A single-phase delta-modulated inverter for UPS ... - IEEE Xplore

341

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 40, NO. 3, JUNE 1993

A Single-phase Delta-Modulated Inverter for UPS Applications Naser Abdel-Rahim, Student Member, IEEE, and john E. Quaicoe, Member, IEEE Abstract-The performance characteristics of the rectangular wave delta modulation (RWDM)scheme for uninterruptible power supply (UPS)applications are investigated in this paper. Normalized characteristic curves that show the effect of various modulator parameters on the frequency spectrum of the inverter output voltage are obtained using discrete Fourier transform (DIT) and harmonic analysis techniques. The performance of a single-phase half-bridge inverter with an L-C filter is discussed and experimental results are provided to validate the predicted and simulated results. It is shown that the harmonic content of the inverter output waveform can be controlled through the control of the modulator parameters.

I. INTRODUCTION

S

TATIC uninterruptible power supply (UPS) systems employ various PWM techniques to improve the quality of the load voltage. Several harmonic elimination techniques have been used to reduce or eliminate low-order harmonics in the inverter output voltage [1]-[3]. This has led directly to a reduction in the size and weight of the UPS filter. Although these techniques have been successfully implemented for UPS applications, they suffer from complex control circuitry and moderate voltage utilization ratios. To further reduce the load filter size, and achieve a UPS system that is compatible with unbalanced and/or nonlinear loads, the third harmonic injection technique has been proposed 141. In this scheme, the inverter switching pattern is predetermined and is kept fixed during the operation of the UPS system. This switching pattern is chosen in accordance with the load filter cutoff frequency, such that a “gap” is obtained between the filter cutoff frequency and the order of the dominant harmonic in the inverter output voltage (usually in the order of 5). This technique has resulted in minimizing the system output impedance and reducing the size of the load filter. In three-phase applications, this fixed switching pattern deprives the UPS system from regulating the load voltage through the control of the inverter switching pattern. To overcome this drawback, load voltage regulation is achieved through the control of the dc link voltage (regulated front-end stage) [4]. Thus a complex control circuitry is required. Manuscript received September 6, 1991; revised June 6, 1992 and September 29, 1992. The authors are with the Memorial University of Newfoundland, St. John’s NFLD, Canada A1B 3x5. IEEE Log Number 9207942.

Rectangular wave delta modulation (RWDM) has become an established alternative to sine PWM in inverter applications for providing a sinusoidal output voltage with low harmonic content and ease of control of inverter output voltage [5]-[8]. RWDM offers the following advantages that make it attractive for UPS applications: 1) very simple circuit implementation, 2) the harmonic content of the inverter output voltage can be controlled using the modulator parameters, and 3) it provides a simple means whereby the output voltage can be regulated. The basic features of RWDM for UPS application are presented in this paper. A parametric study is carried out to investigate the effect of various modulator parameters on the frequency spectrum of the output voltage of a single-phase inverter. Based on the characteristic curves, optimum values of modulator and load filter parameters are selected. The results show that RWDM offers significant improvements in system performance, i.e., improved voltage utilization ratio and significant attenuation of the low-order harmonics in the inverter output frequency spectrum. The latter feature allows small load filters to be used to obtain load voltage waveform with an acceptable total harmonic distortion. The principle of operation of the RWDM can be described with the aid of the block diagram shown in Fig. l [8]. A reference signal c,(t) is compared with a feedback signal or a carrier signal U&>, obtained by integrating the modulator output signal, to produce an error signal e ( [ ) . According to the sign and predetermined magnitude of e(t), the output of the modulator has two possible levels f V,, whereas the time duration between two successive levels is determined by the slope of the reference signal. Figs. l(b) and l(c) show the waveforms at various nodes in the modulator block diagram. It can be seen that the feedback signal tracks the reference signal within the upper and lower boundary levels k AV. From the modulator-operating principles, it can be observed that the output signal is decoded by the integrator in the feedback path. 11. PERFORMANCE ANALYSIS OF THE RWDM INVERTERS The modulator-operating principles show that the modulator parameters determine the modulator output voltage and hence the switching pattern of the inverter. In this section, the effects of the modulator parameters on the performance of a single-phase voltage-source inverter with a resistive load are investigated.

0278-0046/93$03.00 0 1993 IEEE


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A. Analytical Model of the R W M Fig. 2 shows a small portion of the reference signal the carrier wave u,(t> and the modulator output U&). Assuming that the modulator-switching frequency is high enough so that a small portion of the reference sine wave is approximated by a straight line, the time duration for one complete cycle at the modulator output is given by [81 U&),

where sR(t) = instantaneous slope of the reference signal between points A and C,

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Equation (4) shows the following: The modulator switching frequency reaches a maximum value of (SC/4AV) at wt = (k7r/2), where k is an odd number, resulting in an inherent minimum pulse width at the modulator output. Thus, no special effort is needed to provide minimum pulse width duration in the power inverter, as is the case in the sine pulse width modulation scheme [61. The modulator switching frequency has a minimum value of (Sc/4AV)[1 - (wV,/S,)~], resulting in a maximum pulse at the modulator output. The average switching frequency of the modulator is obtained by averaging the modulator instantaneous switching frequency over several cycles of the reference signal and is given by

Since the switching power loss in the inverter depends on the average switching frequency of the modulator,

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ABDEL-RAHIM AND QUAICOE: A SINGLE-PHASE DELTA-MODULATED INVERTER

( 5 ) shows that the system inverter efficiency can be optimized by selecting appropriate values of the modulator parameters. From the operating principle of the RWDM,it can be seen that the modulator parameters that affect the frequency spectrum of the modulator output and hence the inverter output voltage are 1) the hysteresis bandwidth AV, 2) the integrator gain s,, and 3) the amplitude of the reference signal VR.

B. Normalized Modulator Parameters The performance of the RWDM for UPS applications is examined with the aid of characteristic curves. Normalized values of the various modulator parameters are employed to obtain general characteristic curves that show the effect of the modulator parameters on the inverter output switching pattern. The saturation level of the hysteresis comparator, V,, is chosen as the base value for voltages while the angular frequency of the reference signal, w , is chosen as the base frequency. The normalized value of the modulator parameters are then given by M

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where M A = modulation index of the RWDM, A K = normalized value of the hysteresis bandwidth, S,, = normalized value of the integrator gain, 7 = integrator time constant, and w = angular frequency of the reference signal. The following assumptions were used to obtain the characteristic curves for the parametric study of the inverter voltage waveform. 1) DC input to the inverter is ripple free and chosen to be equal to 1.0 pu. 2) Inverter switching devices are ideal. 3) Load impedance (resistive in this case) is chosen as the base value and is equal to 1.0 pu. The characteristic curves were obtained by determining the inverter output switching instants [9]. Since the inverter output waveform is not strictly periodic, discrete Fourier transform (DFT) was used to obtain the harmonic content of the inverter output voltage.

C. Characteristic Curues of RWDM Inrserters The effect of changing the amplitude of the reference signal on the amplitude of the fundamental component of the inverter output voltage waveform is shown in Fig. 3(a). The figure shows that the relationship between the fundamental component of the inverter output waveform and

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the modulation index M A is linear and is described by the equation (9)

where Po, = peak value of the fundamental component of the inverter output voltage. Equation (9) is valid only in the linear region of the modulator characteristic. The equation shows that the value of the hysteresis bandwidth, AV,, does not affect the amplitude of the fundamental component of the modulator output (see also Fig. 3(b)). In UPS applications where voltage regulation capability is one of the system specifications, the inherent linear relationship between the fundamental component of the inverter output voltage and the amplitude of the reference signal at the modulator input provides a means whereby the output voltage of the UPS system can be regulated (within specified limits) independent of the dc supply voltage or load variations. The linear relationship makes the RWDM attractive for UPS applications because it avoids the use of complex circuitry that generally degrades the system reliability. Fig. 3(c) shows the effect of varying MA on the order of the dominant harmonic in the inverter output voltage. The figure shows a fairly weak relationship between the two variables. However, changes in the modulation index affect the amplitude of the dominant harmonic in the inverter output voltage. The figure also shows a significant correlation between the hysteresis bandwidth and the order of the dominant harmonic. To reduce the load filter size, it is desirable to shift the order of the dominant harmonic to higher values by using small values of AVn. However, this results in higher inverter switching frequency and hence higher losses. The effect of changing the slope of the carrier wave (integrator gain), S,,, on the order of the dominant harmonic in the inverter output voltage is depicted in Fig. 3(d). The figure shows that increasing the value of the slope of the carrier wave shifts the order of the dominant harmonic to higher values. However, higher values of the integrator gain has an adverse effect on the amplitude of the fundamental component of the modulator.

D. Experimental Verification and Computer Simulation A single-phase 60-Hz half-bridge inverter with resistive load is employed to obtain experimental waveforms to verify the modulator performance. Figs. 4 and 5 show the effect of changing the value of the hysteresis bandwidth A K on the frequency spectrum of the inverter output voltage. The figures show that changing AV, has negligible effect on the amplitude of the fundamental component (60 Hz) of the inverter output waveform. However, decreasing AV shifts the order of the dominant harmonic in the inverter output frequency spectrum to high values and vice versa. Figs. 4 and 6 show the effect of the slope of the carrier wave S,, on the amplitude of the fundamental component in the inverter output waveform. The


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