Accurate Frequency Tracking Using Morphological Predication of Clarke Components

Accurate Frequency Tracking Using Morphological Predication of Clarke Components

Srihari Mandava, Abhishek Gudipalli^*, Vani shree J, Vidhya Sagar G School of Electrical Engineering

VIT University Vellore, India

ABSTRACT

This article gives an algorithm for the calculation of frequency using the morphological prediction of Clarke components (MPCC) given by αβ-transformation. It uses four operators’ dilation, erosion, opening and closing for different types of frequency varying conditions. It also presents the comparison of two algorithms, MPCC and PLL, in real time signal by creating a grid in MATLAB Simulink. The algorithms were tested with two types of faults, symmetrical and unsymmetrical faults, at the same time the later algorithms will be compared with two types of loads such as linear and non- linear loads. These demonstrations show us, how accurate the MPCC is when compared to PLL in estimating frequency.

Keywords— Frequency estimation, Morphological prediction, PLL, Clarkes Components I. INTRODUCTION

Power system frequency plays an outstanding role in the stability and operation of electric power system. Its guesstimate is significant to a wide range of applications like control and energy quality operations, system protection, interfacing with renewable energy sources etc... [1-6].

In order to make the power system more safe and reliable, an accurate recognition of faulty or uncharacteristic situations is essential to disregard them and consequently to return to the ordinary operation state as soon as possible. During an abnormal condition in an electrical power system, there may be changes in the system frequency and its approximation must be as fast and perfect for the accurate relay process as it became most important in up-to-date power grids with the changes in economy and grid interfacing with the intermittent renewable energy resources [7-9]. In practice, a frequency dissimilarity range for the system operation is maintained as 60-50 Hz. Differences on these limits are continuously witnessed as a consequence of the dynamic destabilize between the generation and load.

Over the years many frequency estimation algorithms have developed and the new algorithms have been keep on developing and upgrading each and every day. Whenever an algorithm has been developed it comes with better accuracy and also at the same time with limitations too [10-12]. There are many techniques present in literature and has been used in industries to know the power system frequency more accurately to the real time value from the voltage or current waveform. Iterative methods like Kalman filtering [13-15], adaptive filter like least mean square filter [16], modified Fourier method [17-18], wavelets using orthogonal filtering, function derivatives of Taylor series are few methods. Some require very sharp filters to filter the harmonic components present in measured power signals before using the algorithm for frequency estimation and thus the accuracy of the methods in literature relies on the performance of filtering.

II. METHODOLOGY DESCRIPTION

The proposed method is a predictive approach which is based Clarke components derived from αβ-transformation of three phase power system signal. The three phase voltage or current measured from the power system is transformed into alpha-beta (𝛼 - 𝛽) for simplifying the analysis. It is possible to apply and obtain a complex signal combined by α and β components So Vα and Vβ components are stated as components of 𝛼 - 𝛽 transformation using the equation (1).

frequency prediction presented in this work uses morphological forecast of Vα and Vβ components.

This is done with the help of two moving data windows one for each signal. Each data window contains three samples. The data windows are given in the form of equations.

𝑊_𝛼(𝑛) = [𝑉_𝛼(𝑛 − 2) 𝑉_𝛼(𝑛 − 1) 𝑉_𝛼(𝑛)] (4) 𝑊_𝛽(𝑛) = [𝑉_𝛽(𝑛 − 2) 𝑉_𝛽(𝑛 − 1) 𝑉_𝛽(𝑛)] (5)

For every new sample, the two existing windows will get renovated and the last two left windows will be discarded. The remaining elements are to be shifted to left and the new coming samples enter into the right position. For each window, the estimation is done with the help of morphological operator’s dilation and erosion the operators are given below in the equations form

(W⨁SE)(𝑛) =^𝑉(𝑛)_𝑆𝐸 (6)

(W⨂SE)(𝑛) =^{𝑉(𝑛−2)}_𝑆𝐸 (7)

Where W indicates the data windows 𝑉(𝑛), 𝑉(𝑛 − 2) represents max and min values of data windows.

After computing the dilation and erosion of data windows, the estimated values of these parameters are estimated according to the following equation

P(n) =¹

2(W⨁SE + W⨂SE) (8)

Then, the computing values for Pα and Pβ are used to configure the complex estimated signal and which is used to calculate the phase shift between 𝑈_𝑒𝑠𝑡 and 𝑈(𝑛) according to the equations (9) and (10).

𝑈_𝑒𝑠𝑡(𝑛) = 𝑃_𝛼(𝑛) + 𝑃_𝛽(𝑛) (9) Δϕ(n) = 𝑈_𝑒𝑠𝑡(𝑛) + 𝑈(𝑛) (10)

In the above equation 𝑈(𝑛)* indicates the complex conjugate of 𝑈(𝑛). The system frequency estimation is given by the equation (11) ,which is a function of phase shift Δϕ(n) and sampling frequency fs f(n) = ^𝑓𝑥

2𝜋∗ tan⁻¹{^{𝑖𝑚[Δϕ(n)]}

𝑅𝑒[Δϕ(n)]} (11)

𝑖𝑚, 𝑅𝑒 represents the real and imaginary parts of (n) and fs represents the sampling frequency. The above technique was also tested with real time signal for uniform frequency and sudden change in frequency and the synthetic signals were applied to six different cases in all cases ,this estimator often showed excellent results. Firstly a three phase reference signal has been generated using the equations as given below.

𝑉_𝐴(𝑛) = 𝐴 ∗ cos[2 ∗ 𝜋 ∗ 𝑓 ∗ 𝑡(𝑛)] (12) 𝑉_𝐵(𝑛) = 𝐴 ∗ cos [2 ∗ 𝜋 ∗ 𝑓 ∗ 𝑡(𝑛) −2𝜋

3 ] (13) 𝑉_𝐶(𝑛) = 𝐴 ∗ cos [2 ∗ 𝜋 ∗ 𝑓 ∗ 𝑡(𝑛) +2𝜋

3 ] (14)

Figure 1: three phase reference signal for 50HZ frequency

Then this three phase waveform is converted in to two phase, the total process is completed for generating an estimated signal .Different types of frequency varying conditions have been generated and estimated using the four operators opening, closing, dilation and erosion.

III. RESULTS AND DISCUSSION

In order to verify or prove the quality of MPCC algorithm, the algorithm was compared with PLL algorithm [16-19]. The comparison was done in Matlab simulink by creating a grid and different types of conditions are tested. Here, the MPCC algorithm was tested under different types of fault conditions such as symmetrical and unsymmetrical faults.

A. Signals with fundamental frequency

Using the MPCC algorithm the estimated signal have been generated for signals with fundamental frequency. Then the main aim of our project is to estimate the fundamental frequency of the signal. The figure (2) shows the estimation of measured signal frequency with respect to reference signal, this proves that MPCC gives us the better results for estimating the measured signal fundamental frequency. Making the things a little bit complex in the next condition the signals with sudden frequency variation was tested to prove the quality of MPCC.

Figure 3: Signals with sudden change in frequency.

From figure.3, it is clear that the frequency of measured signal are accurately estimated by MPCC algorithm during a sudden change in frequency. Similarly as mentioned in previous section, the following conditions have also been estimated based on the given following equations.

C. Comparison of MPCC and PLL algorithms with real time signal

For the comparison of the two algorithms, a grid has been created in Matlab. Here under these conditions the reference frequency is considered as 50HZ and the frequencies of the voltage signal is calculated using PLL and MPCC algorithm. The frequencies calculated using PLL and MPCC algorithm are plotted as shown in figure 4.

Figure 4: Comparison of frequencies measured using PLL and MPCC during normal condition In figure 4, the waveform in red color shows the frequency estimation by PLL and the blue color waveform shows the frequency estimation by the MPCC. It is clear that the MPCC algorithm have the better and accurate results for estimating the frequency for 50HZ power signal than PLL. The MPCC estimates the frequency correctly without any over and under shoots of frequency like PLL. This is not a valid or acceptable situation as the power system frequency estimation must be fast and accurate. So PLL failed to estimate the reference signal and which proves that it is not better than MPCC algorithm.

Figure 5: Comparison of frequencies measured using PLL and MPCC of nonlinear system The grid is connected to a non-linear load whose generation is less compared to load during the time interval 0.3 S to 0.7 S and the frequency of the system is calculated using PLL and MPCC algorithms. Even though the frequency will be keep on varying the PLL algorithm is not able to estimate the varying frequency, but the MPPC algorithm have successfully estimate the varying frequency

D. During Fault Condition

To increase or to make the algorithm more efficient, the MPCC algorithm is tested with a fault signals, by creating the fault externally in a transmission line during the time period 0.3s and 0.7s. Under this condition both the symmetrical and unsymmetrical types of faults are were tested. Under the condition where the generation is greater than load and when an unsymmetrical faults like L-G , L-L, L-L-G and L-L-L-G fault, occurred the frequency estimations have been compared between the PLL and MPCC algorithm.

Figure 6 :With PLL results and MPCC results for L-G fault.

Figure 7 :Frequency estimation for L-L fault with PLL and MPCC

Figure 8 Frequency estimation for L-L-L -G fault with PLL and MPCC

Figure 9 : Frequency estimation for L-L-L fault with PLL and MPCC

For all these conditions under the both symmetrical and unsymmetrical faults whenever the fault has been created as said during the time period 0.3s and 0.7s, the MPCC algorithm predicts the frequency accurately during the time period as shown in figure 6-9. But the PLL algorithm failed to estimate the fault condition as it is not even succeeded to give the fundamental frequency during the other time period when the fault has not occurred. This frequency estimation differences remains same

even when the conditions between the generation and load, such as the generation value is equal to load, generation value is less than load, the estimations and the disadvantages remains same. So, whenever the different types of faults were considered, the same results were observed, i.e. the PLL failed to estimate the frequency, whereas the MPCC gives us the better and accurate results even for the non- linear loads also.

IV. CONCLUSION

Even though there are many frequency estimation algorithms have been estimated the progress will be keep on going and the algorithms will be keep on developing by reducing the backlogs which were presented previously. So up to now considering all the frequency estimation algorithms, this algorithms gives us the best results even in linear and non-linear loads, and also the method have been proved even in case in symmetrical and non-symmetrical fault conditions also. This algorithm gives us the accurate results whenever or at which particular time a fault is created this algorithm is able to estimate the frequency.

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