RECTIFICATION OF UTILITY INPUT
USING DIODE RECTIFIERS
1. INTRODUCTION
Power electronic systems generally get their power from the utility source, as shown by the lock diagram in Fig. 1. Unless a corrective action is taken as described in the next chapter, this power is drawn by means of highly distorted currents, which have a deleterious effect on the power quality of the utility source. Furthermore, the power system disturbances in the utility source can disrupt the power electronics system's operation. Both of these issues are examined in this chapter.
Figure 1 Block diagram of power electronic systems
2. SEKILAS TENTANG DIODA
a. Sejarah Singkat Dioda
Tahun 1883, secara tidak sengaja Edison telah membuat dioda pertama melalui pengujian bola lampunya. Bila salah satu elektroda diberi tegangan positif terhadap kawat (filamen) maka ada arus mengalir antara dua kawat dan bila diberi tegangan negatif maka arus berhenti.
Kata “dioda” adalah:
di = dua
ode = elektroda
Jadi dioda merupakan suatu piranti dua elektroda dengan arah arus yang tertentu.
b. Bentuk Fisik, dan Simbol Dioda
c. Aplikasi Dioda Sebagai Penyearah pada Rangkaian Listrik
Setelah mengetahui konstruksi, karakteristik, dan model dari dioda semikonduktor, diharapkan rekan reakan dapat memahamipula berbagai konfigurasi dioda dengan menggunakan model dalam aplikasinya di rangkaian elektronik.
1. Penyearah Setengah Gelombang
Pada bagian ini akan kita kembangkan metoda analisis dari dioda yang telah dipelajari sebelumnya. Untuk menganalisis rangkaian dioda dengan input yang berubah terhadap waktu seperti gelombang sinusoidal dan gelombang kotak.
Rangkaian sederhana dibawah ini akan kita gunakan untuk mempelajari cara menganalisanya. Metode dioda ideal akan digunakan dalam analisis selanjutnya.
Gambar Penyearah Setengah Gelombang
Rangkaian diatas akan menghasilkan output Vo yang akan digunakan dalam konversi dari AC ke DC yang banyak digunakan dalam rangkaian-rangkaian elektronika.
Selama interval t = 0 à T/2 mengakibatkan dioda ON, dioda selanjutnya dapat digantikan dengan rangkaian ekivalen model idealnya, sehingga outputnya bias diperoleh proses di atas dapat digambarkan seperti di bawah ini
Gambar Daerah dioda konduksi (0 – T/2)
Selanjutnya , selama perioda T/2 à T polaritas dari input Vi berubah mengakibatkan dioda tidak bekerja (OFF), berikut penggambaran prosesnya,
Gambar Daerah dioda Non Kunduksi (T/2 – T)
Sinyal output Vo mempunya nilai rata-rata selama satu siklus penuh dan dapat dihitung dengan persamaan berikut
Vdc = 0.318Vm
Berikut adalah gambar input dan output rangkaian penyearah ½ gelombang
Gambar Sinyal input dan output rangkaian penyearah ½ gelombang
Selain menggunakan model ideal kita juga dapat menggunakan model lain.
2. Penyearah Gelombang Penuh
a. Konfigurasi Bridge
Untuk mengingkatkan DC level yang diperoleh dari input sinusoidal sebanya 100% kita dapat menggunakan rangkaian penyearah gelombang peunh. Konfigurasi yang sangat terkenal adalah konfigurasi Bridg atau jembatan, dengan menggunakan 4 buah dioda dengan penyearah seperti pada gambar berikut:
Gambar Penyearah Gelombang Penuh
Selama periode t = 0 à T/2 polaritas input digambarkan seperti pada gambar berikut
Dari gambar diatas terlihat bahwa D2 dan D3 terkonduksi (ON) sementara D1 dan D4 OFF. Dengan mengganti dioda dengan model ideal diperoleh gambar berikut
Gambar Aliran arus pada fase positif dari Vi
Untuk perioda intpu t = T/2 à T, D2 dan D3 OFF sementara D1 dan D4 ON. Berikut gambar polaritas input, arah arus serta rangkaian ekivalen rangkaian dioda
Gambar Aliran arus pada fase negatif dari Vi
Secara keseluruhan input dan output rangkaian ini adalah
Gambar Sinyal input dan output rangkaian dioda bridge
Nilai rata-rata DC dapat diperoleh dengan persamaan berikut
Vdc = 0.636Vm
b. Center Tapped Transformator
Berikut kedua yang popular dari penyearah gelombang penuh adalah dengan menggunakan 2 buah dioda dan center tapped (CT) transformator konfigurasinya dapat dilihat pada gambar berikut
Gambar Gelombang penuh dengan trafo CT
Selama perioda t = 0 à T/2, D1 akan menjadi ON sedang D2 OFF, seperti gambar berikut
Gambar Kondisi rangkaian pada perioda input t = 0 à T/2
Sebaliknya, selama perioda input T/2 – T kondisi rangkaian adalah seperti gambar berikut
Gambar Kondisi rangkaian untuk perioda input T/2 – T
3. Dan lain-lain J
FUTHER MORE
3. DISTORTION AND POWER FACTOR
To quantify distortion in the current drawn by power electronic systems, it is necessary to define certain indices. As a base case, consider the linear R — L load shown in Fig. 2a which is supplied by a sinusoidal source in steady state. The voltage and current phasors are shown in Fig. 2b, where ϕ is the angle by which the current lags the voltage. Using rms values for the voltage and current magnitudes, the average power supplied by the source is
P = VsIscos ϕ ……………………..(1)
The power factor (PF) at which power is drawn is defined as the ratio of the real average power P to the product of the rms voltage and the rms current:
…………………..(2)For a given voltage, from Eq. 2, the rms current drawn is
…………….(3)This shows that the power factor PF and the current Is are inversely proportional. The current flows through the utility distribution lines, transformers, and so on, causing losses in their resistances. This is the reason why utilities prefer unity power factor loads that draw power at the minimum value of the rms current.
Figure 2 Voltage and current phasors in simple R-L circuit.
a. RMS Value of Distorted Current and the Total Harmonic Distortion (THD)
The sinusoidal current drawn by the linear load in Fig. 2 has zero distortion. However, power electronic systems with diode rectifiers as the front-end draw currents with a distorted waveform such as that shown by is(t) in Fig. 3a. The utility voltage vs(t) is assumed sinusoidal. The following analysis is general, applying to the utility supply that is either single-phase or three-phase, in which case the analysis is on a per-phase basis.
Figure 3 Current drawn by power electronics equipment with diode-bridge front-end.
The current waveform is(t) in Fig. 3a repeats with a time-period T1. By Fourier analysis of this repetitive waveform, we can compute its fundamental frequency (- 1/T1) component isl(t), shown dotted in Fig.3a. The distortion component idhtortlon(f) in the input current is the difference between is(t) and the fundamental-frequency component isl(t):
(4)where idistortion(t) using Eq.4 is plotted in Fig. 3b. This distortion component consists of components at frequencies that are the multiples of the fundamental frequency.
To obtain the rms value of is(t) in Fig.3a, we will apply the basic definition of rms:
(5)Using Eq. 4,
(6)In a repetitive waveform, the integral of the products of the two harmonic components (including the fundamental) at unequal frequencies, over the repetition time-period, equals zero:
(7)Therefore, substituting Eq. 6 into Eq. 5, and making use of Eq.7 that implies that the integral of the third term on the right side of Eq. 6 equals zero,
(8)Or
(9)where the rms values of the fundamental-frequency component and the distortion component are as follows:
(10)Dan
(11)Based on the rms values of the fundamental and the distortion components in the input current is(t), a distortion index called the Total Harmonic Distortion (THD) is defined in percentage as follows:
(12)Using Eq. 9 into Eq.12
(13)The rms value of the distortion component can be obtained based on the harmonic components (except the fundamental) as follows using Eq. 7:
(14)where Ish is the rms value of the harmonic component “h”
b. Displacement Power Factor (DPF) and Power Factor (PF)
Next, we will consider the power factor at which power is drawn by a load with a distorted current waveform such as that shown in Fig. 3a. As before, it is reasonable to assume that the utility-supplied line-frequency voltage vs(t) is sinusoidal, with an rms value of Vs and a frequency f1 . Based on Eq. 7, which states that the product
of the cross-frequency terms has a zero average, the average power P drawn by the load in Fig. 3a is due only to the fundamental-frequency component of the current:
(16)Therefore, in contrast to Eq.1 for a linear load, in a load that draws distorted current, similar to Eq. 1
(17)where ϕ1 is the angle by which the fundamental-frequency current component isl(t) lags behind the voltage, as shown in Fig. 3a.
At this point, another term called the Displacement Power Factor (DPF) needs to be introduced, where
(18)Therefore, using the DPF in Eq. 17,
(19)In the presence of distortion in the current, the meaning and therefore the definition of the power factor, at which the real average power P is drawn, remains the same as in Eq. 2, that is, the ratio of the real power to the product of the rms voltage and the rms current:
(20)Substituting Eq. 19 for P into Eq. 20,
(21)In linear loads that draw sinusoidal currents, the current-ratio (Isl/Is) in Eq.21 is unity, hence PF = DPF . Eq. 21 shows the following: a high distortion in the current waveform leads to a low power factor, even if the DPF is high. Using Eq. 13, the ratio (Isl / I1s) in Eq.21 can be expressed in terms of the Total Harmonic Distortion as
(22)Therefore, in Eq.21,
(23)The effect of THD on the power factor is shown in Fig. 5 by plotting {PF / DPF) versus THD. It shows that even if the displacement power factor is unity, a total harmonic distortion of 100 percent (which is possible in power electronic systems unless corrective measures are taken) can reduce the power factor to approximately 0.7 (or 0.707)
Gambar 5. Relation between PF/DPF and THD
4. DIODE-RECTIFIER BRIDGE "FRONT-ENDS"
Most power electronic systems use diode-bridge rectifiers, like the one shown in Fig.7a, even though they draw currents with highly distorted waveforms and the power through them can flow only in one direction. In switch-mode dc power supplies these diode-bridge rectifiers are supplemented by a power-factor-correction circuit, to meet current harmonic limits, as discussed in the next chapter.
Diode rectifiers rectify line-frequency ac into dc across the dc-bus capacitor, without any control over the dc-bus voltage. For analyzing the interaction between the utility and the power electronic systems, the switch-mode converter and the load can be represented by an equivalent resistance R across the dc-bus capacitor. In our theoretical discussion, it is adequate to assume the diodes ideal.
In the following subsections, we will consider single-phase as well as three-phase diode rectifiers operating in steady state, where waveforms repeat from one line-frequency cycle T1 (= 1 / f1) to the next.
a. Single-Phase Diode-Rectifier Bridge
At power levels below a few kW, for example in residential applications, power electronic systems are supplied by a single-phase utility source. A commonly used full-bridge rectifier circuit is shown in Fig. 8, in which Ls is the sum of the inductance internal to the utility supply and an external inductance, which may be intentionally added in series. Losses on the ac side can be represented by the series resistance Rs .
Figure 8 Full-bridge diode rectifier
As shown in Fig.9, at the beginning of the positive half-cycle of the input voltage vs, the capacitor is already charged to a dc voltage vd . So long as vd exceeds the input voltage magnitude, all diodes get reverse biased and the input current is zero. Power to the equivalent resistance R is supplied by the energy stored in the capacitor up to t1.
Beyond t1, the input current is(= idr) increases, flowing through diodes D1 and D3. Beyond t2, the input voltage becomes smaller than the capacitor voltage and the input current begins to decline, falling to zero at t3. Beyond t3, until one-half cycle later than t1, the input current remains zero and the power to Req is supplied by the energy stored in the capacitor.
Figure 9 Current and voltage waveforms for the full-bridge diode rectifier.
At (t1 + T1 / 2) during the negative half-cycle of the input voltage, the input current flows dirough diodes D2 and D4. The rectifier dc-side current idr continues to flow in the same direction as during the positive half-cycle; however, the input current is = -idr, as
shown in Fig. 9. Fig.10 shows waveforms obtained by PSpice simulations for two values of the ac-side inductance, with current THD of 86% and 62%, respectively (higher inductance reduces THD, as discussed in the next section).
Figure 10 Single-phase diode-bridge rectification. The fact that idr flows in the same direction during both the positive and the negative
half-cycles represents the rectification process. In the circuit of Fig.8 in steady state, all waveforms repeat from one cycle to the next. Therefore, the average value of the capacitor current over a line-frequency cycle must be zero so that the dc-bus voltage is in steady state. As a consequence, the average current through the equivalent load-resistance Req equals the average of the rectifier dc-side current; that is, Id = Idr.
b. Effects of Ls and Cd on the Waveforms and the THD
As Figs. 9 and 10 show, power is drawn from the utility supply by means of a pulse of current every half-cycle. The larger the "base" of this pulse during which the current flows, lower its peak value and the total harmonic distortion (THD). This pulse-widening can be accomplished by increasing the ac-side inductance Ls. Another parameter under the designer's control is the value of the dc-bus capacitor Cd . At its minimum, it should be able to carry the ripple current in idr and in id (which in practice is the input dc-side current, with a pulsating waveform, of a switch-mode converter), and keep the peak-to-peak ripple in the dc-bus voltage to some acceptable value, for example less than 5 percent of the dc-bus average value. Assuming that these constraints are met, lower the value of Cd, lower the THD and higher the ripple in the dc-bus voltage.
In practice, it is almost impossible to meet the harmonic limits specified by the IEEE-519 by using the above techniques. Rather, the power-factor-correction circuits described in the next chapter are needed to meet the harmonic specifications.
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