JP5040553B2 - Power oscillation mode observation device - Google Patents

Description

  The present invention relates to a power oscillation mode observation apparatus that observes a power oscillation mode of a power system.

  Conventionally, in the steady state stability analysis of the power system, the state estimation calculation method for estimating the system bus voltage and the eigenvalue calculation method for calculating the eigenvalue of the coefficient matrix of the state transition equation of the power system are offline. The power fluctuation phenomenon has been evaluated by calculation, which has contributed to stable operation of the power system. This is because the system bus voltage had to be estimated by state estimation calculation, and it was considered that the power fluctuation phenomenon, which is a phenomenon with a period of several seconds, could not be monitored.

  Recently, the phase angle detector PMU (Phasor Measurement Unit) that can directly measure the phase angle of the system bus voltage of the power system has become inexpensive, and the system bus voltage (both magnitude and phase angle) can be measured in near real time. It has become possible to measure. Since the phase bus detector can measure the system bus voltage in real time and grasp the power fluctuation phenomenon in real time, many applications have been proposed for on-line steady state stability evaluation methods. ing.

  For example, by using the phase angle detection device PMU, it is possible to measure remote and multi-point information at the same time, and to monitor and control the system stability of the real-time power system based on wide-area data collection (For example, refer to Patent Document 1).

In the future, the trend of applying the phase angle detection device PMU to system stability evaluation will not be shaken. There are reports on.
JP 2006-2111830 A

  However, in the system stability evaluation using the phase angle detector PMU, the period of the power oscillation mode can be calculated with practical accuracy, but the damping coefficient (attenuation) that plays an important role in the steady state stability evaluation. Regarding the identification of the ratio, the current situation is that sufficient accuracy has not been obtained.

  The reason why the accuracy of the power fluctuation attenuation ratio cannot be obtained is that white noise is included in the system bus voltage (magnitude, phase angle) detected by the phase angle detector PMU, and this component can be removed. What can not be done is raised. For this reason, the steady-state stability evaluation system using the phase angle detection device PMU is a factor that cannot ensure sufficient practical performance.

  FIG. 5 is an explanatory diagram of how to determine the power oscillation attenuation ratio in a conventional steady-state stability evaluation system using the phase angle detector PMU. In general, the transmission power P is expressed by the following equation (1).

P = (V1 · V2 / X) sinΔδ (1)
However, V1: Power transmission end voltage, V2: Power reception end voltage, X: Reactance between power transmission and reception ends, Δδ: Phase difference angle (phase angle deviation) between power transmission end voltage V1 and power reception end voltage V2
Accordingly, when the power P varies, the phase angle deviation Δδ varies. For example, if an event that affects power fluctuation (capacitor insertion, generator insertion, etc.) occurs at time points t1, t2, and t3 in FIG. 5, the phase angle deviation Δδ varies as shown in FIG. Arise. The phase angle detection device PMU detects the phase angle δ of the system bus voltage, and the stationary stability evaluation system obtains the phase angle deviation Δδ from the reference phase angle δ0, and the phase angle of such system bus voltage Data of the deviation Δδ is taken in a window having a predetermined width, and the steady state stability is evaluated.

  If the data of the phase angle deviation Δδ in FIG. 5 is taken in the windows W1, W2, and W3 having small widths immediately after the occurrence of the event at the times t1, t2, and t3, the event at the times t1, t2, and t3 On the other hand, the phase angle deviation Δδ becomes an attenuation waveform and has attenuation ratios d1 ′, d2 ′, and d3 ′. Accordingly, the real part of the eigenvalue of the coefficient matrix in the state transition equation for the phase angle deviation Δδ in the windows W1, W2, and W3 is negative. Since the real part of the eigenvalue is negative, the steady-state stability evaluation system evaluates that the power fluctuations p1, p2, and p3 are attenuated and stabilized.

  On the other hand, when the phase angle deviation Δδ of FIG. 5 is captured in the window W4 having a large width so as to include all the events at the time points t1, t2, and t3, the phase is changed with respect to the events at the time points t1, t2, and t3. The angle deviation Δδ is a divergent waveform at first and then becomes an attenuation waveform, and becomes attenuation ratios d1, d2, and d3 ′. Accordingly, the real part of the eigenvalue of the coefficient matrix in the state transition equation with respect to the phase angle deviation Δδ of the window W4 may be positive. At this time, the real part of the eigenvalue is positive. It will be evaluated that the fluctuation p4 diverges and becomes unstable.

  As described above, depending on the size of the window for taking in the phase angle deviation Δδ, the identification of the damping ratio having an important role in the steady state stability evaluation differs, and sufficient accuracy may not be obtained.

  An object of the present invention is to provide a power oscillation mode observation apparatus capable of accurately identifying an attenuation ratio having an important role in the evaluation of steady state stability using a phase angle detection apparatus.

  The power oscillation mode observation apparatus according to the invention of claim 1 is provided in each of a plurality of subsystems divided so as to enable analysis of the power oscillation mode of the power system, and the magnitude of the system bus voltage of each subsystem. And a phase measurement device for measuring a phase angle, and a system bus voltage for each subsystem measured by the phase measurement device with respect to each subsystem other than the reference with any one of the plurality of subsystems as a reference And a data input processing means for obtaining a phase angle deviation and a frequency deviation based on the phase angle and frequency of a reference subsystem based on the phase angle, Observation data storage for storing phase angle deviation and frequency deviation of system bus voltage for each subsystem obtained by processing means as observation data The observation data of each subsystem is randomly extracted from a plurality of sub-windows whose width is smaller than the width of the main window having the same period width as the observation data stored in the observation data storage unit. Observation data extraction means, state transition equation creation means for creating a state transition equation for each sub-window with the phase angle deviation and frequency deviation of the observation data taken out by the observation data extraction means as a state variable, and the state transition equation creation An eigenvalue calculating means for obtaining an eigenvalue of a coefficient matrix of the state transition equation for each subwindow created by the means, and an output process for displaying and outputting a distribution of eigenvalue groups for each subwindow calculated by the eigenvalue calculating means as a complex plane Means.

  The power oscillation mode observation apparatus according to the invention of claim 2 is provided in each of a plurality of subsystems divided so as to enable analysis of the power oscillation mode of the power system, and the magnitude of the system bus voltage of each subsystem. And a phase measurement device for measuring a phase angle, and a system bus voltage for each subsystem measured by the phase measurement device with respect to each subsystem other than the reference with any one of the plurality of subsystems as a reference And a data input processing means for obtaining a phase angle deviation and a frequency deviation based on the phase angle and frequency of a reference subsystem based on the phase angle, Observation data storage for storing phase angle deviation and frequency deviation of system bus voltage for each subsystem obtained by processing means as observation data The observation data of each subsystem is randomly extracted from a plurality of sub-windows whose width is smaller than the width of the main window having the same period width as the observation data stored in the observation data storage unit. Observation data extraction means, state transition equation creation means for creating a state transition equation for each sub-window with the phase angle deviation and frequency deviation of the observation data taken out by the observation data extraction means as a state variable, and the state transition equation creation Eigenvalue calculating means for obtaining the eigenvalue of the coefficient matrix of the state transition equation for each subwindow created by the means, and eigenvalue extraction for obtaining the most probable eigenvalue from the eigenvalue group for each subwindow calculated by the eigenvalue calculating means Means.

  According to a third aspect of the present invention, there is provided the power fluctuation mode observation device according to the second aspect of the present invention, wherein the frequency / attenuation ratio calculating means calculates the frequency and attenuation ratio in the subsystem of the power system based on the eigenvalue obtained by the eigenvalue extracting means. It is provided with.

  According to the present invention, observation data for each subsystem measured by the phase measurement device is sequentially extracted in a time series in the same predetermined main window, and the extracted observation data is obtained from the width of the main window. Since the observation data is randomly extracted from multiple subwindows with a small width and different widths, the distribution of the eigenvalue group of the coefficient matrix of the state transition equation obtained from the observation data of the multiple subwindows is obtained and displayed. From the display result, a probable eigenvalue can be obtained. As a result, it is possible to accurately identify the frequency and attenuation ratio calculated from the eigenvalues.

  In addition, the most probable eigenvalues can be obtained from the calculated eigenvalue groups for each subwindow, and the frequency and attenuation ratio in the power system subsystem can be obtained based on the obtained eigenvalues. The damping ratio can be identified.

  First, the focus of the present invention will be described. In the past, the data window (window) from which the observation data was extracted was fixed, but the observation data was extracted from the consideration that the power fluctuation phenomenon was caused by white noise existing in the power system. A plurality of windows with different widths are prepared as windows, and data is extracted from observation data by applying the window at random and utilizing the empirical rule that eigenvalues obtained from each window form a probability distribution. .

  FIG. 1 is a configuration diagram when the power fluctuation mode observation device according to the embodiment of the present invention is applied to a power system. The power system is divided into a plurality of subsystems 11 so that the power fluctuation mode can be analyzed, and a phase measuring device 12 is provided in each of the divided subsystems 11. FIG. 1 shows a case where the power system is divided into three subsystems 11a, 11b, and 11c, and phase measuring devices 12a, 12b, and 12c are provided in the respective subsystems 11a, 11b, and 11c.

  The phase measuring devices 12a, 12b, and 12c are phase measuring devices having a time synchronization function for inputting time information from a GPS (Global Positioning System) 13 and adding time information to observation data, and each subsystem 11a, 11b. 11c, the magnitude and phase angle of the system bus voltage are measured.

  The observation data measured by the phase measuring devices 12a, 12b, and 12c are input to, for example, the arithmetic device 14 that constitutes the computer system, and are stored in the storage device 15 in time series. The computing device 14 analyzes the power oscillation mode of the power system based on the observation data stored in the storage device 15 and outputs the analysis result to the display device 16 and the output device 17.

In this case, any one of the plurality of subsystems 11a, 11b, and 11c is used as a reference. For example, when the reference sub-system 11a, based on the phase angle δa of the reference subsystem 11a, the arithmetic unit 14, other subsystems 11b, 11c phase angle [delta] _b, the phase angle between the [delta] _c The deviations Δδ _ba and Δδ _ca are obtained, the power oscillation mode of the power system is analyzed, and the analysis result is output to the display device 16 and the output device 17.

  FIG. 2 is a configuration diagram of the power oscillation mode observation apparatus according to the embodiment of the present invention. FIG. 2 shows a power oscillation mode observation apparatus when the power system is divided into n subsystems. The phase measuring devices 12a to 12n of each subsystem detect the magnitude of the system bus voltage at the reference time and the phase angle from the reference time with reference to the time information from the GPS 13 shown in FIG. The magnitude and phase angle of the system bus voltage of each subsystem detected by the phase measuring devices 12a to 12n of each subsystem are input to the data input processing means 18 of the arithmetic unit 14 at a predetermined cycle, and the storage device 15 Are stored in the observation data storage unit 19 in time series.

  The data input processing means 18 obtains the frequency of the system bus (the angular velocity of the generator connected to the system bus) by time differentiation of the input phase angle, and the frequency of the reference subsystem and the subsystem other than the reference. The frequency deviation from the frequency is calculated and stored in the observation data storage unit 19 of the storage device 15 in time series. For the phase angle, the deviation between the phase angle of the reference subsystem and the phase angle of the subsystem other than the reference is calculated, and stored in the observation data storage unit 19 of the storage device 15 in time series as the phase angle deviation x2. To do. Thereby, the magnitude, phase angle, frequency deviation, and phase angle deviation of the synchronized system bus voltage are stored in the observation data storage unit 19 for each subsystem.

  Next, in order to evaluate the power system oscillation mode, the observation data extraction unit 20 extracts the observation data stored in the observation data storage unit 19. First, a main window having the same period width is prepared in order to extract observation data in a synchronized period for each subsystem.

  FIG. 3 is an explanatory diagram of the main window W. FIG. 3 shows a case where the observation data is a frequency deviation and the period width of the main window W is T [s]. Such a main window W is applied in synchronization with observation data (frequency deviation) of each subsystem. For example, the main window W is sequentially applied to new time-series observation data such that the first time is the period width T from the start time t11 of the power oscillation mode and the period width T is from the start time t12 of the second power oscillation mode. Will be applied.

The observation data extracting means 20 extracts a random observation data subsystems in one main window W in different plurality of sub-windows in w ₁ to w _n. The width of the sub-window w ₁ to w _n is smaller than the width of the main window W, the size of each width is made different. The maximum width T _max of the sub-windows w _{1 to} w _n is an estimated time from the occurrence of an event (capacitor insertion, generator insertion, etc.) that affects power fluctuations to decay to a predetermined range. The minimum width T _min of the windows w _{1 to} w _n is set to the minimum time required to reproduce the observation data. This is derived from the sampling theorem.

In FIG. 3, the case of frequency deviation as observation data has been described. However, in the observation data extraction unit 20, among the observation data of each subsystem, not only the frequency deviation but also the phase angle deviation includes a plurality of subwindows w _{1 to} w _n. Take out at random. This is because it is appropriate to use two state variables of frequency deviation and phase angle deviation as modeling for analyzing the power fluctuation of each subsystem.

The frequency deviation and the phase angle deviation for each subwindow of each subsystem extracted by the observation data extracting unit 20 are input to the state transition equation creating unit 21. The state transition equation of modeling for analyzing the power fluctuation mode of the power system is expressed by the following equation (1).

x ₁ , x ₃ ,..., x _2n−1 are frequency deviations of the system bus voltage, and x ₂ , x ₄ ,... x _2n are phase angle deviations of the system bus voltage. That is, x ₁ and x ₂ are frequency deviations and phase angle deviations of the subsystem 1, x ₃ and x ₄ are frequency deviations and phase angle deviations of the subsystem ₁ , and x _2n−1 and x _2n are frequency deviations of the subsystem n. And the phase angle deviation. Further, the dot “·” attached to the upper part of the frequency deviations x ₁ , x ₃ ,... X _2n−1 and the phase angle deviations x ₂ , x _{4 ,.} Thus, the frequency deviation _{x 1,} x 3, _... time derivative of _{x 2n-1} denotes the angular acceleration of the generator connected to the system bus, the phase angle deviation _{x 2, x 4, ... x} 2n frequency deviation Means. _{Also, a 11 ~a (2n-1} ) n is a coefficient.

The state transition equation creation means 21 inputs the frequency deviation and phase angle deviation of the system bus voltage for each sub-window of each subsystem excluding the reference subsystem, and the coefficients a _{11 to} a _(2n ) in the equation (1). _{-1) A} state transition equation is generated by using, for example, the least square method so that _n is fitted to the observation data of the frequency deviations x ₁ , x ₃ ,... X _2n−1 shown in FIG. Thus, (1) a state transition equation, will be generated by the number of sub-windows w ₁ to w _n.

  Next, the eigenvalue calculating unit 22 obtains eigenvalues of the coefficient matrix of the state transition equation created by the state transition equation creating unit 21. Since the state transition equation is created for each sub-window, there are a plurality of eigenvalues for the observation data of the main window W. This eigenvalue group is stored in the eigenvalue group storage unit 23 of the storage device 15. Then, the output processing unit 24 displays and outputs the eigenvalue group for the observation data of the main window W stored in the eigenvalue group storage unit 23 of the storage device 15 on the display device 16 and, if necessary, an output device such as a printing device. 17 is printed out.

In addition, the eigenvalue extraction unit 25 obtains the most probable eigenvalue from the eigenvalue group for the observation data of the main window W stored in the eigenvalue group storage unit 23. In obtaining the most probable eigenvalue, an average value of the eigenvalues may be obtained, or may be obtained using the method of least squares as shown in equation (2).

In equation (2), α _i is the real part of the eigenvalue to be obtained, β _i is the imaginary part of the eigenvalue to be obtained, n is the number of remaining subsystems other than the reference subsystem (subsystem number −1), and m is the subwindow. The number, a _ij is the real part of the eigenvalue group, and b _ij is the imaginary part of the eigenvalue group.

The frequency / attenuation ratio calculation means 26 obtains the frequency and attenuation ratio in the subsystem of the power system based on the most probable eigenvalue obtained by the eigenvalue extraction means 25. The frequency f _i of the subsystem is obtained from the equation (3a), and the attenuation ratio d _i of the subsystem is obtained from the equation (3b).

The output processing unit 24 displays and outputs the subsystem frequency f _i and the subsystem attenuation ratio d _i obtained by the frequency / attenuation rate calculating unit 26 to the display device 16 and outputs the printing device or the like as necessary. Print output to the device 17.

  FIG. 4 is a plan view showing an example of the display screen of the eigenvalue group for the observation data of the main window W displayed on the display device 16. FIG. 4 shows a case where the electric power system is divided into three subsystems, one is a reference subsystem, and eigenvalue groups M1 and M2 of the two subsystems are displayed. The power oscillation mode has two modes 1 and 2 (the number of subsystems −1), and the distribution of the eigenvalue group M1 of mode 1 and the eigenvalue group M2 of mode 2 is displayed by x marks on the complex plane. The distribution of the real part groups Re (M1) and Re (M2) of the eigenvalue groups M1 and M2 and the distribution of the imaginary part groups Im (M1) and Im (M2) of the eigenvalue groups M1 and M2 are displayed in a graph. Yes.

  The mode 1 eigenvalue (α1 + jβ1) and the mode 2 eigenvalue (α2 + jβ2) obtained by the eigenvalue extraction unit 25 are displayed together on the complex plane, and the mode 1 and mode 2 decay rates obtained by the attenuation rate computation unit 26 are displayed. d1 and d2 are also displayed.

  In the above description, the eigenvalue extraction unit 25 and the attenuation rate calculation unit 26 are provided, and the eigenvalues of modes 1 and 2 obtained by the eigenvalue extraction unit 25 and the attenuation rates d1 and d2 obtained by the attenuation rate calculation unit 26 are also displayed. However, these displays may be omitted. That is, the distribution of the eigenvalue groups M1 and M2 is displayed on the complex plane, and the distribution of the real part groups Re (M1) and Re (M2) of the eigenvalue groups M1 and M2 and the imaginary part group Im ( The distribution of M1) and Im (M2) may be simply displayed as a graph.

  In this case, it is not necessary to provide the eigenvalue extraction unit 25 and the frequency / attenuation rate calculation unit 26, and by observing the distribution of the eigenvalue group of the power fluctuation mode displayed for each subsystem, Therefore, a probable eigenvalue is determined by visual inspection. Then, the frequency and attenuation ratio in the subsystem are obtained from the obtained eigenvalue.

  As described above, in the embodiment of the present invention, using observation data accumulated for a certain period, observation data is randomly extracted from the accumulated observation data in a plurality of subwindows prepared in advance, and based on the extracted observation data. To estimate the power oscillation mode. The estimated mode (the eigenvalue group of the coefficient matrix of the state transition equation) becomes a data string having a certain variance depending on the position of the subwindow. Therefore, a probable eigenvalue is obtained from the eigenvalue group. For example, since the distribution of the identification calculation result of the eigenvalue group is often a normal distribution, the least square method is applied to this data string to obtain a highly reliable power oscillation mode estimation value.

  According to the embodiment of the present invention, the power oscillation mode is calculated using observation data accumulated for a certain period of time as compared with the conventional detailed analysis, so that the calculation time is long and the online performance is slightly sacrificed. However, the power oscillation mode can be calculated with high accuracy. The data to be observed has a steady state stability and is not required to be online, and it is possible to appropriately give the current operation state index of the power system to the system operator.

The block diagram at the time of applying the electric power fluctuation mode observation apparatus concerning embodiment of this invention to an electric power grid | system. The block diagram of the electric power fluctuation mode observation apparatus concerning embodiment of this invention. Explanatory drawing of the main window in embodiment of this invention. The top view which shows an example of the display screen of the eigenvalue group with respect to the observation data of the main window displayed on the display apparatus in embodiment of this invention. Explanatory drawing of how to obtain | require the attenuation ratio of the power oscillation in the conventional steady state stability evaluation system using the phase angle detection apparatus PMU.

Explanation of symbols

DESCRIPTION OF SYMBOLS 11 ... Subsystem, 12 ... Phase measuring device, 13 ... GPS, 14 ... Arithmetic device, 15 ... Storage device, 16 ... Display device, 17 ... Output device, 18 ... Data input processing means, 19 ... Observation data storage part, 20 ... Observation data extraction means, 21 ... State transition equation creation means, 22 ... Eigen value calculation means, 23 ... Eigen value group storage section, 24 ... Output processing means, 25 ... Eigen value extraction means, 26 ... Frequency / attenuation ratio calculation means

Claims (3)

A phase measurement device that is provided in each of a plurality of sub-systems divided so as to enable analysis of the power oscillation mode of the power system, and measures the magnitude and phase angle of the system bus voltage of each sub-system;
Based on any one of the plurality of subsystems, the magnitude and phase angle of the system bus voltage for each subsystem measured by the phase measuring device for each subsystem other than the reference in time series A data input processing means for obtaining a phase angle deviation and a frequency deviation based on the phase angle and frequency of a reference subsystem based on the phase angle;
An observation data storage unit for storing the phase angle deviation and the frequency deviation of the system bus voltage for each subsystem obtained by the data input processing means as observation data;
Observation data for randomly extracting observation data of each subsystem in a plurality of sub-windows whose width is smaller than the width of the main window having the same period width as the observation data stored in the observation data storage unit. Take-out means;
A state transition equation creating means for creating a state transition equation for each sub-window with a phase angle deviation and a frequency deviation of the observation data extracted by the observation data extracting means as state variables;
Eigenvalue calculating means for obtaining eigenvalues of the coefficient matrix of the state transition equation for each subwindow created by the state transition equation creating means;
An electric power fluctuation mode observation device comprising: output processing means for displaying and outputting the distribution of the eigenvalue group for each subwindow calculated by the eigenvalue calculating means as a complex plane. A phase measurement device that is provided in each of a plurality of sub-systems divided so as to enable analysis of the power oscillation mode of the power system, and measures the magnitude and phase angle of the system bus voltage of each sub-system;
Based on any one of the plurality of subsystems, the magnitude and phase angle of the system bus voltage for each subsystem measured by the phase measuring device for each subsystem other than the reference in time series A data input processing means for obtaining a phase angle deviation and a frequency deviation based on the phase angle and frequency of a reference subsystem based on the phase angle;
An observation data storage unit for storing the phase angle deviation and the frequency deviation of the system bus voltage for each subsystem obtained by the data input processing means as observation data;
Observation data for randomly extracting observation data of each subsystem in a plurality of sub-windows whose width is smaller than the width of the main window having the same period width as the observation data stored in the observation data storage unit. Take-out means;
A state transition equation creating means for creating a state transition equation for each sub-window with a phase angle deviation and a frequency deviation of the observation data extracted by the observation data extracting means as state variables;
Eigenvalue calculating means for obtaining eigenvalues of the coefficient matrix of the state transition equation for each subwindow created by the state transition equation creating means;
A power oscillation mode observation apparatus comprising: eigenvalue extraction means for obtaining the most probable eigenvalue from the eigenvalue group for each subwindow calculated by the eigenvalue calculation means.   3. The power fluctuation mode observation device according to claim 2, further comprising frequency / attenuation ratio calculating means for obtaining a frequency and an attenuation ratio in a subsystem of the power system based on the eigenvalue obtained by the eigenvalue extracting means.

Images