# Delta Modulation with PI Controller A Comparative Study

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2 46 Delta Modulation with PI Controller A Comparative Study V/f Characteristics In delta modulation, finding the base frequency i.e. frequency up to which the DM retains constant V/f characteristic, is quite important. Above the base frequency the inverter enters constant voltage region (CVR). The CVR may lead to the saturation of the motor s magnetic core and is to be avoided [2]. Figure 2 shows the V/f relationship of fundamental voltage versus the operating frequency of the input source V r. 2. Performance Parameters of DM Various performances of DM are discussed by: ) Changing the time constants of DM 2) Changing the hysteresis gap of the DM 3) Changing voltage amplitude of the input source Vr. 4) Using PI controller with DM. 2. Changing the Time Constant ( ) In delta modulation circuit shown above the positive and negative slops of carrier wave V2 depends on the time constant τ =R3C of inverter circuit, using some variations in the time constant by changing R3, different ripple frequency of the carrier waveform can be achieved. Fourier analysis for the harmonic variation of V with the changes in time constant τ is carried out for the various values of operating frequencies of the source VR. The results are shown in Figures 2 and 3. It has been observed, that by making time constant of inverter circuit to τ/3 by changing R3 to 27k, the linearity stage of V/f characteristic is extended to 3Hz. This is three times the standard base frequency which is Hz, and the fundamental voltage amplitude is reduced and also there is change in harmonic amplitude of V. Using a time constant of 3τ (R3=24k) harmonic amplitude of switching output voltage of DM (V) is reduced, however the base frequency has been reduced to 5 Hz, this is two times smaller than base frequency(hz). Therefore, it is found from DM operation that, the base frequency is inversely proportional to the inverter time constant τ. A range of R3 value from 27k to 68k is attractive for optimal performance of the DM circuit. 2.2 Changing the Hysteresis Gap of Delta Modulator The hysteresis gap can be changed by changing feed forward resistor R2 having VR and the τ as constants. Thus by using hysteresis 5 %,% and 2 % by changing resistor R2, Fourier analysis for the harmonic variation of V was carried out for various frequencies of VR. V/f characteristic with variation of hysteresis gap from 5% to 2% is shown in Figure 4. The actual harmonic normalised voltage frequency (c) Figure 2. Normalized voltage verses frequency distribution with time constant τ, V/f characteristic with time constant 3τ, (c) V/f Characteristic with time constant τ/3 spectrum is not shown as the aim of Delta modulation is to boost the fundamental output voltage (V), which is shown in its normalized form. It is found from the DM performance that, a lower hysteresis gap provides for a wider base frequency, but the changes in the base frequency are minimal for the various values of hysteresis gap. R2 range of k to 2k is optimal for optimum performance of the DM. Copyright 29 SciRes

3 Delta Modulation with PI Controller A Comparative Study Figure 3. Fundamental component of normalized voltage verses frequency for different time constant HYSTERESIS COMPARISON Properties of DM with PI Control A PI controller is used to boost up the fundamental voltage of the delta modulator [6,8].The PI controller is inte grated to the delta modulator (DMPI) as shown in Figure 6. Fourier analysis was done for three different values of the feedback resister Rf. The respective fundamental output voltages are shown in Figure 6. As observed from the test that, PI controller helps to boost the fundamental voltage widening the gap between the fundamental and harmonic voltages, and it is also observed that the PI introduces a disturbance to the linearity of the V/f characteristics. The low voltage percentage boost is calculated from the above figures for each value of Rf based on the general DM circuit in Figure & Figure 6 means Rf value equals to infinity. It is clear from the above tabulated %hysteresis 5% hysteresis 2% hysteresis Figure 4. Effect of Constant V/f characteristic with variation of Hysteresis gap, 5%, %, and 2% Figure 6. Circuit schematic of Delta-modulator with PI controller FUNDAMENTAL VOLTAGE AT VARIOUS "Rf" VALUES Figure 5. Normalized fundamental voltage vs. frequency characteristics for variation of VR from 2V to 8V 2.3 Changing the Reference Signal Amplitude (VR) Under this mode the time constant and the hysteresis gap are kept constant. In normal DM operation, VR is held constant. However, if in some applications the base frequency needs to be varied without changing the time constant and the hysteresis gap, it can be achieved by changing VR only. It is found that VR is inversely related to the base-frequency fb. This is shown in Figure 4. A range of 3 to 5 volts for the input source VR is suitable for optimum performance of DM FOR Rf=68K FOR Rf=K FOR Rf=5K Figure 6. A comparison of fundamental normalized voltage for different values of the Rf Copyright 29 SciRes

4 48 Delta Modulation with PI Controller A Comparative Study Table. Low voltage boosting through R f Rf (Ω) Fundamental Value at fm 5Hz Low Voltage Boost Infinity K % K % 68K % 45K (optimal) results that with proper selection of Rf, the fundamental voltage amplitude can be boost up to 35.% as long as the operating frequency is within the base frequency. A range of 45k to k is suitable for Rf value for the optimum performance of DMPI. 3. Optimized Delta Modulator with PI Control A final and optimum performance based Delta Modulator with PI controller is suggested for inverter (VSI) with the following optimal values: R2=25K, R3=45K, Rf=45k. The harmonic spectrum of switching output voltage of DM (V) is obtained with suggested optimized DMPI with modulating frequency of 5Hz and Hz are shown in Figure 7. As one can see in the above figures, the optimized DMPI with modified component values shifts the dominant harmonics towards higher frequencies preferably from the th harmonic position. This optimized DMPI model is now used as a driver circuit for the voltage source inverter. 4. Delta Modulator as the Driver We have selected the above discussed delta modulation (basic DM, DM with PI) techniques for generating the switching gate signal for the IGBT s of inverter. Analysis of the performance of proposed rectifier-inverter topology [4] carried out for resistive-inductive load. 4. Performance of Inverter with Basic DM Rectified DC supply is applied given to an IGBT inverter with the basic delta modulator and it is tested for a RL load(r=8ohms, L=95mH) at 5Hz and Hz operating Frequencies (see in Figures 8 and 9). 4.2 Performance of Inverter with DMPI Study is conducted with the delta modulator inverted with PI controller, and it is observed for same resistive inductive load at 5 and Hz operating frequencies as shown in Figures and. It can be seen in the Figure, there is an % boost in the amplitude of fundamental component of output phase voltage of inverter for 5 Hz operation of DMPI with respect to basic DM characteristics shown in Figure Performance Comparison of Inverter with Basic DM and with DMPI The output phase voltage of the inverters has been studied for both the delta modulation (DM and DMPI) techniques for a range of frequencies with R-L load. The normalized fundamental voltage versus frequency characteristics is plotted and it is shown below. It is seen from the Figure 2, that introduction of PI controller helps to boost up the fundamental voltage compared to that of basic DM. The PI controller also introduces slight disturbance to the V/f characteristic but the linearity is still maintained up to the range of base frequency of Hz. 5. Optimized DMPI with IGBT Inverter Figure 7. Harmonic spectrum of switching output voltage of DM i.e. V at modulating frequency 5Hz Hz Rectifier-inverter performance is studied with the optimized DMPI, which we have discussed earlier. Optimized DMPI is used to drive the driver circuit for the overall three phase inverters and the output harmonic spectrum generated by the inverter circuit is shown below. It is observed that improved version of DMPI is able to shift the more dominant harmonics to the higher frequencies. Copyright 29 SciRes

5 Delta Modulation with PI Controller A Comparative Study 49 Figure 8. Phase voltage waveform with basic DM at 5 Hz. Phase voltage frequency spectrum at 5 Hz Figure 9. Phase voltage waveform with basic DM at Hz. Phase voltage frequency spectrum at Hz Figure. Phase voltage waveforms with DM with PI, at 5 Hz. Phase voltage frequency spectrum at 5 Hz Figure. Phase voltage waveform with DM with PI, at Hz. Phase voltage frequency spectrum at Hz Copyright 29 SciRes

6 5 Delta Modulation with PI Controller A Comparative Study 5. Experimental Results & Drive Application Figure 4 shows the time domain sample of DM output waveform captured from oscilloscope (Fluke spectrum analyzer). The voltage is normalized with respect to the inverter input dc bus voltage. The spectrum shows the absence of the low frequency harmonics and a high (96.8%) fundamental DM output voltage. Traces of 3 rd harmonic still is present due to imperfection in gating signal timing. The output characteristics of the experimental prototype Delta-Modulator is studied at different modulating signal Vr frequency and magnitude levels in order to achieve maximum inverter fundamental output voltage. The results are compared and confirmed with the ones from simulation. In submersible motor pump application, the DMPI method uses either the voltage or the current variation to maintain the constant slip operation. This is known as the speed variation and is used because the pump production and the efficiency are dependent on the speed of the pump. The operational characteristic of the overall system is shown in Figure 5. The experimental motor employed is a.5 HP squirrel cage submersible induction motor. The motor parameters are given in the Appendix. The variation of inverter voltage, frequency and the resulting motor slip are obtained for a sudden change in load, as shown in Figure 5. When the motor load is increased, the slip increases resulting in a slowdown. The inverter responds by increasing the terminal voltage and frequency. The motor slip eventually decreases and settles to the steady state value after few oscillations. These characteristics also reflect the constant v/f operation of the DM inverter. 6. Conclusions From the above study of DM techniques, and various comparisons between them, it has been concluded that delta modulation with PI controller helps to provide constant V/F characteristics and boosting of the fundamental voltage especially at low operating frequency. The opti- Figure 3. Harmonic spectrum for VSI output voltage using optimized DM with PI Figure 4. Inverter output waveform from oscilloscope FUNDAMENTAL VOLTAGE FUNDAMENTAL HARMONIC COMPARISON BETWEEN BASIC DM AND DMPI DMPI BASIC DM Figure 2. The normalized fundamental voltage versus frequency characteristics Figure 5. Change of slip, frequency and fundamental voltage for an increase in load at 5Hz operation mized DM brings about a significant decrease in the harmonic contents towards the 3th harmonic. The DMPI inverter with higher voltage boosting capability and constant V/f characteristic without the feed-back complexity leads to lighter and more economical inverter and the optimized DM inverter with attenuation of low-order harmonics lead to reduced filter size. It was observed that the motor torque and speed can be instantaneously computed solely from its terminal elec- Copyright 29 SciRes

7 Delta Modulation with PI Controller A Comparative Study 5 trical parameters. It was shown how the DMPI does eliminate the problems existing in SMM. The results of the experimental setup show that the proposed method handles load change overshoots and oscillations with ease, especially where frequency variation with load change is not warranted. REFERENCES [] P. D. Ziogas, The delta modulation techniques in static PWM inverters, IEEE Transactions on Ind. Applications, pp.99 4, Mar/Apr. 98. [2] M. A. Rahman, J. E. Quacioe, and M. A. Chowdhury, Performance analysis of delta modulated PWM, IEEE Transactions in Power Electronics, Vol. PE 2, No. 3, pp , July 987. [3] T. C. Green, J. C. Salmon and B. W. Willams, Investigation of delta modulation and of subharmonic elimination techniques, IEEE PESC Record, Vol., April 988. [4] M. A. Rahman, J. E. Quacioe, and M. A. Chowdhury, Harmonic minimization in Delta modulated inverters using Tuned filters, IEEE PESC Record, Vol., April 988. [5] A. I. Maswood, P. D. Ziogas, and G. Joos, Problems and solutions associated with the operation of phase controlled rectifiers under unbalanced input voltage conditions, IEEE Transactions on Industry Applications, U.S.A, Vol. 27, No. 4, pp , July/August 99. [6] A. I. Maswood and M. A. Rahman, A survey of delta modulation techniques, characteristics & sub harmonic elimination for VSI, Electric Machines and Power Systems Journal, U.S.A., Vol. 26, No. 6, pp , July 998. [7] A. I. Maswood and S. Wei, A novel current source PWM drive topology with specific harmonic elimination switching patterns, IEEE Canadian Conference on Electrical & Computer engineering, CCECE, Halifax, Nova Scotia, May 8, 2. [8] A. I. Maswood and M. A. Rahman, A PWM voltage source inverter with PI controller, performance parameters under non-ideal conditions, published in the Electric Power Systems Research [EPSR] Journal, U.S.A, Vol. 38, No., pp 9 24, 996. [9] A. I. Maswood and M. H. Rashid, A novel method of harmonic assessment generated by 3 Phase AC-DC converters under unbalanced supply conditions, IEEE Transactions on Industry Applications, U.S.A, Vol. 24, No. 4, pp , July/August 988. [] M. H. Kheraluwala and D. M. Divan, Delta modulation strategies for resonant link inverters, IEEE Transactions on Power Electronics, Vol. 5, No. 2, pp , April 2. Copyright 29 SciRes

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