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Güç sistemleri için digital frekans ölçme algoritmaları

Başlık çevirisi mevcut değil.

  1. Tez No: 75314
  2. Yazar: KARABET ŞENYAN
  3. Danışmanlar: DOÇ. DR. ÖMER USTA
  4. Tez Türü: Yüksek Lisans
  5. Konular: Elektrik ve Elektronik Mühendisliği, Electrical and Electronics Engineering
  6. Anahtar Kelimeler: Belirtilmemiş.
  7. Yıl: 1998
  8. Dil: Türkçe
  9. Üniversite: İstanbul Teknik Üniversitesi
  10. Enstitü: Fen Bilimleri Enstitüsü
  11. Ana Bilim Dalı: Elektrik Mühendisliği Ana Bilim Dalı
  12. Bilim Dalı: Belirtilmemiş.
  13. Sayfa Sayısı: 62

Özet

ÖZET Frekans, güç sistemlerinin önemli bir işletme parametresidir. Bir elektrik güç sisteminde sabit frekans üretilen aktif güçle tüketilen aktif güç arasındaki dengenin varlığını gösterir. Bu dengenin bozulması sistem frekansındaki değişme ile algılanabilir. Bu nedenle elektrik güç sistemleri frekansının hızlı ve doğru olarak ölçülmesi sistem kontrolü ve korunması için çok önemlidir. Bu tez çalışmasında BÖLÜM 2' de frekans ölçme yöntemleri olan Sıfır-Geçiş Yöntemi (Zero-Crossing Technique), Seviye-Geçiş Yöntemi (Level Crossing Technique), Nümerik Yöntem, En Az Hata Kareleri Yöntemi (A Least Error Squares Technique) ve gerilimin faz açısının değişimine göre fekansın ölçülmesi hakkında bilgi verilmiştir. BÖLÜM 3' te frekans ölçme yöntemlerinden Seviye Geçiş Yöntemiyle (Level Crossing Technique) Sıfır-Geçiş Yöntemiyle (Zero-Crossing Technique) ilgili algoritmalar geliştirilmiştir. BÖLÜM 4 te elde edilen algoritmalar örneklenmiş gerilim işaretlerine uygulanmış ve elde edilen frekansların grafikleri çizilmiştir. Vll

Özet (Çeviri)

SUMMARY MEASUREMENT OF FREQUENCY USING ZERO CROSSING AND LEVEL CROSSING TECHNIQUES 1. Introduction When controlling a power system considerable effort is made to ensure the generated power matches the consumed power. This balance is required to maintain a constant operating frequency. Generation-load mismatches cause the system frequency to deviate from its nominal value. When the consumed power is greater than the generated power, the generators decelerate and frequency becomes lower than the nominal value. This indicates that the system is overloaded. Underfrequency relays are used to detect these conditions and disconnect load blocks. This results in acceleration of the generators and an increase in frequency. Ideally power balance should be restored when the frequency is at the nominal 50 Hz. When the generated power is greater than the consumed power, frequency is higher than the nominal value. This indicates that the system has more generation than load. These conditions are detected by overfrequency relays provided at generator terminals. Overfrequency relays are also used to protect generators from overspeeding during start-ups. With the growth of power systems, permissible frequency deviations have been reducing while at the same time frequency-bias (expressed as megawatts per 0,1Hz ) have been increasing. The advent of frequency sensitive relays, load behaviour modelling and other real-time control loops have necessitated measurements of power system frequency with a degree of speed, precision and stability, not provided by conventional electromechanical instruments. VIIIIn order to measure the power system frequency, different methods have been suggested. Takata [1] has the methods based on measurement of the time between zero- crossings. This technique is called Zero-Crossing Technique. Nguyen and Srinivisan [2,3] have suggested a method for computation of small frequency deviations. The explicit computation of the time period between zero-crossings is supplemented by multiple computations of the time periods between various non-zero voltage level crossing. This method is called Level-Crossings Technique. Sachdev and Giray [4,5] have suggested a method called A Least Error Squares Technique. In this technique the frequency is obtained by using Taylor Series equations. Moore, Carranza and Johns [6] have also suggested a numeric technique decomposing input signal into two components, eavh orthogonal in phase, by using two finite impulse response (FIR) filters. In this study, Level-Crossing Technique is propesed. This Technique is based on a generalization of Zero-Crossing Technique. Therefore, firstly the Zero-Crossing Technique is explained then Level-Crossing Technique is explained. 2. Zero Crossing Technique The measurement of frequency using a zero crossing technique is investigated using an algorithm which detects the zero-crossing in each voltage cycle and uses the time between succeessive zero-crossings to determine the frequency. The line voltage signal is sampled, af: a. uniform sample rate of N samples per nominal frequency period, the time interval between samples is At. Assuming a nominal system frequency of 50 Hz, the sampling frequency is IXfs = N x 50 (1) The interval At between two samples is At 1 / fs 0,02 / N (2) Consequently, the frequency of the actual voltage signal is, I / T = N / ( 0,02 x Nc) (3) Where T is the period and Nc is the number of samples between two +Ve going zero-crossings. The accurancy of this technique is limited because the first and last samples are unlikely to occur at the exact position of the zero-crossings. A more accurate technique is obtained by approximating the waveform of the line voltage near a zero crossing by a straight line. Page 4 illustrates the computation of the time period T using samples taken immediately before and after the zero crossing. The curve AB and CD is assumed to be. a straight line, hence: X, = (V, / V2 ) x X2 = [(V, / V2) x At] /[l + (V, / V2)] (4) The first +Ve going zero-crossing is To, = T, + X, (5) Similarly, the second +Ve zero-crossing is o2 = Tj, + (V, / V4 ) x X4 = F(V, / V4) x At] /[I + (V, / V4)] (6)The frequency of the signal, f = 1 / (To2 - To, ) Hz (7) 3. Level Crossing Technique 3.1 Computation of Time Period This algoritm is based on a generalization of zero- crossing detection to level crossing detection. Unlike zero- crossing, which only provides one or two estimates per cycle this method gives several estimates per cycle. This method is particularly attractive when implemented with other power system tasks which require analogue to digital conversion of the voltage signal. Page 18 illustrates the computation of one estimate of the time period T from the measurement of V(t), the most recent voltage sample, V(t-At), the previous sample and V(t-NAt), N samples in the past. At is the fixed sampling time interval. By lineer interpolation between samples: z, (t) = NAt - T = V(t-NAt) - Vft).At ¦> (8) V(t-At) - V(t) The following points are noteworthy regarding the above method of time period (or frequency ) determination. - One new estimate of the time period is available at each sampling instant from each phase signal. - The approach is similar to the zero-crossing time interval determination. The latter is possible only once or twice per cycle, whereas thid approach gives more estimates per cycle.3.2 Correction of Linear Interpolation Let Z| (t) be the estimate of NAt - T given by Equation (8). Another estimate of the same time deviation may be given by z2 (t) as: z2 (t) = Vft-NAt) - V(t). At V(t-NAt)- V(t-NAt+At) (9) Averaging these two estimates leads to the following: z (t) = f V(t)-V(t-NAt )1 -T D(t)+ D(t-NAt+At)l. At 2. D(t). D(t-NAt+At) (10) Where D(t) = V(t) - V(t-At) (11) The frequency calculation from equation (10) has the following features: - Four samples are used : The most recent, the one previous, two samples slightly more and slightly less than a complete timeperiod behind. - For sinusoidal waveforms, the precision of the result is highest near zero crossings and lowest near peaks when the denominator terms are close to zero and difference between two large numbers are needed to compute a small value. XII3.3 Best Estimate of Time Period Estimation Using equation (10) an estimate of the time period is possible at each new sampling instant. In order to get a composite best estimate, a weighted mean of several individual estimates can be computed, the weights being inversly proportional to the imprecision. The weighting factor, W(t) =[V(t) - V(t-At) ] x [ V(t-NAt+At) - V(t-NAt)] (12) has the following desired features: - It is minimum near peaks and troughs when the estimates are least precise. - It is maximum near zero crossing when the estimates are most precise. - The sum of the weighting factors over each complete half cycle is constant in time. 3.4 Time Period Deviation from an Arbitrary Number of Samples. ; The weighted mean of m estimates of z(t) from Equation (10) with weights Equation (12) is given Equation (13). z(m,t) (m-l).At Z t = 0 z(t) W(t) (13) (m-l).At Z t=0 W(t) which can be simplified to Equation (14) XIII(m-l).At I I [V(t) - V(t-At)][ D(t) - D(t-NAt+At)] z(m,t) = t=0 2.At (m-l).At X [ D(t) - D(t-NAt+At)] t=0 (14) Finally, frecuency is calculated as f = 1 / [ NAt-z(m,t)] (15) XIV

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