CN104217112A - Multi-type signal-based power system low-frequency oscillation analysis method - Google Patents

Abstract

The invention discloses a power system low-frequency oscillation analysis method based on multi-type signals, which belongs to the field of power system stability analysis. The method mainly includes: analyzing the internal physical connection between the multi-type curves of the unit; formulating the evaluation index of amplitude deviation and phase deviation based on the connection, and evaluating the accuracy of the oscillation mode extracted by the Prony algorithm; A certain type of signal is covered up, and the amplitude of different types of signals is converted; a method for identifying the dominant oscillation pattern is given, and a comprehensive evaluation index for multi-machine signals is established to reflect the credibility of the Prony algorithm. The index system proposed by the invention has engineering application value, can reflect the reliability of the information of the oscillation mode extracted, and can select the appropriate order of the Prony algorithm according to the comprehensive index.

Description

A Method for Analyzing Low-Frequency Oscillations of Power Systems Based on Multiple Types of Signals

technical field

The invention belongs to the field of power system stability analysis, and in particular relates to a low-frequency oscillation analysis method of a power system based on multi-type signals.

Background technique

The low-frequency oscillation of the power system directly affects the operation of the interconnected system. The characteristic root method based on the linearization model has a clear physical concept and provides a wealth of information, but it is difficult to calculate for large systems and it is difficult to reflect the influence of nonlinearity. The disturbed trajectory of the system can contain nonlinear effects, and the trajectory acquisition is less affected by the system scale. With the introduction of the Wide Area Measurement System (WAMS), it is possible to monitor the operation of the system in real time without relying on the system model, which provides important information for low-frequency oscillation analysis. disturbed trajectory.

Trajectory-based analysis of low-frequency oscillations mainly includes analysis of stationary oscillation characteristics and non-stationary oscillation characteristics. At present, the analysis of non-stationary oscillation characteristics is mainly based on a single trajectory. Common methods include window Fourier ridge, wavelet ridge, HHT, etc.; stationary oscillation characteristic analysis is applicable It is suitable for single trajectory and multi-machine disturbed trajectory. The common method is Prony algorithm. This algorithm is simple to calculate, but the anti-interference performance is poor, and the appropriate model order needs to be selected. At present, the determinant method and singular value decomposition method are commonly used to determine the order of Prony algorithm. These methods are mainly used to distinguish effective data space and noise space, and it is difficult to evaluate the identification results of different orders of Prony algorithm. For systems with certain nonlinearity, using this method to determine the order of the algorithm may cause overfitting. There are many types of curves in the disturbed trajectory of the power system. Traditionally, a single generator power angle curve, speed curve or tie line power curve is used for oscillation analysis, and the relationship between different types of curves is ignored.

Contents of the invention

The purpose of the present invention is to propose a low-frequency oscillation analysis method for power systems based on multi-type signals. Based on the internal relationship of multi-type curves, the amplitude deviation and phase deviation indicators for evaluating the reliability of the oscillation modes extracted by Prony are established, and the Prony A comprehensive evaluation index for algorithm credibility.

A method for analyzing low-frequency oscillations of power systems based on multi-type signals proposed by the present invention includes the following steps:

(1) Read data of different types of curves and analyze the relationship between different types of curves;

(2) Converting the amplitudes of different types of curves;

(3) Set the initial order N of the multi-machine Prony algorithm, the increased order ΔN and the highest order N _max each time, and set the target values of the comprehensive evaluation indicators η _AmplitudeΣ and η _PhaseΣ

(4) Perform Prony algorithm calculation on different types of curves to obtain the dominant oscillation mode;

(5) Calculate the amplitude deviation percentage and phase deviation percentage of each dominant oscillation mode, and evaluate the accuracy of each dominant oscillation mode;

(6) Calculate the comprehensive evaluation index η _AmplitudeΣ of the amplitude deviation and the comprehensive evaluation index η _PhaseΣ of the phase deviation, and evaluate the credibility of the Prony algorithm; if the comprehensive evaluation index is less than the set target value, then output the result; if the comprehensive evaluation index is greater than the set The target value of the Prony algorithm is increased by ΔN _, and it is judged whether the order of the Prony algorithm is greater than the highest order N _{max .} , then output the result when η _AmplitudeΣ and η _PhaseΣ are minimum.

In the aforementioned step (1), for the generator set, its power angle curve and speed curve are different types of curves,

The expressions are:

${\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}\mathrm{<span\; class="notranslate">\; t</span>}}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&phi;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

Among them: δ _i (t) represents the power angle of unit i relative to the center of inertia, ν _i (t) represents the rotational speed of unit i relative to the center of inertia, -σ _j ±iω _j represents the jth oscillation mode, and n represents the oscillation mode δ _i0 represents the DC component of the power angle curve, A _j represents the amplitude of the jth oscillation mode of the power angle curve, φ _j0 represents the initial phase of the jth oscillation mode of the power angle curve, and B _j represents the jth oscillation mode of the speed curve amplitude of the oscillatory mode, Indicates the initial phase of the jth oscillation mode of the speed curve.

There is a relationship between the aforementioned power angle curve and speed curve: v _i (t) = δ′ _i (t),

Among them, δ′ _i (t) represents the derivative of δ _i (t);

From the relationship between the above power angle curve and speed curve:

The corresponding relationship between amplitude and oscillation mode:

$\frac{{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}{{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}<span\; class="notranslate">\; =</span>\sqrt{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

The relationship between phase difference and oscillation mode:

In the aforementioned step (2), converting the amplitudes of different types of curves includes the following steps:

2-1) Assuming that there are m curves of the same type of signal curve x, and q sampling points, after the signal is subjected to DC isolation processing, the average oscillation energy of the same type of signal is established

${\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; E.</span>}}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; =</span>\frac{\sqrt{\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; q</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i\&Delta;t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}}{\mathrm{<span\; class="notranslate">\; m</span>}}$

Among them, x _k indicates that the k-th signal curve is power angle curve δ _i (t) or speed curve ν _i (t), i indicates the i-th sampling point, and Δt is the sampling step size;

2-2) Perform DC block processing on another type of signal curve y to obtain the average oscillation energy

2-3) Taking the signal curve x as a reference, multiply all y signal curves by Perform amplitude conversion.

In the aforementioned step (4), obtaining the dominant oscillation mode includes the following steps:

4-1) The calculation expression of the percentage η _j of the jth oscillation mode in the total energy is:

${\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}{{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; 100</span>}<span\; class="notranslate">\; \%</span><span\; class="notranslate">\; =</span>\frac{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; l</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; (</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; q</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}\mathrm{<span\; class="notranslate">\; k\&Delta;t</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}{\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; (</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; l</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; (</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; q</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}\mathrm{<span\; class="notranslate">\; k\&Delta;t</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; 100</span>}<span\; class="notranslate">\; \%</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

Among them: P _j is the oscillation energy of the jth oscillation mode, P _Σ is the total energy of all oscillation modes, l is the total number of all different types of curves, q is the number of sampling points, n is the number of oscillation modes, A _ij is the i-th curve j the amplitude of the oscillatory mode;

4-2) The oscillation modes are sorted according to the energy proportion of the oscillation mode, and a threshold ε is set, and the mode whose energy proportion of the oscillation mode exceeds ε is the dominant oscillation mode.

In the aforementioned step (5),

The calculation formula of the amplitude deviation percentage η _jAmplitude of the dominant oscillation mode j is as follows:

${\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; jAmplitude</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}{{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}<span\; class="notranslate">\; -</span>\sqrt{{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\sqrt{{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; 100</span>}<span\; class="notranslate">\; \%</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$

The calculation formula of the phase deviation percentage η _jPhase of the dominant oscillation mode j is as follows:

The larger the η _jAmplitude and η _jPhase data, the less credible the dominant oscillation mode is.

In the aforementioned step (6),

The comprehensive evaluation index η _AmplitudeΣ of described amplitude deviation is:

${\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; Amplitude\&Sigma;</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; jAmplitude</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 8</span>}<span\; class="notranslate">\; )</span>$

The comprehensive evaluation index η _phaseΣ of described phase deviation is:

${\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; phase\&Sigma;</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; jphase</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 9</span>}<span\; class="notranslate">\; )</span>$

Among them, m is the number of dominant oscillation modes.

Compared with the existing low-frequency oscillation analysis, the present invention has the following advantages:

(1) The low-frequency oscillation information of the power system exists in various types of curves. Traditionally, a certain type of curve is usually selected for information extraction, and it is difficult to judge the reliability of the analysis results. The present invention analyzes multi-type information based on the relationship between different types of curves. The physical connection of the system, the evaluation index is constructed, and the accuracy of the oscillation mode information extracted by the Prony algorithm is evaluated;

(2) the present invention has set up comprehensive evaluation index, can reflect the credibility of Prony algorithm;

(3) The comprehensive evaluation index system proposed by the present invention has engineering application value, and the appropriate order of Prony algorithm can be selected according to the comprehensive evaluation index.

Description of drawings

Fig. 1 is a flow chart of the method of the present invention.

Detailed ways

In order to make the purpose, technical solution and advantages of the present invention clearer, the present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments.

As shown in Figure 1, the multi-type signal-based power system low-frequency oscillation analysis method of the present invention includes the following steps:

Step 1. Read data of different types of curves. For generator sets, power angle curves and speed curves belong to two different types of curves.

In a multi-machine system, the unit power angle curve and speed curve are generally displayed using the relative inertia center or angle center. Due to the initial phase difference of the power angle, the power angle curve of the multi-machine system generally contains a DC component, while the speed curve of the units in synchronous operation generally does not contain a DC component. Since the power angle curve and speed curve of each unit contain the same oscillation mode information, the expression is:

${\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}\mathrm{<span\; class="notranslate">\; t</span>}}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&phi;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

In the formula: δ _i (t) represents the power angle of the i-th unit relative to the center of inertia; ν _i (t) represents the rotational speed of the i-th unit relative to the center of inertia, -σ _j ±iω _j represents the j-th oscillation mode, and n represents The number of oscillation modes, δ _i0 represents the DC component of the power angle curve, A _j represents the amplitude of the jth oscillation mode of the power angle curve, φ _j0 represents the initial phase of the jth oscillation mode of the power angle curve, B _j represents the first phase of the rotation speed curve the magnitudes of the j oscillatory modes, Indicates the initial phase of the jth oscillation mode of the speed curve.

Different from simple signal processing, the power system is a physical system, and there is an internal relationship between different types of signal curves. In the actual system, there is a derivative relationship between the power angle curve and the speed curve, that is, v _i (t) = δ′ _i (t ),

Comparing the corresponding coefficients, we can see that

There is a relationship between the amplitude and the mode of oscillation:

$\frac{{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}{{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}<span\; class="notranslate">\; =</span>\sqrt{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

There is a relationship between the phase difference and the oscillation mode:

In step 2, in order to avoid excessive difference in the amplitudes of different types of curves, resulting in signal flooding, it is necessary to convert the amplitudes of different types of curves.

Let the curve of the same type be type x, and the curve of another type be type y, for example, if the power angle curve is type x, then the speed curve is type y.

After the x-type curve is cut off, the average oscillation energy is obtained

Where: q is the number of sampling points; Δt is the step size; m is the number of x-type curves.

In the same way, after the y-type curve is processed by direct isolation, the average oscillation energy is obtained

Taking signal curve x as reference, all y signal curves are multiplied by Perform amplitude conversion to eliminate the huge difference in amplitude caused by different types of curves due to different dimensions.

For example: the curves of the power angle curve y and y' are as follows, y' is the speed curve, the sampling step is 0.05s, and the sampling time is 5s,

y=6e ^-0.5t sin(10t)+2e ^-0.1t sin(20t),

y'=60.08e ^-0.5t sin(10t+1.52)+40.00e ^-0.1t sin(20t+1.57),

Due to the large difference in signal amplitude, according to the amplitude conversion processing method in step 2, with reference to y, the amplitude of y' is processed, and the calculation is So the y' signal is multiplied by 13.77.

Step 3, set the initial order N of the multi-machine Prony algorithm, the increased order ΔN and the highest order N _max each time, and set the target values of the comprehensive evaluation indicators η _AmplitudeΣ and η _PhaseΣ

Step 4, perform Prony algorithm calculation on different types of curves to obtain the dominant oscillation mode.

Considering the influence of noise and nonlinearity, the oscillation mode information obtained by the signal processing method, the signal with a large energy ratio has a higher reliability. For the oscillation mode obtained by the high-order Prony algorithm, it is necessary to sort the extracted mode information to obtain the dominant oscillation mode. The dominant oscillation mode is related not only to the initial amplitude of the oscillation but also to its damping. For the multi-machine disturbed trajectory, the energy of the oscillation mode is included in all oscillation curves, and the calculation formula of the percentage η _j of the jth oscillation mode in the total energy is:

${\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}{{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; 100</span>}<span\; class="notranslate">\; \%</span><span\; class="notranslate">\; =</span>\frac{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; l</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; (</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; q</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}\mathrm{<span\; class="notranslate">\; k\&Delta;t</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}{\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; (</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; l</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; (</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; q</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}\mathrm{<span\; class="notranslate">\; k\&Delta;t</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; 100</span>}<span\; class="notranslate">\; \%</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

in: is the oscillation energy of the jth oscillation mode,

$P_{\mathrm{\&Sigma;}}=\underset{j=1}{\overset{\mathrm{no}}{\mathrm{\&Sigma;}}}\left(\underset{i=1}{\overset{l}{\mathrm{\&Sigma;}}}\left(\underset{k=1}{\overset{q}{\mathrm{\&Sigma;}}}{\left(A_{\mathrm{ij}}{e}^{-{\mathrm{\&sigma;}}_j\mathrm{k\&Delta;t}}\right)}^2\right)\right)$ is the total oscillation energy,

l is the total number of all different types of curves, q is the number of sampling points, n is the number of oscillation modes, and A _ij is the amplitude of the jth oscillation mode of the ith curve.

The oscillation modes are sorted according to the energy proportion of the oscillation mode, and a threshold ε is set, and the mode whose energy proportion of the oscillation mode exceeds ε is the dominant oscillation mode.

Step 5, calculating the amplitude deviation percentage and phase deviation percentage of each dominant oscillation mode, and evaluating the accuracy of each dominant oscillation mode;

The amplitude deviation percentage η _jAmplitude and the phase deviation percentage η _jPhase of the dominant oscillation mode j, as shown in formulas (6) and (7),

${\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; jAmplitude</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}{{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}<span\; class="notranslate">\; -</span>\sqrt{{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\sqrt{{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; 100</span>}<span\; class="notranslate">\; \%</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$

The accuracy of each dominant oscillation mode can be reflected by the corresponding η _jAmplitude and η _jPhase , the larger the data, the lower the accuracy of the dominant oscillation mode, and vice versa, the higher the accuracy of the dominant oscillation mode.

Step 6, calculate the comprehensive evaluation index η _AmplitudeΣ of the amplitude deviation of the output result of the Prony algorithm and the comprehensive evaluation index η _PhaseΣ of the phase deviation, and evaluate the reliability of the Prony algorithm.

For signals with multiple dominant oscillation modes, it is necessary to establish a comprehensive evaluation index to reflect the credibility of the Prony algorithm. In a multi-machine system, each unit has multiple η _jAmplitude and η _jPhase , and it is necessary to establish a comprehensive evaluation index to reflect the credibility of the results. The comprehensive evaluation index needs to reflect the energy proportion, amplitude and phase deviation of each oscillation mode. The construction of comprehensive evaluation indicators is shown in formulas (8) and (9).

${\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; Amplitude\&Sigma;</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; jAmplitude</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 8</span>}<span\; class="notranslate">\; )</span>$

${\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; phase\&Sigma;</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; jphase</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 9</span>}<span\; class="notranslate">\; )</span>$

Among them, η _AmplitudeΣ is the comprehensive evaluation index of amplitude deviation, η _phaseΣ is the comprehensive evaluation index of phase deviation, m is the number of dominant oscillation modes, and η _j is the energy percentage of dominant oscillation mode j.

If the comprehensive evaluation index is less than the set target value, that is It indicates that the calculation of the Prony algorithm is credible, and then output the calculation result of the Prony algorithm; if the comprehensive evaluation index is greater than the set target value, then increase the order of the Prony algorithm ΔN, and judge whether the order of the Prony algorithm is greater than the highest order N _max , if it is less than the highest If the order is N _max , return to step 4 to recalculate. If it is greater than the highest order N _max , it indicates that the Prony algorithm cannot meet the accuracy requirements. Then search for the Prony algorithm when η _AmplitudeΣ and η _PhaseΣ are the smallest during the calculation process, and output the result.

Taking the aforementioned y and y' signals as an example, the noise is 5dB, 10dB and 20dB respectively, and the order of the Prony algorithm is 10, 20 and 40 respectively, and the energy proportion of each oscillation mode is calculated according to the formula (5), and the energy proportion of the oscillation mode is The output results of the dominant oscillation mode are shown in Table 1.

Table 1 Prony algorithm output results

It can be seen from Table 1 that the more accurate the extracted dominant oscillation mode information is, the smaller the corresponding η _jAmplitude and η _jPhase deviations are. It can be seen that the established indicators can be used to evaluate the accuracy of the identification results. Noise will have a certain impact on the output of the Prony algorithm. The signal with a small signal-to-noise ratio has a large amplitude and phase deviation. The high-order Prony algorithm is beneficial to filter white noise, making the result of the dominant oscillation mode more accurate. Analyzing the signals with SNR of 5dB and 10dB, it is found that with the increase of the order of Prony algorithm, the calculation accuracy of the 20th-order model and the 40th-order model has not been significantly improved. It can be seen that there is no need to use an excessively high model if the requirements are met. Order.

The above embodiments are only to illustrate the technical ideas of the present invention, and cannot limit the protection scope of the present invention with this. All technical ideas proposed according to the present invention, any changes made on the basis of technical solutions, all fall within the protection scope of the present invention. Inside.

Claims (7)

1. based on a low-frequency oscillation analysis method for power system for polymorphic type signal, it is characterized in that, comprise the following steps:

(1) read dissimilar curve data, and analyze the relation between dissimilar curve;

(2) conversion process is carried out to the amplitude of dissimilar curve;

(3) the initial exponent number N of multi-machine Prony algorithm is set, the exponent number Δ N of each increase and top step number N _max, comprehensive evaluation index η is set _{amplitude Σ}and η _{phase Σ}desired value

(4) calculating of Prony algorithm is carried out to dissimilar curve, obtain control oscillation modes;

(5) calculate amplitude excursion percentage and the phase deviation percentage of each control oscillation modes, evaluate the accuracy of each control oscillation modes;

(6) the comprehensive evaluation index η of calculated amplitude deviation _{amplitude Σ}with the comprehensive evaluation index η of phase deviation _{phase Σ}, the confidence level of assessment Prony algorithm; If comprehensive assessment index is less than the desired value of setting, then Output rusults; If comprehensive assessment index is greater than the desired value of setting, then increases Prony algorithm exponent number Δ N, and judge whether Prony algorithm exponent number is greater than top step number N _maxif be less than top step number N _max, then return step (4) and recalculate, if be greater than top step number N _max, then η is exported _{amplitude Σ}, η _{phase Σ}result time minimum.

2. a kind of low-frequency oscillation analysis method for power system based on polymorphic type signal according to claim 1, is characterized in that, in described step (1), for genset, its power-angle curve and speed curves are dissimilar curve,

Expression formula is respectively:

${\mathrm{\&delta;}}_i\left(t\right)={\mathrm{\&delta;}}_{i0}+\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{A}_j{e}^{-{\mathrm{\&sigma;}}_{j}t}\sin ({\mathrm{\&omega;}}_{j}t+{\mathrm{\&phi;}}_{j0})---\left(1\right)$

Wherein: δ _it () represents merit angle, i platform unit relative inertia center, ν _it () represents the rotating speed at i-th relative inertia center of unit ,-σ _j± i ω _jrepresent a jth mode of oscillation, n represents mode of oscillation number, δ _i0represent power-angle curve DC component, A _jrepresent the amplitude of a power-angle curve jth mode of oscillation, φ _j0represent the first phase of a power-angle curve jth mode of oscillation, B _jrepresent the amplitude of a speed curves jth mode of oscillation, represent the first phase of a speed curves jth mode of oscillation.

3. a kind of low-frequency oscillation analysis method for power system based on polymorphic type signal according to claim 1 and 2, is characterized in that there is relation between described power-angle curve and speed curves: v _i(t)=δ ' _i(t),

Wherein, δ ' _it () represents δ _ithe derivative of (t);

Obtained by the relation between above-mentioned power-angle curve and speed curves:

Amplitude and relation corresponding to mode of oscillation:

$\frac{B_j}{A_j}=\sqrt{{\mathrm{\&sigma;}}_j^2+{\mathrm{\&omega;}}_j^2}---\left(3\right)$

Relation between phase differential and mode of oscillation:

4. a kind of low-frequency oscillation analysis method for power system based on polymorphic type signal according to claim 1, is characterized in that, in described step (2), carries out conversion process comprise the following steps the amplitude of dissimilar curve:

2-1) establish same type signal curve x to have m bar, sampled point is q, carries out, after straight process, setting up the mean oscillatory energy of signal of the same type to signal

${\stackrel{\&OverBar;}{E}}_x=\frac{\sqrt{\underset{k=1}{\overset{m}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{q}{\mathrm{\&Sigma;}}}{\left(x_k\left(\mathrm{i\&Delta;t}\right)\right)}^2}}{m}$

Wherein, x _krepresent that kth bars curve is power-angle curve δ _i(t) or speed curves ν _i(t), i represents i-th sampled point, and Δ t is sampling step length;

2-2) another type signal curve y is carried out equally every straight process, obtain mean oscillatory energy

2-3) with signal curve x for reference, all y signal curves are multiplied by carry out amplitude conversion.

5. a kind of low-frequency oscillation analysis method for power system based on polymorphic type signal according to claim 1, is characterized in that, in described step (4), obtains control oscillation modes and comprises the following steps:

4-1) jth mode of oscillation accounts for the percentage η of gross energy _jcalculation expression be:

${\mathrm{\&eta;}}_j=\frac{P_j}{P_{\mathrm{\&Sigma;}}}\&times;100\%=\frac{\underset{i=1}{\overset{l}{\mathrm{\&Sigma;}}}\left(\underset{k=1}{\overset{q}{\mathrm{\&Sigma;}}}{\left(A_{\mathrm{ij}}{e}^{-{\mathrm{\&sigma;}}_j\mathrm{k\&Delta;t}}\right)}^2\right)}{\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}\left(\underset{i=1}{\overset{l}{\mathrm{\&Sigma;}}}\left(\underset{k=1}{\overset{q}{\mathrm{\&Sigma;}}}{\left(A_{\mathrm{ij}}{e}^{-{\mathrm{\&sigma;}}_j\mathrm{k\&Delta;t}}\right)}^2\right)\right)}\&times;100\%---\left(5\right)$

Wherein: P _jfor the oscillation energy of jth mode of oscillation, P _Σfor the gross energy of all mode of oscillation, l is all dissimilar curve sums, and q is sampling number, and n is mode of oscillation number, A _ijit is the amplitude of i-th curve jth mode of oscillation;

4-2) sort to mode of oscillation according to mode of oscillation energy accounting, and set up threshold epsilon, mode of oscillation energy accounting takes mode of oscillation as the leading factor more than the pattern of ε.

6. a kind of low-frequency oscillation analysis method for power system based on polymorphic type signal according to claim 1, is characterized in that, in described step (5),

The amplitude excursion percentage η of described control oscillation modes j _jAmplitudecomputing formula as follows:

${\mathrm{\&eta;}}_{\mathrm{jAmplitude}}=|(\frac{B_j}{A_j}-\sqrt{{{\mathrm{\&sigma;}}_j}^2+{\mathrm{\&omega;}}_j^2})/\sqrt{{{\mathrm{\&sigma;}}_j}^2+{\mathrm{\&omega;}}_j^2}|\&times;100\%---\left(6\right)$

The phase deviation percentage η of described control oscillation modes j _jPhasecomputing formula as follows:

Described η _jAmplitudeand η _jPhasedata are larger, represent that this control oscillation modes is more insincere.

7. a kind of low-frequency oscillation analysis method for power system based on polymorphic type signal according to claim 1, is characterized in that, in described step (6),

The comprehensive evaluation index η of described amplitude excursion _{amplitude Σ}for:

${\mathrm{\&eta;}}_{\mathrm{Amplitude\&Sigma;}}=\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}({\mathrm{\&eta;}}_j\&times;{\mathrm{\&eta;}}_{\mathrm{jAmplitude}})---\left(8\right)$

The comprehensive evaluation index η of described phase deviation _{phase Σ}for:

${\mathrm{\&eta;}}_{\mathrm{phase\&Sigma;}}=\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}({\mathrm{\&eta;}}_j\&times;{\mathrm{\&eta;}}_{\mathrm{jphase}})---\left(9\right)$

Wherein, m takes mode of oscillation number as the leading factor.