode of (2) will excite forced oscillation of the voltage, the mechanism is similar to resonance and is not called resonance component. Therefore, the mode information of the voltage oscillation can be obtained through the analysis of the power spectrum of the resonance component.
Disclosure of Invention
The invention aims to provide a voltage fluctuation analysis method under generalized forced oscillation, which obtains mode information of voltage oscillation by calculating a resonance component power spectrum so as to realize analysis of voltage fluctuation under generalized forced oscillation.
Therefore, the invention adopts the following technical scheme: a method of voltage fluctuation analysis under generalized forced oscillation, comprising:
step 2, carrying out load flow calculation point by point according to the network parameters of the power system and the power fluctuation time domain curve of each node to obtain a time domain curve of voltage fluctuation proportion components;
step 3, subtracting the time domain curve of the voltage fluctuation and the time domain curve of the voltage fluctuation proportion component to obtain a resonance component time domain curve;
and 4, calculating to obtain a voltage fluctuation resonance component power spectrum and voltage oscillation mode information from the resonance component time domain curve according to a power spectrum calculation formula.
The method comprises the steps of firstly decomposing voltage fluctuation under generalized forced oscillation into a proportional component and a resonance component, then calculating the proportional component of the voltage fluctuation through power fluctuation and a power flow equation of a network, obtaining the resonance component of the voltage fluctuation by making a difference between a voltage fluctuation curve of a concerned node and the proportional component, and finally obtaining a power spectrum of the resonance component and mode information of the voltage oscillation through a power spectrum calculation formula.
As a supplement to the above technical solution, the specific content of step 1 includes: and obtaining a power fluctuation time domain curve of a load and a generator node in the network and a voltage fluctuation time domain curve of a voltage oscillation node in the network through a PMU or RTU device of the power system.
As a supplement to the above technical solution, the specific content of step 2 includes: after network parameters required by load flow calculation in a known power system are known, power and voltage values of load nodes and generator nodes at all times are obtained by utilizing power fluctuation time domain curves of all nodes, and voltage of all nodes is calculated point by point through a load flow equation to obtain a time domain curve of voltage fluctuation proportion components.
As a supplement to the above technical solution, the specific content of step 4 includes: and 3, after the time domain curve of the resonance component is obtained in the step 3, the voltage fluctuation resonance component is processed by a power spectrum calculation formula to obtain a power spectrum of voltage oscillation, and then the main mode of the voltage oscillation is determined by the peak of the power spectrum.
The invention also provides a system for analyzing voltage fluctuation under generalized forced oscillation, which comprises:
an acquisition module: acquiring a time domain curve of power fluctuation and voltage fluctuation of each node in a network;
a load flow calculation module: carrying out load flow calculation point by point according to the network parameters of the power system and the power fluctuation time domain curve of each node to obtain a time domain curve of the voltage fluctuation proportion component;
a time domain curve difference module: the time domain curve of the voltage fluctuation and the time domain curve of the voltage fluctuation proportion component are subjected to difference to obtain a resonance component time domain curve;
a resonance component time domain curve calculation module: and according to a power spectrum calculation formula, calculating a voltage fluctuation resonance component power spectrum and voltage oscillation mode information by using the resonance component time domain curve.
The invention has the following beneficial effects: the voltage fluctuation under the generalized forced oscillation is decomposed into a proportional component and a resonance component, then the voltage fluctuation power spectrum and the proportional component power spectrum are subjected to difference to obtain a resonance component power spectrum, and finally the voltage oscillation detailed mode information resonance component is obtained through the power spectrum peak value of the resonance component, so that the analysis of the voltage fluctuation under the generalized forced oscillation is realized.
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The drawings are not intended to be drawn to scale. In the drawings, each identical or nearly identical component that is illustrated in various figures may be represented by a like numeral. For purposes of clarity, not every component may be labeled in every drawing.
FIG. 1 is a diagram illustrating the relationship between excitation and response under a narrowly defined forced oscillation in the background of the present invention;
FIGS. 2-3 are schematic diagrams illustrating the relationship between input and output under generalized forced oscillation in the background of the present invention;
FIG. 4 is a diagram illustrating a mathematical model of a system in the background of the invention when a power excitation causes a generalized forced oscillation of the system;
FIG. 5 is a flow chart of a method for analyzing voltage fluctuation under generalized forced oscillation according to an embodiment of the present invention;
FIG. 6 is a system wiring diagram of the 4-machine 2 area in the embodiment of the present invention;
FIG. 7 is a time domain plot of narrow band power excitation when resonance is excited in an embodiment of the present invention;
FIG. 8 is a time domain plot of voltage response under narrow band power excitation when resonance is excited in an embodiment of the present invention;
FIG. 9 is a time domain plot of the proportional component of the voltage response when resonance is excited in an embodiment of the present invention;
FIG. 10 is a time domain plot of voltage response resonance components when resonance is excited in an embodiment of the present invention;
FIG. 11 is a graph comparing power spectra of components of power excitation and voltage response when resonance is excited in an embodiment of the invention.
Detailed Description
In order to better understand the technical content of the present invention, specific embodiments are described below with reference to the accompanying drawings.
In this disclosure, aspects of the present invention are described with reference to the accompanying drawings, in which a number of illustrative embodiments are shown. Embodiments of the present disclosure are not necessarily intended to include all aspects of the invention. It should be appreciated that the various concepts and embodiments described above, as well as those described in greater detail below, may be implemented in any of numerous ways, and that the concepts and embodiments disclosed herein are not limited to any embodiment. In addition, some aspects of the present disclosure may be used alone, or in any suitable combination with other aspects of the present disclosure.
Example 1
In connection with the flow chart of a method for analyzing voltage fluctuation under generalized forced oscillation according to some embodiments of the present invention shown in fig. 5, a method for analyzing voltage fluctuation under generalized forced oscillation according to some embodiments of the present invention includes the following steps: step 1, acquiring a time domain curve of power fluctuation and voltage fluctuation of each node in a network; step 2, calculating point by point to obtain a time domain curve of voltage fluctuation proportion components according to a power flow equation of the network and power fluctuation time domain curves of all nodes; step 3, subtracting the time domain curve of the voltage fluctuation and the time domain curve of the voltage fluctuation proportion component to obtain a resonance component time domain curve; and 4, calculating to obtain a voltage fluctuation resonance component power spectrum and voltage oscillation mode information from the resonance component time domain curve.
An exemplary implementation of the foregoing steps of the present embodiment is described in more detail below.
In a typical 4-machine 2-division example system, as shown in fig. 6, the step 1 obtains a time domain curve of power fluctuation and voltage fluctuation of each node in the network, which specifically includes:
the power fluctuation curves of the load and generator nodes in the network and the voltage fluctuation curves of the nodes where voltage oscillation occurs in the network are obtained by PMU or RTU devices of the power system, as shown in fig. 7 and 8.
In some examples, the step 2 performs load flow calculation point by point according to the power system network parameters and the power fluctuation curve of each node to obtain a time domain curve of the voltage fluctuation proportion component, and specifically includes:
after the network parameters required by the load flow calculation in the power system are known, the node power and the voltage value of the load node and the generator at each moment are obtained by using the power fluctuation curve of each node, and the voltage of each node is calculated point by point through the load flow equation to obtain a time domain curve of the voltage fluctuation proportion component, as shown in fig. 9.
In some examples, the step 3 is to obtain a time domain curve of the resonance component by subtracting the time domain curve of the voltage fluctuation and the time domain curve of the voltage fluctuation proportion component, and specifically includes:
the voltage fluctuation curve of the voltage oscillation node is obtained through the step 1, and after the time domain curve of the voltage fluctuation proportion component is obtained through the step 2, the two curves are subtracted to obtain a resonance component time domain curve, as shown in fig. 10.
In some examples, in step 4, the voltage fluctuation resonance component power spectrum and the voltage oscillation mode information are calculated from the resonance component time domain curve according to a power spectrum calculation formula, and the specific implementation includes:
after the time domain curve of the resonance component is obtained in step 3, the voltage fluctuation resonance component is subjected to a power spectrum calculation formula to obtain a power spectrum of voltage oscillation, and then a main mode of the voltage oscillation is determined by a peak of the power spectrum, as shown in fig. 11.
Example 2
The present embodiment provides a system for analyzing voltage fluctuation under generalized forced oscillation, including:
an acquisition module: acquiring a time domain curve of power fluctuation and voltage fluctuation of each node in a network;
a load flow calculation module: carrying out load flow calculation point by point according to the network parameters of the power system and the power fluctuation time domain curve of each node to obtain a time domain curve of the voltage fluctuation proportion component;
a time domain curve difference module: the time domain curve of the voltage fluctuation and the time domain curve of the voltage fluctuation proportion component are subjected to difference to obtain a resonance component time domain curve;
a resonance component time domain curve calculation module: and according to a power spectrum calculation formula, calculating a voltage fluctuation resonance component power spectrum and voltage oscillation mode information by using the resonance component time domain curve.
Although the present invention has been described with reference to the preferred embodiments, it is not intended to be limited thereto. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the invention. Therefore, the protection scope of the present invention should be determined by the appended claims.
Claims (2)
1. A method for analyzing voltage fluctuation under generalized forced oscillation is characterized by comprising the following steps:
step 1, acquiring a time domain curve of power fluctuation and voltage fluctuation of each node in a network;
step 2, carrying out load flow calculation point by point according to the network parameters of the power system and the power fluctuation time domain curve of each node to obtain a time domain curve of voltage fluctuation proportion components;
step 3, subtracting the time domain curve of the voltage fluctuation and the time domain curve of the voltage fluctuation proportion component to obtain a resonance component time domain curve;
step 4, calculating to obtain a voltage fluctuation resonance component power spectrum and voltage oscillation mode information by a resonance component time domain curve according to a power spectrum calculation formula;
the specific content of the step 1 comprises:
obtaining a power fluctuation time domain curve of a load and a generator node in a network and a voltage fluctuation time domain curve of a voltage oscillation node in the network through a PMU or an RTU device of a power system;
the specific content of the step 2 comprises:
after each network parameter required by load flow calculation in a known power system is obtained, the power fluctuation time domain curve of each node is utilized to obtain the power and the voltage value of each load node and generator node at each moment, and the voltage of each node is calculated point by point through a load flow equation to obtain a time domain curve of voltage fluctuation proportion components;
the specific content of the step 4 comprises:
and 3, after the time domain curve of the resonance component is obtained in the step 3, the voltage fluctuation resonance component is processed by a power spectrum calculation formula to obtain a power spectrum of voltage oscillation, and then the main mode of the voltage oscillation is determined by the peak of the power spectrum.
2. A system for analyzing voltage fluctuations under generalized forced oscillation, comprising:
an acquisition module: acquiring a time domain curve of power fluctuation and voltage fluctuation of each node in a network;
a load flow calculation module: carrying out load flow calculation point by point according to the network parameters of the power system and the power fluctuation time domain curve of each node to obtain a time domain curve of the voltage fluctuation proportion component;
a time domain curve difference module: the time domain curve of the voltage fluctuation and the time domain curve of the voltage fluctuation proportion component are subjected to difference to obtain a resonance component time domain curve;
a resonance component time domain curve calculation module: according to a power spectrum calculation formula, calculating a voltage fluctuation resonance component power spectrum and voltage oscillation mode information by using a resonance component time domain curve;
the acquisition module acquires a power fluctuation time domain curve of a load and a generator node in a network and a voltage fluctuation time domain curve of a voltage oscillation node in the network through a PMU or RTU device of the power system;
the load flow calculation module obtains the power and voltage values of the load nodes and the generator nodes at each moment by using the power fluctuation time domain curves of the nodes after the network parameters required by the load flow calculation in the power system are known, and calculates the voltage of each node point by point through a load flow equation to obtain a time domain curve of the voltage fluctuation proportion component;
the resonance component time domain curve calculation module obtains the time domain curve of the resonance component through the time domain curve difference module, obtains the power spectrum of the voltage oscillation through the voltage fluctuation resonance component by the power spectrum calculation formula, and then determines the main mode of the voltage oscillation through the peak of the power spectrum.
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