A power quality fast disturbance detection method based on improved K-S transformation

Abstract

The application discloses a power quality fast disturbance detection method based on improved K-S transformation, which comprises the following steps: obtaining a discrete sampling sequence of a power grid detection node; performing fast Fourier transformation to obtain a signal spectrum; performing iterative cycle filtering processing on the signal spectrum, and calculating a maximum value of the filtered spectrum as a frequency feature point; performing improved K-S transformation on the signal to obtain a transformed matrix; extracting a fundamental frequency part from the transformed matrix to obtain a one-dimensional time signal, which represents a waveform of a fundamental wave in a signal duration time, and calculating a maximum value, a minimum value and a sudden change time point of the one-dimensional time signal to obtain a time domain disturbance feature, so that the disturbance amplitude, the starting time and the ending time of voltage sag, voltage swell, voltage interruption and flicker are detected; and the frequency, the amplitude and the duration time of each frequency component are determined according to the transformed matrix, so that the frequency domain disturbance including harmonics and transient oscillation is detected.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of power quality composite disturbance detection, and particularly considers a power quality fast disturbance detection method based on improved K-S transformation. BACKGROUND

[0002] The demand for electric energy continues to grow, and the protection of power quality has also put forward higher requirements. Good power quality is not only related to the safe and economic operation of the power grid, but also directly affects the national economic benefit. However, with the continuous change of the power grid structure, large-scale access of nonlinear loads, new energy power generation and power electronic equipment, the power quality problem is becoming more and more complex. Voltage fluctuation, harmonic pollution and other phenomena occur frequently, threatening the normal operation of equipment and may cause serious economic losses. In view of this challenge, it is crucial to quickly and accurately identify and classify power quality disturbances (PQD).

[0003] The power quality disturbance detection method can be roughly divided into time domain analysis, frequency domain analysis and time-frequency domain analysis according to its transform domain. Among them, time domain analysis and frequency domain analysis are only effective for a single type of disturbance, such as time domain disturbance and frequency domain disturbance. For example, time domain analysis method cannot detect harmonic disturbance in frequency domain, so time-frequency joint analysis method is born. Domestic and foreign researchers have made many high-quality achievements in this field, such as short-time Fourier transform, wavelet transform, S transform and other methods. In the above methods, short-time Fourier transform cannot be applied to the actual application of power quality disturbance detection due to its fixed window width, frequency spectrum leakage, fence effect and large amount of calculation; the accuracy of wavelet transform is highly dependent on the selected mother wavelet and decomposition scale, and the presence of noise will worsen its disturbance detection ability; S transform, as the inheritance and development of short-time Fourier transform and wavelet transform, is the most popular disturbance detection method at present, but its Gaussian window characteristics and large amount of calculation make it difficult to be directly applied to practice.

[0004] In summary, in today's distributed energy access and high power electronicization of power systems, in order to achieve accurate detection of power quality composite disturbance signals, a power quality fast disturbance detection method is needed. SUMMARY

[0005] In order to solve the problem that power quality composite disturbance is difficult to accurately detect, the present application proposes a power quality fast disturbance detection method based on improved K-S transformation, which can be applied to modern high-proportion renewable energy power electronic systems for power quality composite disturbance detection. The technical scheme of the present application is as follows:

[0006] A power quality fast disturbance detection method based on improved K-S transformation, comprising the following steps:

[0007] Step 1: Obtain voltage signal from grid detection node, discretize it to get discrete sampling sequence;

[0008] Step 2: Perform fast Fourier transform on discrete sampling signal to get signal spectrum;

[0009] Step 3: Perform iterative circular filtering on signal spectrum to remove noise of interference characteristic frequency extraction, and take maximum value of filtered spectrum as frequency characteristic point;

[0010] Step 4: Perform improved K-S transform on signal to obtain transformed matrix, which represents frequency components contained in measured signal in rows, and represents amplitude of each frequency component of signal changing with time in columns, and modulus of matrix is amplitude of frequency component, and only selected characteristic frequency row after iterative circular filtering in step 3 is calculated, and other non-frequency characteristic rows are set to 0;

[0011] Step 5: Pre-set range of fundamental voltage amplitude change when voltage sag and voltage interruption interference occurs; extract fundamental frequency part from transformed matrix to obtain one-dimensional time signal representing waveform of fundamental wave in signal duration, and obtain time domain disturbance characteristics by calculating maximum value, minimum value and mutation time point to detect disturbance amplitude, starting time and ending time of voltage sag, voltage swell, voltage interruption and flicker;

[0012] Step 6: Determine frequency, amplitude and duration of each frequency component according to transformed matrix, i.e. harmonic frequencies f1, f2, f3, …, corresponding amplitudes A1, A2, A3, …, and existence time t1, t2, t3, … of frequency component, to detect frequency domain disturbance including harmonic and transient oscillation.

[0013] Further, let the discrete sampling sequence obtained in step 1 be x s (nT s ), wherein T s is sampling interval time of grid sampling device, and n is sampling point number; in step 2, fast Fourier transform is performed on discrete sampling signal x s (nT s ) to obtain signal spectrum X0(m) as follows:

[0014]

[0015] In the formula, m, n = 0, 1, …, N-1, and N is total sampling point number.

[0016] Further, the method of step 3 is as follows:

[0017] Perform iterative circular filtering on signal spectrum:

[0018]

[0019] In the formula, l = 1, 2; d = 0, 1, 2, ...; m = 2, 3, ..., N-3. The maximum value of the above formula is obtained, and a threshold η is set to remove noise interfering with the extraction of feature frequencies. The feature frequency point m that satisfies the following formula is selected. i :

[0020] X d+1 (m i -1) <X d+1 (m i )>X d+1 (m i +1)

[0021] X d+1 (m i )>η

[0022] Record the obtained frequency feature points m i The location.

[0023] Furthermore, step 4 involves performing an improved KS transform on the signal to obtain the transformed matrix.

[0024] The improved KS transform formula for the signal is as follows:

[0025]

[0026] Where, ω G (τ-t,f) is a Gaussian window function, where τ is the oscillation decay factor. The parameter η1 is used to adjust the rate of change of the window shape with frequency f, η2 is used to adjust the window shape at the fundamental frequency, and I0(·) is the modified zero-order Bessel function of the first kind.

[0027] Furthermore, in step 5, a rise in the fundamental voltage amplitude of 10% to 80% is defined as a voltage spurt; when the fundamental voltage amplitude exhibits sinusoidal oscillation characteristics, it is defined as a voltage flicker disturbance; when the fundamental voltage amplitude drops by 10% to 90% during the disturbance, it is defined as a voltage sag; and a drop of 90% to 100% is defined as a voltage interruption.

[0028] Furthermore, in step 6, the fundamental frequency is 50 Hz. When one or more frequency components other than the fundamental frequency component appear between 0 Hz and 700 Hz, and these components exist in the entire time domain of the input signal, it is defined as a harmonic disturbance. When a frequency component between 700 Hz and 1600 Hz appears and it lasts only 0.01 s to 0.06 s, it can be identified as a transient oscillation disturbance.

[0029] Further, the composite disturbance is the superposition of voltage sag, voltage swell, voltage interruption, voltage flicker, harmonic and transient oscillation disturbance, and the detection is performed by judging the characteristics according to the judgment methods in steps 5 and 6. BRIEF DESCRIPTION OF DRAWINGS

[0030] Figure 1 Voltage sag waveform chart

[0031] Figure 2 Voltage swell waveform chart

[0032] Figure 3 Voltage interruption waveform chart

[0033] Figure 4 Voltage flicker waveform chart

[0034] Figure 5 Harmonic disturbance waveform chart

[0035] Figure 6 Transient oscillation waveform chart

[0036] Figure 7 Voltage interruption + harmonic disturbance + transient oscillation waveform chart

[0037] Figure 8 50 Hz and 500 Hz window function frequency response comparison chart

[0038] Figure 9 Kaiser window variable beta time domain waveform

[0039] Figure 10 Frequency characteristic point extraction result

[0040] Figure 11 Improved K-S transformation detection result

[0041] Figure 12 50 Hz fundamental frequency amplitude curve extraction result

[0042] Figure 13 Disturbance frequency domain amplitude chart DETAILED DESCRIPTION

[0043] The technical scheme and technical feasibility of the present application will be described and verified first as follows.

[0044] Step 1: Establish 21 different power quality disturbance signal mathematical models.

[0045] Let the sampling device detection input signal in the power system be x(t), and the normal voltage signal model can be established as:

[0046] x(t) = Asin(ω0t)

[0047] Where A is the standard voltage amplitude, t is the time value, the angular frequency ω0=2πf0, the alternating frequency of our country's alternating current is 50hz, so the subsequent modeling is unified as f0=50hz. The single disturbance of power system is divided into voltage sag, voltage swell, voltage interruption, voltage flicker, harmonic, transient oscillation, and the modeling of the above six single disturbances is as follows:

[0048] Voltage sag:

[0049] x(t)=[1-A[ε(t-t1)-ε(t-t2)]]sin(ω0t)

[0050] Voltage sag is defined as the rapid drop of the effective value of supply voltage to 90%-10% of the rated value, where ε(t) is a step function, and its definition expression is

[0051]

[0052] t1 is the starting time of voltage sag, t2 is the ending time of voltage sag, A is the depth of voltage sag, the parameter value range is 0.1

[0053] Voltage swell:

[0054] x(t)=[1+A[ε(t-t1)-ε(t-t2)]]sin(ω0t)

[0055] Voltage sag is defined as the rapid drop of the effective value of supply voltage to 90%-10% of the rated value, where ε(t) is a step function, and its definition expression is

[0056] Voltage interruption:

[0057] x(t)=[1-A[ε(t-t1)-ε(t-t2)]]sin(ω0t)

[0058] Voltage interruption is defined as the rapid drop of the effective value of supply voltage to 90%-100% of the rated value, where t1 is the starting time of voltage interruption, t2 is the ending time of voltage interruption, A is the depth of voltage interruption, the parameter value range is 0.9

[0059] Voltage flicker:

[0060] Voltage flicker is a sinusoidal voltage signal amplitude that changes slowly with time, and its mathematical modeling is

[0061] x(t) = [1 + Asin(2πf f t)]]sin(ω0t)

[0062] where A is the flicker amplitude, generally 0.1<A<0.2, f f is the flicker frequency, 5Hz<f f <25Hz harmonic:

[0063]

[0064] Harmonic disturbance is the existence of nonlinear components with frequency higher than the fundamental frequency in power system, which is shown as the sum of multiple sinusoidal waves in mathematical model, where A i is the amplitude of each harmonic, is the initial phase angle of each harmonic, i is the harmonic order, and the harmonic in power system is usually considered as an integer multiple of the fundamental frequency, so i = 1, 2, 3, …, n.

[0065] Transient oscillation:

[0066]

[0067] where A is the oscillation amplitude, 0.1~0.8; t1, t2 are the start and end time of oscillation, 0.5T<t2-t1<3T; τ is the oscillation decay factor, 25~330, and f is the oscillation frequency, generally 700~1600Hz.

[0068] Step 2: Replace the window function of S transform and improve its parameters.

[0069] The expression of S transform is defined as

[0070]

[0071] x(t) is the input power quality disturbance signal, ω G (τ-t, f) is a Gaussian window function, whose expression is:

[0072]

[0073] where σ(f) is the Gaussian window function window width adjustment factor, used to adjust the main lobe width of the window function.

[0074] The expression of Kaiser window function is defined as

[0075]

[0076] β is the Kaiser window function adjustment factor, used to adjust the ratio between the main lobe and the side lobe, and I0(·) is the first kind of modified zero-order Bessel function,

[0077] The adjustment factor β is improved, and the Kaiser window function is changed to

[0078]

[0079] wherein The parameter η1 is mainly used to adjust the rate of change of the window shape with the frequency f, and η2 can more conveniently adjust the window shape at the fundamental frequency, both of which are constant parameters.

[0080] The Gaussian window in the S transform is replaced by the improved Kaiser window, and the improved K-S transform expression is obtained

[0081]

[0082] Step 3: Extract the frequency feature points of the disturbance signal

[0083] The disturbance signal x(t) is discretized to obtain the discrete disturbance signal x s (nT s ), wherein T s is the sampling interval time of the power grid sampling device, and n is the sampling point number. The fast Fourier transform is performed on the discrete signal x s (nT s ) to obtain the signal spectrum X0(m),

[0084]

[0085] In the formula, m, n = 0, 1, …, N-1, and N is the total number of sampling points.

[0086] The signal spectrum is subjected to iterative circular filtering

[0087]

[0088] In the formula, l = 1, 2; d = 0, 1, 2, …; m = 2, 3, …, N-3, the maximum value of the above formula is calculated, and a suitable threshold η is set to remove the noise of the extracted disturbance characteristic frequency. The characteristic frequency point m satisfying the following formula is selected i

[0089] X d+1 (m i -1)<X d+1 (m i )>X d+1 (m i +1)

[0090] X d+1 (m i )>η

[0091] The obtained frequency feature point m is recordedi the position of the feature point.

[0092] Step 4: K-S transformation is performed on the feature points to detect the power quality composite disturbance

[0093] The 21 kinds of disturbance signals are mathematically modeled in Matlab software, and 30dB Gaussian white noise is added to the disturbance signals, and the disturbance signals are sampled to simulate the real power grid sampling process, and the improved K-S transformation expression obtained in step 2 and the convolution theorem can deduce

[0094]

[0095] In the formula, X(f+v) is the frequency spectrum of the disturbance signal after frequency shift, W GK (v, a, b) is the improved Kaiser window function spectrum, so this process can be quickly calculated by fast Fourier transform and inverse Fourier transform.

[0096] According to the spectrum of the disturbance signal, a disturbance signal frequency shift matrix X (M+1)×N

[0097]

[0098] M is floor(N / 2), and the window function spectrum matrix is constructed in the same way, and the Hadamard product (corresponding elements are multiplied) of the two is obtained, and the non-characteristic frequency part is skipped, and the fast inverse Fourier transform of the obtained matrix can quickly obtain the result matrix of the improved K-S transformation. The row of the matrix represents the change of the signal frequency component with time, and the power quality disturbance signal can be detected by observing the data of the matrix.

[0099] The improved K-S transformation-based power quality fast disturbance detection method proposed in the application will be described in detail in combination with the drawings and examples.

[0100] (1) 21 different power quality disturbance signal mathematical models are established

[0101] According to the above mathematical model, 6 kinds of single disturbance waveforms are established by Matlab as shown in the following table 1. Figures 1 to 6 From this, composite disturbances can be constructed. Conventionally, voltage sag, voltage swell, voltage interruption and voltage flicker can be specified as time domain disturbances, and harmonics and transient oscillation can be specified as frequency domain disturbances. The power system composite disturbance is composed of time domain disturbance and frequency domain disturbance. 21 different power quality disturbance signals are shown in Table 1. Now, a typical example of composite disturbance is given, and other examples are not described in detail. The example is voltage interruption+harmonic disturbance+transient oscillation disturbance, and the waveform diagram is as follows. Figure 7 .

[0102] Table 1

[0103] C1 dip C8 harmonic + interruption C15 oscillation + swell C2 interruption C9 harmonic + swell C16 flicker + harmonic + swell C3 swell C10 harmonic + oscillation C17 flicker + harmonic + dip C4 harmonic C11 flicker + swell C18 harmonic + oscillation + swell C5 flicker C12 flicker + swell C19 harmonic + oscillation + dip C6 transient oscillation C13 flicker + dip C20 harmonic + oscillation + interruption C7 harmonic + dip C14 oscillation + dip C21 harmonic + oscillation + flicker

[0104] (2) Replace the window function of the S-transform and improve its parameters.

[0105] The expression for the S-transform is:

[0106]

[0107] The original S-transform uses a Gaussian window whose width varies with frequency. The main lobe width of the spectral window gradually widens as the signal frequency f increases. This means that the time resolution of the S-transform gradually improves with increasing signal frequency f. Therefore, the S-transform has the characteristics of strong frequency resolution in the low-frequency band and high amplitude detection accuracy in the high-frequency band. However, detecting time-domain disturbances such as voltage sags in power systems requires better time resolution and amplitude detection accuracy, while detecting mid-to-high frequency disturbances such as harmonics and oscillations requires better frequency resolution. The effect of the Gaussian window is contrary to these requirements. Therefore, the Kaiser window is considered to replace the Gaussian window for the S-transform here. The frequency response comparison of the two at 50 Hz and 500 Hz is shown in the figure below. Figure 8 As shown, at the low frequency of 50 Hz, the Kaiser window has a main lobe width similar to that of the Gaussian window, but achieves lower side lobe attenuation, thus effectively suppressing spectral leakage. At the high frequency of 500 Hz, the Kaiser window achieves a narrower main lobe width than the Gaussian window, thus obtaining higher frequency resolution for detecting frequency domain disturbances.

[0108] Define the Kaiser window function expression as follows:

[0109]

[0110] β is the Kaiser window function adjustment factor, used to adjust the ratio between the main lobe and the side lobes; I0(@) is the first-order modified zero-order Bessel function. In the formula, β is a constant function, and the Kaiser window-variable β time-domain waveform is as follows: Figure 9 As shown, to enable Kaiser to have adaptive window width adjustment capability in power quality detection, the adjustment factor β is improved, and the Kaiser window function is changed to...

[0111]

[0112] in The parameter η1 is mainly used to adjust the rate of change of the window shape with frequency f, while η2 can more easily adjust the window shape at the fundamental frequency. Both are constant parameters. In practical applications, it is only necessary to control α(f) between 90 and 100 to obtain good detection results.

[0113] (3) Extract frequency feature points of disturbance signal

[0114] The S transform has a huge amount of calculation, mainly because the K-S matrix is a characteristic frequency of the earth's surface in each row, but in the actual working condition, most of the frequency points cannot provide effective information. If only the frequency characteristic points are calculated, the calculation efficiency will be greatly improved, so this paper adopts an iterative filtering method to extract the frequency characteristics. First, the disturbance signal x(t) is discretized to obtain the discrete disturbance signal x s (nT s ), where T s is the sampling interval time of the power grid sampling device, n is the sampling point number, and the discrete signal x s (nT s ) is subjected to fast Fourier transform to obtain the signal spectrum X0(m),

[0115]

[0116] where m, n = 0, 1, …, N-1, and N is the total number of sampling points.

[0117] The signal spectrum is subjected to iterative loop filtering

[0118]

[0119] where l = 1, 2; d = 0, 1, 2, …; m = 2, 3, …, N-3, the maximum value of the above formula is calculated, and a suitable threshold η is set to remove the noise of the extracted interference characteristic frequency. The characteristic frequency point m i

[0120] X d+1 (m i -1)<X d+1 (m i )>X d+1 (m i +1)

[0121] X d+1 (m i )>η

[0122] The position of the obtained frequency characteristic point m i is recorded. After completing the above steps, the frequency characteristic points will be recorded in the function of K-S transform in the form of index. In the final matrix calculation, only the characteristic part is calculated and the non-characteristic part is skipped. Taking the voltage sag + three five seven harmonic + transient oscillation composite disturbance signal as an example, the result of extracting the frequency characteristic points by iterative filtering is shown in Figure 10 . The red dots are the frequency characteristic points. It can be seen that the result accurately retains the frequency characteristics, greatly reducing the amount of calculation.

[0123] (4) K-S transform is performed on the feature points to detect power quality composite disturbance

[0124] The improved K-S transform expression obtained from step 2 and the convolution theorem can be deduced as

[0125]

[0126] In the formula, X(f+v) is the frequency spectrum of the disturbance signal after frequency shift, W GK (v, α, β) is the improved Kaiser window function spectrum, so the process can be calculated quickly by fast Fourier transform and inverse Fourier transform. The detection result of the voltage interruption + harmonic + transient oscillation disturbance is shown in Figure 11 The 50Hz fundamental frequency amplitude curve ( Figure 12 ) is extracted and observed alone, and it can be seen that there is a voltage interruption disturbance from 0.08 to 0.14 seconds. The disturbance amplitude graph in the frequency domain ( Figure 13 ) can be observed, and it can be seen that there are three, five and seven harmonics in the whole process, and there is a 1kHz transient oscillation from 0.04 to 0.06 seconds. The composite disturbance can be detected more accurately.

[0127] In summary, the present application proposes a power quality fast disturbance detection method based on improved K-S transform, which can be applied to modern high proportion of renewable energy power electronic system for power quality composite disturbance detection.

[0128] Finally, it should be noted that: the above examples are only used to illustrate the technical solutions of the present application but not to limit it, although the present application has been described in detail with reference to the above examples, those skilled in the art should understand that: the specific embodiments of the present application can be modified or replaced by the same, without departing from the spirit and scope of the present application. Any modification or equivalent replacement, which should be covered in the protection scope of the claims of the present application.

Claims

1. A power quality fast disturbance detection method based on improved K-S transformation, comprising the following steps: Step 1: Obtain the voltage signal from the grid detection node, and discretize it to obtain a discrete sampling sequence; Step 2: Perform fast Fourier transform on the discrete sampling signal to obtain the signal spectrum; Step 3: Perform iterative circular filtering on the signal spectrum to remove noise extracted by interference characteristic frequency, and take the maximum value of the filtered spectrum as the frequency characteristic point; Step 4: the signal is improved K-S transform to obtain the transformed matrix, the matrix row represents each frequency component contained in the measured signal, the column represents the change of each frequency component amplitude of the signal with time, and the modulus of the matrix is the frequency component amplitude. When forming the matrix, only the rows of the characteristic frequencies selected after the iterative loop filtering processing in step 3 are calculated, and the remaining non-frequency characteristic rows are set to 0; wherein, The method for performing improved K-S transformation on the signal is as follows: The transformation formula for performing improved K-S transformation on the signal is as follows where ω G (τ - t, f) is a Gaussian window function, τ is an oscillation decay factor, The parameter η1is used to adjust the rate of change of the window shape with frequency f, η2is used to adjust the window shape at the fundamental frequency, and I0(·) is the first kind of modified zero-order Bessel function. Step 5: Preset the fundamental voltage amplitude variation range when voltage sag, voltage interruption disturbance occurs; extract the fundamental frequency part from the transformed matrix to obtain a one-dimensional time signal representing the waveform of the fundamental wave in the signal duration, and obtain the time domain disturbance characteristics by calculating the maximum value, minimum value and mutation time point to detect the disturbance amplitude, starting time and ending time of voltage sag, voltage swell, voltage interruption and flicker; Step 6: Determine the frequency, amplitude and duration of each frequency component according to the transformed matrix, i.e. the harmonic frequency f1, f2, f3, …; the corresponding amplitude A1, A2, A3, … of each harmonic; and the existence time t1, t2, t3, … of the frequency component, to detect the frequency domain disturbance including harmonics and transient oscillation.

2. The method of detecting a fast power quality disturbance according to claim 1, characterized in that, Let the discrete sampling sequence obtained in step 1 be x(nT) s (nT s ), wherein T s is the sampling interval time of the power grid sampling device, and n is the sampling point number; in step 2, the fast Fourier transform is performed on the discrete sampling signal x s (nT s ) to obtain the signal spectrum X0(m). Wherein m, n = 0, 1, …, N-1, N is the total number of sampling points.

3. The method of detecting a fast disturbance of power quality according to claim 2, characterized in that, The method of step 3 is: Perform iterative circular filtering on the signal spectrum: In the formula, l = 1, 2; d = 0, 1, 2, …; m = 2, 3, …, N-3, a maximum value is taken for the above formula, and a threshold value η is set to remove noise of the extracted interference characteristic frequency, and a characteristic frequency point m satisfying the following formula is selected i : X d+1 (m i -1)<X d+1 (m i )>X d+1 (m i +1) X d+1 (m i )>η Record the position of the frequency feature point m i resulting from the recording.

4. The method of detecting a fast power quality disturbance of claim 1, wherein, In step 5, when the fundamental voltage amplitude rises by 10% to 80%, it is defined as voltage swell; when the fundamental amplitude shows sinusoidal oscillation, it is defined as voltage flicker disturbance; when the disturbance fundamental voltage amplitude drops by 10% to 90%, it is defined as voltage sag; and when it drops by 90% to 100%, it is defined as voltage interruption.

5. The method of detecting a fast power quality disturbance of claim 1, wherein, In step 5, the fundamental frequency is 50 Hz, when one or more frequency components other than the fundamental frequency component appear between 0 Hz and 700 Hz, and they exist in the whole time domain of the input signal, it is defined as harmonic disturbance; and when frequency components appear between 700 Hz and 1600 Hz and only last for 0.01 s to 0.06 s, it is identified as transient oscillation disturbance.

6. The method of detecting a fast power quality disturbance of claim 1, wherein, Composite disturbance is the superposition of voltage sag, voltage swell, voltage interruption, voltage flicker, harmonic and transient oscillation disturbance, which is detected by judging its characteristics according to the judgment method in steps 5 and 6.

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