KR20040061152A - A Method for Calculating Power Oscillation Damping Ratio Using Optimization Technique - Google Patents

Abstract

PURPOSE: A method is provided to calculate a power oscillation damping ratio in an easy and convenient manner by using the data transmitted from the energy measurement system of a power company. CONSTITUTION: A method comprises a step(20) of determining a time area effective power data section measured by a pager measurement unit; a step(21) of initializing a wash-out circuit state variable; a step(22) of removing a direct current offset by a wash-out circuit; a step(23) of checking an oscillation frequency from the absolute value resulted from a fast Fourier transform; a step(24) of fitting the time area measurement data where a direct current offset is removed; and a step(25) of outputting the result of damping ratio.

Description

A Method for Calculating Power Oscillation Damping Ratio Using Optimization Technique}

The present invention relates to a method for calculating a power vibration damping rate using an optimization technique. More particularly, the present invention relates to discrete vibration time-domain data measured by a real-time power vibration monitoring device or an on-line pacer monitoring device in a power system. It relates to a method of calculating the damping rate of.

Conventionally, as a method for calculating the power damping ratio of a power system, the paper J.F.Hauer "APPLICATION OF PRONY ANALYSIS TO THE DETERMINATION OF MODAL CONTENT AND EQUIVALENT MODELS FOR MEASURED POWER SYSTEM RESPONSE", IEEE Trans. on Power Systems, Vol. 6, No. 5, August 1991. and J. F. Hauer, C. J. Demeure, L.L. Scharf, "INITIAL RESULTS IN PRONY ANALYSIS OF POWER SYSTEM RESPONSE SIGNALS", IEEE Transaction on Power Systems, Vol. 5, No. 1, February 1990. The Prony interpretation was published. The technique is a method of calculating the damping rate of power oscillation using a linear prediction model. The calculation algorithm of the Penny analysis is as follows.

Linear, time-invariant dynamic system Initial state Suppose you are in Next, when the input is removed and there is no disturbance, it is expressed by the following differential equation.

here, , Is the vector of state variables of the system, silver The order of the vector. , , Let be the eigenvalues of the A (nxn) matrix, the right eigenvectors, and the left eigenvectors, respectively. Then, Equation 1 can be expressed as follows.

here, Is a symbol representing Sigma, Is the (nxn) residue matrix. At this time, Is a constant value. Eigenvalue Determines the mode's response to The model response distribution of an element is entirely determined by the eigenvectors. As a result, Information about Can be extracted by Modal Decomposition for. Assuming there is one output on the system, the form looks like this:

The Frony method and its modifications are designed to directly estimate the exponential term in equation (2a) or the parameter in equation (3). This measured equation (4) Calculated by fitting to In doing so, it is necessary to model heterogeneous elements, noise, and offsets.

Measured time domain data Assume that N consists of N samplings. then, , k = 0,1, ..., N-1, and the time intervals are equal intervals ( )to be. The strategy for obtaining the Penny interpretation is as follows.

Step 1: Construct a discrete linear prediction model (LPM).

Step 2: Find the multiply roots of the LPM.

Step 3: Determine the Amplitude and Phase for each mode using the Root.

The above procedures are performed in the z-domain. In power system applications, these eigenvalues are usually converted to the s-domain. Pronie's main contribution is in Step 1. To achieve the initial goal, assume that N = 2n and the measured signal is noise-free. If equation 4 is put back in exponential form like equation 5, the notation becomes simple.

Sample time In Equation 5 is compressed as follows.

The end purpose is for all k To be Wow To find. This method can be found using Step 3 above.

The Signal to Noise Ratio (SNR) can be used as a measure of the fitness.

Here, the unit is decibels (dB).

However, the conventional Penny analysis method as described above has the following problems.

First, the conventional Frony method of calculating the damping rate of power oscillation does not know the order of the whole system in advance, which requires a lot of trial and error to determine the order. The calculation time is long because it tries to fit the measured waveforms in higher order.

Second, the power vibration damping rate is calculated by applying two fitting techniques. In the LPM, we first use the fitting technique to calculate the multiple characteristic roots, and secondly we apply the fitting technique to determine the amplitude and phase. Therefore, the calculation time is long because two fitting techniques are applied.

Accordingly, the present invention is to solve the above disadvantages and problems of the prior art, the power vibration damping rate from the discrete time domain data measured in the real-time power vibration monitoring device or pager device for the stable operation of the power system It is an object of the present invention to provide a method for quick and easy calculation.

1 is a system application of the damping rate calculation method of the present invention.

2 is a computational algorithm of the present invention.

3 is a z-region washout circuit of the present invention.

4 is a generator power oscillation (Power Oscillation) in a system accident of the present invention.

5 is a DC component removal using the washout circuit of the present invention.

FIG. 6 is an FFT frequency analysis result of FIG. 5 of the present invention. FIG.

7 is a comparison of the measured data of the present invention with the fitted results.

The above object of the present invention is to determine the time-domain effective power data interval measured in the pager measuring device, initializing the washout circuit state variable, removing the DC offset by the washout circuit, FFT (Fast Fourier Transform) Application result Power oscillation damping rate applying optimization method consisting of checking the fluctuation frequency at the absolute value of magnitude, fitting the time domain measurement data from which the DC offset is applied by the optimization technique, and outputting the damping rate result Achieved by the calculation method.

Details of the above object and technical configuration of the present invention and the effects thereof according to the present invention will be more clearly understood by the following detailed description with reference to the drawings showing preferred embodiments of the present invention.

In order to solve the above problem, the effective value data measured by the pager measuring device is found for each mode frequency using the FFT. The determined number of frequency modes is the actual system order contained in the measured waveform. The process of determining the mode frequency using the FFT is as follows.

As shown in (20) of FIG. 2, the number of discrete active power data measured by the pager measuring device and the Nyquist Criterion frequency of the discrete data measured by the pager device are determined. If the fundamental frequency If the measured active power in a pager device with computes and outputs 120 data per second, the Nyquist condition frequency is 60 Hz. In other words, it can be considered that the measured time-domain discrete value data includes shaking mode information within 60 Hz. The active power data for 30 seconds measured at any moment consists of N = 3600 time domain discrete data. this Suppose that k = 0,1, ..., N-1. When determining this data, it is best to use data that contains as much dynamic dynamics as possible.

The next step is to initialize to remove the DC offset using a washout circuit as shown in (21). Where the washout time constant Can be set from 1.0 to 10 sec. The z-domain washout circuit of Equation 8 is shown in FIG.

The z-domain integrator uses a modified Euler method. Before removing the DC offset, initialize the washout state variable as follows: The state variable for washout is (33), By setting the value, it is assumed that the steady state without disturbance when t = 0. therefore, Degree It will have a value.

The next step is to remove the DC offset using a washout circuit as shown in (22). At this time, Is equal to the sampling time interval. In the example above sec.

In order to obtain the vibration frequency included in the measured discrete time domain active power, FFT analysis is performed on the signal from which the DC offset is removed in FIG. Since the result of the FFT is a real value and an imaginary value, the absolute value of the two values is also calculated. And, since the calculated FFT is computed only by the sampling number, Considering the time interval on the axis Multiply by In this way, the FFT calculation results are analyzed to find the vibration frequency.

In the method of the present invention, the FRONI method uses two fitting techniques. However, in the method of the present invention, after checking the mode using the FFT, Set the initial value and calculate the damping rate, amplitude, and phase with a single fit technique. At this time, the measured data suitable for optimization is the data from which the DC offset is removed in (22) of FIG. Use The optimization formulation can be represented by the least squares method as shown in Equation (9). Finally, the optimization technique is applied to calculate the damping rate, amplitude, and phase to minimize equation (9). The optimization technique uses the fast convergence Gauss-Newton method.

The method used in the present invention, the washout and the initialization method of the z-domain state variable, is an effective method of removing a DC offset containing data measured as a valid value, and the verification of the frequency mode using the FFT applies an optimization technique. Frequency mode in equation (4) to find the damping rate This is to stabilize the convergence of the optimization technique. The Gauss-Newton method, one of the optimization methods, is more efficient in terms of computation time than other methods because of its fast convergence speed.

4 is a generator power vibration in case of a system accident of the present invention. Generator output at steady state Suppose that an accident occurred in the system suddenly and the following power vibration occurred.

here,

Initial Amplitude: , ,

Attenuation Rate: , ,

Fluctuation frequency: , ,

Phase: , ,

In Equation 10, the vibration of 40.34 Hz can be considered to be a generator shaft twist mode, 1.56 Hz is a generator mode, and 0.80 Hz is an inter-area mode. If the real-time power vibration monitoring device measures this power vibration and stores the discrete time domain data at 120 Hz for about 30 seconds, the number of data becomes about N = 3600 and the response to this is shown in FIG. 4 is not actually measured data, but is a value calculated by a computer at a 120 Hz sampling rate using Equation 10.

The power vibration attenuation rate is calculated by the method of the present invention as follows.

First, the steady state data for 0.83sec before the accident is removed, and 3600 data for 30 seconds from the accident are determined as analysis data. Then, the DC offset is removed using the washout circuit. In this case Assumed to be sec. The initialization of the z-domain state variable of the washout circuit is determined by the steady state generator output of 300 MW before the accident.

5 shows the result of removing the DC component by the washout circuit. Since also analyzes the data to remove the direct current component of the FFT 5 shows a calculation result of the real part and the imaginary part Imag_ Real_ _{FET FET} as an absolute value, it did not take into account the sampling time during the FFT analysis of the FFT frequency axis Multiply the axis by 120. Here, the vibration frequency can be determined almost accurately. The determined frequencies were 40.33 Hz, 1.56 Hz, and 0.80 Hz, which were almost equal to the true values of Equation 10.

FIG. 6 is an FFT frequency analysis result of FIG. 5. Since the absolute value of the FFT result is very large, it is shown on the y-axis using dB of Equation 11.

Y_ _FET = 20log10 (Mag (Real_ _FET , Imag_ _FET ))

Finally, the least squares method of Equation 9 is used to fit the data from which the DC offset of FIG. 5 is removed. Except the vibration frequency calculated in FFT analysis, the amplitude, damping rate, and phase should be chosen as reasonable values, but the initial values are set as follows.

, ,

Attenuation Rate: , ,

Phase: , ,

For optimization, the Gauss-Newton method of Matlab and Mixed Polynomial Interpolation search method are applied. The calculation results were fitted almost equally indistinguishable from FIG. 5.

7 is a comparison of the measured data of the present invention with the fitted results. The results converged by applying the optimization technique are as follows.

, ,

Attenuation Rate: , ,

Phase: , ,

The true value amplitude and the converged amplitude of Equation 10 show a slight difference, but are acceptable. The converged power vibration attenuation value is almost identical to the true value of Equation 10. The converged phase value and the phase value of Equation 10 are different because the phase value when the system accident occurs at 0.83 sec in FIG. 4 is different from the phase value of Equation 10. In FIG. Therefore, it can be considered that the converged phase values of Equation 13 are almost the same as the phase values at the time of actual accident occurrence. For reference, the calculation time to get the above result was only 9.8 seconds on a notebook computer with a Pentium 4 processor.

Therefore, the method of calculating the power vibration damping rate to which the optimization technique of the present invention is applied has the following advantages.

First, the power vibration damping rate generated in the power system can be calculated more easily and faster than the conventional Penny analysis method.

Second, the power vibration method by the conventional Penny analysis method requires a lot of trial and error and some experience, the calculation method of the present invention can calculate the power vibration damping rate more easily and simply.

Third, since the algorithm of the calculation method of the present invention is obvious, the algorithm can be easily applied to a power vibration monitoring device or a pager measuring device as shown in FIG. In the case of a system, the power vibration damping rate can be easily and quickly calculated using the data transmitted from the utility company's EMS.

Fourth, when using the FFT analysis method using the washout of the present invention, it is possible to easily determine the power vibration frequency from the measured active power.

And, due to the advantages as described above there is an effect that contributes to the stable power supply of the power system.

Claims (5)

Determining a time domain effective power data interval measured by a pager measuring device; Initializing the washout circuit state variable; Removing the direct current offset by the washout circuit; Confirming the fluctuation frequency in absolute value magnitude as a result of FFT application; Fitting time domain measurement data from which a DC offset is applied by applying an optimization technique; And Power vibration damping rate calculation method using an optimization method characterized in that the step of outputting the damping rate results The method of claim 1, The washout circuit is a power vibration damping rate calculation method using an optimization method characterized by a z-domain integrator using a modified Eluer method. The method of claim 1, The step of fitting the time-domain measurement data from which the DC offset is applied by applying the optimization technique is to check the mode by using the FFT, and then the identified frequency is expressed by Equation 4 below. Power Vibration Damping Rate Calculation Method Using Optimization Technique Set to Initial Value and Calculation of Damping Rate, Amplitude, and Phase with One Fit Method The method of claim 1, The step of fitting the time-domain measurement data from which the DC offset is applied by applying the optimization technique is performed using the Gauss-Netwon method. The method of claim 1, In the step of fitting the time domain measurement data from which the DC offset is applied by applying the optimization technique, the method of calculating the power vibration damping rate using the optimization technique is characterized by using a mixed polynomial interpolation search method.