Paper Identification No- 74
Harmonic Reduction in AC to AC Converter by Trapezoidal Modulation Technique Anshul Agarwal, Student Member, IEEE
Vineeta Agarwal, Senior Member, IEEE
Electrical Engineering Department. MNNIT Allahabad, India
[email protected]
Electrical Engineering Department MNNIT Allahabad, India
[email protected]
Abstract— Trapezoidal modulation technique has been applied in AC to AC converter to reduce harmonics in the output. Both step up and step down operation of the converter has been studied for different output frequencies. Simulation results are shown for single-phase to single-phase converter configuration using the software SIMULINK. Minimum total harmonic distortion in the output has been found to be 5% for cyclo-inverter operation for a frequency range of 500 to 750 Hz. During cyclo-converter operation it reduces to 1.2% up to a frequency range of 1 Hz to 16.66 Hz which is generally recommended mode of cycloconverter.
The analysis of harmonic characteristics for harmonic sources in power systems, such as converters and cyclo-converters, is essential for harmonic suppression or harmonic filter design [3]. Some of the methods which can be employed for harmonic suppression are the modulation techniques [4] and conventional filter system [5]. The conventional filter cannot be used for reduction of harmonics in AC to AC converter because the output frequency is varying and using tuned filter for each harmonic is not feasible. Various Modulation Techniques which are employed to improve the quality of load voltage are sinusoidal PWM [6-7], Space vector PWM [8] and Delta modulation [9-11]. This paper presents trapezoidal modulation scheme for an AC to AC Converter both in step-up and step-down operation mode. Contrary with the SPWM method proposed, the scheme offers several advantages compared to the SPWM. Due to its simplicity, it can be implemented easily using digital method. Further-more it produces a higher fundamental output voltage and reduces harmonics to a much extent.
. Keywords – Trapezoidal modulation, Harmonics, AC to AC converter.
I. INTRODUCTION An AC to AC converter is a power electronic device used to convert constant voltage constant frequency AC power to adjustable voltage and adjustable frequency AC power without a DC link. A direct AC-to AC converter has been designed in [1], which uses self commutated device and eliminate the need for external commutation circuit. The output of this converter is however rich in harmonics. Harmonic contents in the output of any converter affect the efficiency of the process which is being carried out. Different type of loads can also have an effect on “purity” of the voltage waveform. Some loads cause the voltage and current waveforms to lose the pure sine wave appearance and become distorted. This distortion may consist of predominately harmonics, depending on the type of load and system impedances. [2]. An unbalanced transformer (where either the output current, winding impedance or input voltages on each leg are not equal) will cause harmonics, as well as over-voltage saturation of a transformer. Applications of highpower industrial drives, large converters and large cycloconverters used as high-power motor drives are main power loads in industrial power networks or distributions. They are main harmonic sources. Harmonics generated from these converters are injected into power network and caused the electric wave distortions. The problem of harmonic pollution, harnessing and limitation become an important issue.
II. PRINCIPLE OF OPERATION . Fig. 1 shows the power circuit of AC to AC converter that requires four bi-directional switches capable of blocking voltage and conducting current in both directions. In the absence of bidirectional switch module, the common emitter anti-parallel IGBT, with diode pair as shown in Fig. 2 is used. The diodes provide reverse blocking capability to the switch module. The IGBT were used due to its high switching capabilities and high current carrying capacities desirable for high-power applications. The output can be synthesized by suitable toggling of the switches subject to the conditions that ensures the switches do not short-circuit the voltage sources, and do not open-circuit the current sources. In order to optimize the harmonics and to improve the output of AC to AC converter, gate pulses to different IGBTs are modulated using Trapezoidal modulation technique and their performance is obtained in terms of total harmonic distortion in the output.
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Paper Identification No- 74
Where n is the harmonic order while V (θ) represents trapezoidal waveform. S1a
S1b S2a
S2b
⎫ ⎧1 ⎪α 0 < θ < α ⎪ V (θ) = ⎨ ⎬ ⎪1 α < θ < 90 o ⎪ ⎭ ⎩
LOAD
Vi(t) S3a
S3b S4a
(2)
S4b
Now (1) can be rewritten as α ⎡ ⎤ α 4 ⎢⎛ − θCos(nθ) ⎞ 1 An = Cos(nθ)dθ⎥ ⎜ ⎟ + ⎥ n απ ⎢⎝ ⎠0 n 0 ⎣ ⎦
∫
Figure 1. Power circuit of AC to AC converter
+
4 π
π/ 2
∫ Sin (nθ) dθ
(3)
0
Equation (3) can be simplified into the general equation as given below:
An =
4 n 2π
×
Sin (nα) α
(4)
Figure 2. Common emitter configuration of AC to AC converter
III. IMPLEMENTATION OF TRAPEZOIDAL MODULATION Trapezoidal modulation technique is a technique to advance the control ability by using on-line computation of PWM patterns. This is based on the classical uni-polar PWM switching. In this method a modulating trapezoidal signal Vm(t) with an amplitude (Ar) and the frequency (fs) is compared with a carrier triangular signal Vtri(t) which is a train waveform with a frequency fc and amplitude Ac. The output frequency of the converter is decided with the frequency of the modulating wave The intersection between reference signal and carrier signal defines the switching instant of the PWM pulses. Trapezoidal itself comprises of two linear segments, namely the slope line and the horizontal line. The waveform of the trapezoidal depends on the location of its slope angle, α. Different locations of α will result in different shape and harmonic contents. The magnitude of harmonics for the trapezoidal waveform having α within 0o to 90o, can be calculated using Fourier analysis. Assuming quarter-wave symmetry, only the odd sine terms are to be considered. Thus the sine-term Fourier coefficients can be given by(1)
4 An = π
π/2
∫ V(θ) Sin(nθ) dθ
(1)
0
Figure 3. Trapezoidal modulation technique
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Paper Identification No- 74 In order to use in motor drives, it is desirable to increase the fundamental magnitude of output. Clearly, each α value yields a different harmonics content of the trapezoidal. However, it should be noted that the fundamental component magnitude will also be reduced if α is selected towards 90o. Therefore, to gain high fundamental magnitude, α should be placed nearby 0o. By eliminating a number of dominant harmonics, an output voltage with high fundamental magnitude and low harmonic content can be obtained. The method of trigger pulse generation for a particular frequency is described in [11]. These logical gating pulses for that particular frequency of the converter are ANDed with the logical Trapezoidal output and the resulting pulses, after amplification to the required gating power level, are fed to the respective IGBTs. The output voltage produced by the AC to AC converter contains the fundamental component of which the sine wave is a replica. In addition, it contains harmonic components which are located in bands around multiples of the triangle frequency [12].
Figure 4. Output & THD of AC to AC converter with at fo =150Hz.
IV. SIMULATION RESULTS SIMULINK software and its facilities are used to model the AC to AC converter loaded with inductive load. The results of simulation are reported for different output frequency first for cyclo-inverter operation and then for cyclo-converter operation using Trapezoidal modulation technique. A detailed study of AC to AC converter with Sinusoidal PWM and Delta modulation scheme has been given in [13]. It has been observed there that THD is lowest for modulation index around 1 for any output frequency. Any decrease or increase in modulation index increases the THD in the output. It has also been observed that with an increase in carrier frequency, switching frequency increases, but the total harmonic distortion does not reduce significantly. So in the present study the value of modulation index has been taken as 1 and carrier frequency fc is 2 kHz. Fig.4 shows the output waveform of AC to AC converter along with its THD for an output frequency fo= 3 × fi i.e., 150 Hz. The THD for this case is found approximately equal to 8%. However when fo is increased and say taken as 500 Hz, then the output though contain harmonics but THD reduces to 5 % as shown in Fig.5.
Figure 5. Output & THD of AC to AC converter at fo =500 Hz.
With Further increase in frequency say fo = 15 × fi, i.e. 750 Hz, THD remains 5 %. This is minimum THD for output frequency 15 times of input frequency as shown in Fig.6.. Now for an output frequency fo= 20 × fi, THD again increases and is coming out to be approx. 12% (Fig. 7) and it remains constant as 12% for fo = 1.25 kHz as shown in Fig. 8
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Paper Identification No- 74 Fig. 9 to Fig.12 show the step-down operation of the AC to AC converter at different output frequencies again when modulation index, m is 1 and the carrier frequency is 2 KHz. At an output frequency of 25 Hz, the THD is coming out to be 3%.shown in Fig. 9. When the output frequency is reduced i.e. fo = 12.5 Hz the THD is coming out to be almost same as 23% shown in Fig. 11. With further reduction in the output frequency i.e. when output frequency fo = 10 Hz the THD is constant as 2% shown in Fig.12. Figure 6. Output & THD of AC to AC converter
at fo = 750 Hz.
Figure 7. Output & THD of AC to AC converter at fo =1 kHz.
Figure 9. Output & THD of AC to AC converter at fo = 25 Hz
Figure 10. Output & THD of AC to AC converter at fo = 16.66 Hz.
Figure 8. Output & THD of AC to AC converter at fo =1.25 kHz.
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Paper Identification No- 74
Figure 13. Performance analysis of cyclo-inverter
Figure 14 shows the performance evaluation of converter in step-down mode for different output frequencies. For this case THD has been found to decrease with a decrease in the output frequency. As cyclo-converter is generally used at the frequency below than 16.66 Hz where THD has been found to be in the range of 2-1.5 % in case of trapezoidal modulation, it is recommended to use the trapezoidal modulation (TM) technique for cyclo-converter. Figure 11. Output & THD of AC to AC converter at fo = 12.5Hz.
Figure 14. Performance analysis with different frequency for cycloconverter
V. CONCLUSIONS Trapezoidal modulation technique has been implemented in an AC to AC converter in order to reduce the harmonics in the output of the converter. The Trapezoidal wave is suitable for on-line computation and its waveform varies from a rectangular wave to a triangular wave. Besides being easy to realize and simulate, the controllability of trapezoidal modulator is wide and versatile. The modulation technique increases the fundamental output voltage up to 15% as compared to conventional Sine PWM. The harmonics in the output of AC to AC converter is also reduced to a large extent. Minimum THD has been found to 5% during cyclo-inverter operation for a frequency range of 500 to 750 Hz. During cyclo converter operation it reduces to 1.2% for a frequency of 1 Hz. It is in the range of 1 to 2.5 % for a frequency range of 1 to 16.66 Hz which is generally recommended mode of cyclo-converter. It is therefore advisable to use this technique for cyclo-converter operation.
Figure 12. Output & THD of AC to AC converter at fo = 10Hz
Figure 13 shows the performance analysis of AC to AC converter in step-up mode for different modulation index (m). It is shown in the figure that for cyclo-inverter operation, with an increase in the modulation index THD reduces much more in trapezoidal modulation (TM) as compare to SPWM scheme. It reduces to 5% in case of trapezoidal modulation at an modulation index aound 1. Where as in SPWM technique minimum THD obtained is 8%.
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