An excel-based program for waveform synthesis and analysis

IEEE MULTIDISCIPLINARY ENGINEERING EDUCATION MAGAZINE, VOL. 2, NO. 4, DECEMBER 2007

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An Excel-Based Program for Waveform Synthesis and Analysis
Thavatchai Tayjasanant, Member, IEEE, and Naruporn Sookmak

Abstract—This letter presents a developed Excel-based program for waveform synthesis and analysis. The program utilizes an automatic-update feature and available functions of MS OfficeExcel. As soon as the required data is copied into specific cells, results can be generated and updated automatically. The program can facilitate the analysis of power system harmonics. An example of actual data is used to test the developed program. Index Terms—Waveform power quality, harmonics. synthesis, waveform analysis,

Fig. 1. Relationship between waveform synthesis and analysis.AVEFORM synthesis and analysis are basic computations for power quality assessment. Waveform synthesis is an operation that obtains the instantaneous waveform in time domain from the spectral data in frequency domain. Waveform analysis is an operation that converts the frequency-domain data back to the time-domain data. Fig. 1 illustrates the relationship between waveform synthesis and analysis. Oneof the applications is the harmonic analysis. Harmonic component according to IEC 61000-4-30 [1] is defined as “Any of the components having a frequency which is an integer multiple of the fundamental frequency”. These harmonics cause the waveform to distort. In order to assess the distortion level of the signal, waveform analysis is required. The index called Total Harmonic Distortion (THD) istypically used to assess the level of harmonic distortion. This letter is organized as follows. Section II presents the background on the waveform synthesis. The algorithm used in the Fourier series. In Section III, the waveform analysis is described. The index THD is explained in more detail. Section IV describes the developed Excel-based program. Steps for using the program are provided. Theconclusions are summarized in Section V. II. WAVEFORM SYNTHESIS Waveform synthesis can be achieved using two methods: 1) inverse Fourier transform (IFT) and 2) Fourier series. This letter presents only the second method. All assumptions of

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I. INTRODUCTION

Fourier series such as periodicity property are applied for the analysis. The waveform synthesis can be performed by combining allfrequency components (harmonics) together to obtain the resultant waveform. The instantaneous voltage signal can be written as the sum of the DC, fundamentalfrequency (f1) and harmonic components as shown in (1).

V ( t ) = Vdc + V1 cos(2π f1t + θ1 ) + … + Vh cos(2π f ht + θ h ) (1)
where Vdc is the DC component, V1 and θ1 are fundamentalfrequency magnitude and phase angle, and Vh and θh are hthharmonic magnitudes and phase angles, respectively. At each time instant (with a step of ∆t), an individual frequency component is calculated. In other words, at t = 0, ∆t, 2∆t, …, T, values of Vdc, V1, …, Vh are calculated where the time step ∆t = T/N = 1/(N×f1), N is the sample size (in 1 period) and T is the fundamental-frequency period (T = 1/f1). Then the resultant waveform is the sum of allcomponents as shown in (1). Therefore, knowing the harmonic spectral information, the plot between V(t) and t can be done. III. WAVEFORM ANALYSIS In practice, the instantaneous waveform is sampled and recorded in the discrete values. The definition of a discrete periodic signal is given in (2).

f [n] = f [n + mN ]
where m = 1, 2, 3, … and N is the sample size (in 1 period).

(2)

T. Tayjasanantand N. Sookmak are with the Department of Electrical Engineering, Chulalongkorn University, Bangkok 10330 Thailand (e-mail: Thavatchai.T@chula.ac.th or tayjasanant@yahoo.ca) Publication Identification Number 1558-7908-052007-03 1558-7908 © 2007 IEEE Education Society Student Activities Committee (EdSocSAC) http://www.ieee.org/edsocsac

The algorithm called discrete Fourier transform (DFT) is...