A performance comparison of static VAr compensator based on Goertzel and FFT algorithm and experimental validation
© Kececioglu et al. 2016
Received: 2 January 2016
Accepted: 20 March 2016
Published: 31 March 2016
The main objective of the present paper is to introduce a new approach for measuring and calculation of fundamental power components in the case of various distorted waveforms including those containing harmonics. The parameters of active, reactive, apparent power and power factor, are measured and calculated by using Goertzel algorithm instead of fast Fourier transformation which is commonly used. The main advantage of utilizing Goertzel algorithm is to minimize computational load and trigonometric equations. The parameters measured in the new technique are applied to a fixed capacitor–thyristor controlled reactor based static VAr compensation system to achieve accurate power factor correction for the first time. This study is implemented both simulation and experimentally.
Reactive power compensation is a very important issue in the expansion planning and operation of electrical power systems. Traditional solution of the compensation is to use fixed-capacitors or reactors for providing and absorbing reactive power respectively (Miller 1982; De La Rosa 2006). Another way of the compensation is to use static VAr compensator (SVC) to compensate reactive power. Since SVC system is fast, smooth and reliable, it has been widely used in power systems (Gelen and Yalcinoz 2010; Mathur and Varma 2002; Lee et al. 2001; Uzunoglu and Onar 2008).
Static VAr systems are generally used in the fast changing events such as arc furnaces and steel industry where the current alters rapidly (El-Saady 2001). This type of industry and rising population of power electronics-based loads causes the increase of harmonic distortion in the power systems. A large proportion of the industrial, commercial and domestic loads are now non-linear. The more use of nonlinear loads has increased harmonic pollution on the power system (De La Rosa 2006). This causes to complicate measuring and calculating the fundamental components of active and reactive power. It is needed to be developed more precise measurement method for existing distortions.
The main problem is how these power components are properly described in non-sinusoidal conditions. In the case of non-sinusoidal current and voltage, it becomes essential to use signal processing methods for power measurement. For this purposes, Fourier transform-based methods are usually used for analyzing power system harmonics. Fast Fourier transformation (FFT) algorithm is generally used for these purposes (Ozdemir and Ferikoglu 2004; Sekkeli 2005). In this study, Goertzel algorithm is preferred to utilize according to FFT algorithm to measure fundamental components of the active and reactive power. Goertzel algorithm is superior with respect to FFT algorithm to include less trigonometric equations (Sekkeli and Tarkan 2013).
In this study, power components measured and calculated by using Goertzel algorithm has been applied in FC–TCR based on SVC system in order to achieve fast and accurate reactive power compensation. SVC system is studied in single-phase under static load conditions. This work is performed both simulation and experimentally. In previous studies, power measurement by using Goertzel algorithm is seriously investigated by some researchers. It is summarized a related study below. Ozdemir and Ferikoglu (2004) worked on a new technique for power measurement. In their study power components are measured by using Goertzel algorithm. Najafi and Yatim (2011) have worked on a static compensator. In that study fundamental components of the power are obtained from the Goertzel algorithm and applied to a static synchronous compensator (STATCOM).
This paper is organized as follows: “Basic FC–TCR based SVC configuration” section briefly presents theory about the TCR–FC based SVC systems. The measurement theory of the Goertzel algorithm is discussed in “The measurement principle” section. “Simulation study and results” section, presents the simulation study and the results obtained for the SVC; in “Experimental results” section includes experimental studies. The main contributions of this paper are summarized in “Conclusions” section.
Basic FC–TCR based SVC configuration
A SVC is a system capable of rapid compensation. This system can be used for several purposes such as, voltage control, system stability, increasing system capacity and reactive power compensation. SVC can quickly supply variable reactive power to the system using supervising the firing angles of thyristors (Ke et al. 2010). Most of the current thyristor-controlled SVCs are based on providing variable shunt impedance. It can be provided switching shunt capacitors and/or reactors by synchronously in order to control changeable reactive power. Desired reactive power can be achieved by the coordination of switching of capacitor and reactor properly (Kodsi et al. 2006; Liu et al. 2012; Zhijun et al. 2009; Kazemi and Badrzadeh 2004). The main types of SVCs used generally can be identified as follows. Saturated reactor (SR), thyristor controlled reactor (TCR), fixed capacitor–thyristor controlled reactor (FC–TCR), thyristor switched capacitor (TSC) and thyristor controlled reactor–thyristor switched capacitor (TCR–TSC) (Kassem 2012; Petersa et al. 2010).
This paper deals with the FC–TCR based SVC. The working principle of TCR is controlling the firing angle of the thyristor so that adjusting the current in the reactor. TCR current is pure inductive reactive and with 90° lagging. If TCR is combined with a proper capacitor, the compensation system can produce reactive power as required (Kazemi and Badrzadeh 2004; Hooshmand and Esfahani 2011). The circuit mainly consists of two thyristors connected in parallel opposite each other with a series reactor (TCR) and fixed capacitor in parallel (FC). These systems are connected in delta in the 3-phase implementations (Rao et al. 2009). The basic components of the reactor currents through the control of thyristor firing angle is so adjusted that, at the output of the reactive power of the entire system whether lagging or leading (Teleke et al. 2008).
The measurement principle
The measurement process is very important for SVC system. In order to achieve fast and accurate reactive power compensation, measurement and calculation process has to be performed precisely and accurately (Ozdemir and Ferikoglu 2004). Active, reactive power and power factor parameters of the load and power sources are computed using current and the voltage measured from the system (Novotny and Sedlacek 2009). Because of the non-sinusoidal form of the voltage and current pattern, signal processing methods are very important to calculate the fundamental component of the power (Wang et al. 2008). FFT algorithm is utilized in industrial application (Ozdemir and Ferikoglu 2004).
In this study, in order to calculate fundamental harmonic of the signal, Goertzel algorithm is preferable utilized instead of FFT. In order to find the first harmonic of the signals. It can be shown that Goertzel is preferable algorithm according to FFT in respect to requiring less calculation (Proakis and Manolakis 1996). While Goertzel algorithm is required a few points of the frequency spectrum, FFT is needed whole spectrum of the signals (Chaparro 2010; Shenoi 2006). Fallowing values are obtained when Goertzel algorithm is compared with to a direct N-point discrete Fourier transform (DFT). Goertzel algorithms are required 50 % multiplication, the same number of real additions, and nearly 1/N number of trigonometric equations according to DFT algorithm (Najafi and Yatim 2011). Because the algorithm is performed in the time domain, the application process begins with the arrival of the first signal. On the contrary, DFT must obtain whole spectrum in order to begin the computations. When these two algorithms are compared in respect to a number of multiplication, addition, and trigonometric equations, Goertzel need N multiplication, 2N addition and two trigonometric equations response to DFT, which needs 2N multiplications, 2N addition and 2N trigonometric equations per frequency. The Goertzel algorithm is obtained from usual DFT equation as below (Ozdemir and Ferikoglu 2004).
Power calculation of the γ th harmonic by the Goertzel algorithm
In Eqs. (5) and (6), for γ = 1, the coefficients a 1, b 1, β 1 and α 1 should be computed in order to find the first component of the active and reactive power from the equations v(k) and i(k), by utilizing the Goertzel algorithm (Rao et al. 2009).
Simulation study and results
Parameters of simulation and power system
Simulation step time
Fundamental components of the power are calculated by using both Goertzel and FFT algorithms respectively. Computation times were calculated for each algorithm within the sampling period.
Loads: 300 W + 200 VAr
It can be safely said that Goertzel algorithm is faster and superior than FFT compared with computation times. It is seen in Table 2, as an example computation time is 0.055 s. for the Goertzel algorithm while FFT is 0.080 s. According to the Table 2, while the power factor value of the load is 0.832 lagging before compensation, it is brought just 1.00 value by using Goertzel and FFT algorithms after compensation in case of first load condition. Thus the power factor (cos φ) is nearly close to 1.00 and SVC system has led to the improvement of power factor. In order to provide approximate values obtained from both simulation and experimental studies, the selected parameters for the simulations presented in Table 2 are based on as possible as the same values used in the experimental working.
In this study, only harmonic is analyzed by using Goertzel and FFT algorithms in order to obtain fundamental components of voltage and current to calculate power components and power factor. Any harmonic filter design is not implemented to eliminate any harmonic order.
Loads: 300 W + 200 VAr
The setting values and results obtained from the experimental study for each working conditions are shown in Table 3. Voltage, current, active, reactive, apparent power and power factor values obtained both working conditions are given in the same table separately. 300 W resistive and 200 VAr inductive load is used in the experiment. According to the Table 3, it can be clearly seen that the SVC system can successfully improve the parameters in accordance with the condition of before compensation in the case of using Goertzel and FFT algorithms. As can be seen from the Table 3, current, reactive, apparent power and power factor values obtained from both Goertzel and FFT algorithms are almost very close to each other for three experiments in the case of before and after compensation. While the power factor value of the load is 0.82 lagging before compensation, it is brought just 0.99 values by using Goertzel and FFT algorithms after compensation in case of firs load condition. Similar results are obtained in the other load groups. At the same time, current, apparent and reactive power values are reduced to desired values by using both algorithms in case of after compensation. It is clearly said that power factor of the load is successfully improved by the use of SVC system.
In addition to that, voltage, current, active, reactive and apparent power and power factor values are displayed on the screen by the use both algorithms before and after compensation respectively.
In this experimental work, a new method is developed for the FC–TCR based SVC system. In this method, Fundamental components of voltage and current are obtained from the harmonic content network by using Goertzel algorithm instead of FFT. These values are utilized for the calculation of active, reactive, apparent power and power factor for the use of SVC system in order to achieve fast and accurate compensation. This study is realized both simulation and experimental. Simulation studies have shown that the computation time measured by using Goertzel algorithm is faster than FFT algorithm. In this way, power components and power factor values are measured and calculated by minimal hardware and reduced computational time through the use of Goertzel algorithm instead of classical FFT. Power measurement and calculation by utilizing Goertzel algorithm is applied to the FC–TCR based SVC system for the first time in this experimental study.
MS provide the basic idea of the research and supervise. FK and AG researched the background literature and performed Goertzel based Static VAr Compensator in experimental study, organized and drafting of the manuscript. All authors read and approved the final manuscript.
The authors declare that they have no competing interests.
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