Space Vector Based Pulse Density Modulation Scheme for Two Level Voltage Source Inverter

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Vector quantized spread spectrum Pulse Density Modulation for four level inverters

Article · June 2011 DOI: 10.1109/ICIEA.2011.5975671

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Biji Jacob M.R. Baiju College of Engineering Trivandrum Kerala public Service Commission

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Biji Jacob, M.R. Baiju College of Engineering, Trivandrum, India biji @ece.cet.ac.in, [email protected]

Abstract—A Space Vector based Pulse Density Modulation The motivation for adopting the principle of Pulse Density scheme for spreading the spectra of Voltage Source Inverters is Modulation in the case of two level inverter is that all proposed in this paper. The proposed scheme employs first order switching converters can be considered as analog-to-digital Sigma-Delta Modulator. The principle of Vector Quantization is converters [10]–[12]. Switching converters output are discrete applied for quantizing the reference voltage Space Vector in the digital signal which is equivalent to the quantized analog Sigma Delta Modulator. For the spatial quantization, the inverter reference input. Sigma Delta Modulators are used in over voltage vector space is divided into seven Voronoi regions. In this sampling analog-to-digital converters to reduce quantization paper, a method is proposed to code these Voronoi regions using noise by spreading the spectra of the quantization noise [13]– instantaneous reference phase amplitudes without using lookup [14]. Of the different Pulse Density Modulation schemes, table. To avoid fractional arithmetic sixty degree coordinate Sigma-Delta Modulator is the minimum distortion scheme system is used. The proposed scheme automatically selects the apex vectors in the over-modulation condition and hence results [15]. Sigma-Delta Modulation with scalar quantizer has been in a smooth transition from linear to over-modulation region. In applied to two-level inverters for power control [15]–[20]. Pulse Density Modulation, the switching frequency varies Hexagonal quantizer can also be used in Sigma-Delta randomly, resulting in the spreading of harmonic spectra. The Modulator to control the Voltage Source Inverters [10]–[12], proposed scheme uses only instantaneous reference phase The concept of Vector Quantization is used instead of scalar amplitudes to obtain switching vectors without using lookup table quantization for efficient quantizing in digital communication and timer. The proposed scheme is implemented and tested with and data compression [22]. 11.5 kVA two-level inverter driving 2-HP three phase induction motor. Experimental results of proposed scheme are compared In the proposed scheme, Space Vector based Pulse Density with Space Vector PWM and Random Space Vector PWM. Modulation is used to generate switching signals for the two- level voltage source inverter. First order Sigma Delta Keywords- Pulse Density Modulation; Space Vector; Spread Modulator is used to obtain Pulse Density Modulation. The Spectrum; Three Level Inverter; Vector Quantization. principle of Vector Quantization is applied for quantizing reference space vector in the Sigma Delta Modulator. The scheme has been experimentally verified for 11.5kW, 415V I. INTRODUCTION two-level inverter topology driving 2-HP induction motor. The adjustable speed drives, based on Inverter fed Induction Motors have become popular which need efficient II. PRINCIPLES OF SIGMA-DELTA MODULATION AND control of both frequency and voltage. In Pulse Width Modulated (PWM) inverters, frequency and voltage control is VECTOR QUANTIZATION achieved by varying the duty ratio of inverter switches [1]-[3]. Sigma-Delta Modulators are widely used in over-sampling The PWM schemes with constant switching frequency will Analog-to-Digital Converters (ADC) to reduce quantization generate prominent harmonic clusters in the output of voltage noise. The principle of Vector Quantization utilized in image and current spectra [3]-[4]. The output frequency spectra of and audio compression for efficient quantization. This paper inverter will determine the electromagnetic interference emitted uses the principle of Sigma-Delta Modulation to control the by inverters and acoustic noise generated by electric machine inverters and the principle of Vector Quantization to realize the driven by the inverters [3]-[9]. In Random Pulse Width quantizer in Sigma-Delta Modulator. Basic principles of Modulation techniques, the switching frequency is varied Sigma-Delta Modulation and Vector Quantization are randomly to spread the voltage and current harmonics over a described in this section. wide frequency range without affecting the fundamental A. First Order Sigma-Delta Modulator frequency component [5]-[7]. The Switching frequency modulation techniques can be classified into three types: Block diagram of a first order sigma-delta modulator is periodic, randomized and chaotic [6]. Variable switching shown in Fig. 1 [15]. The modulator consists of a difference frequency PWM schemes require precise timing calculation node (delta), a discrete time integrator (sigma), a quantizer in with the help of high performance DSP processor for pulse forward path and a digital-to-analog converter (DAC) in the pattern generation. feedback path. To simplify the analysis, the quantizer is often linearised and modeled by a quantization noise source e[n], In this paper, a Pulse Density Modulation scheme, with added to the integrated error signal y[n], to produce the variable switching frequency similar to that used in the case of quantized output signal s[n] = y[n] + e[n]. analog-to-digital converters, is proposed for two level inverters.

978-1-4244-8756-1/11/$26.00 c 2011 IEEE 1227 The corresponding time domain version of the modulator output is s[n] = v[n-1] + e[n] – e[n-1]. That is the output of sigma delta modulator consists of input signal delayed by one sampling clock period v[n-1] and first order differentiation of quantization noise e[n] – e[n-1]. Therefore the input signal passes through the system unaffected and the quantization noise is high pass filtered by the differentiator thus increasing the signal-to-noise ratio (SNR) in the frequency band of interest.

B. Vector Quantization In the proposed scheme, principle of Vector Quantization is used to implement quantizer in the Sigma–Delta Modulator. The Vector Quantizer maps k-dimensional vectors in the vector k space R into a finite set of vectors Y = {yi: i = 1, 2, ..., N}. Each vector yi is called a code vector or a codeword, and the set of all the codewords is called a codebook. Associated Fig. 2. Proposed Vector Quantized Space Vector Pulse Density with each codeword, yi, is a nearest neighbour region called Modulator Voronoi region, and it is defined by: = { ∈ k − ≤ − ≠ } Vi x R :|| x yi || || x y j ||, for all j i Each codeword resides in its own Voronoi region. In space vector modulation schemes, the input reference space vector is realised by switching the discrete inverter voltage levels. The switching converter output are at discrete levels which are equivalent to the quantized analog reference input. The switching converters can be therefore considered as Analog to Digital Converters. Sigma-Delta Analog to Digital Converter is used to quantize the reference space vector in the present work. Difference between the reference space vector and modulator output vector generate an error space vector. The error space vector is random in nature with varying Fig. 3. Two level Space Vector diagram with 60° hexagonal amplitude and phase. The error space vector is a point in vector coordinates space region of 2-level inverter. In the present work, vector space region of 2-level inverter is divided into seven non- The instantaneous values of three phase reference voltages overlapping Voronoi regions with the eight 2-level inverter Va, Vb, Vc are resolved into sixty degree (m-n) coordinate switching vectors as its centroids. 2-level inverter switching system (Fig. 3) instead of Cartesian coordinate to reduce the vectors are assigned as codeword in each Voronoi region. The computational overhead [23]-[24] in the first block of proposed principle of Vector Quantization is used to quantize the Space Vector Pulse Density Modulation Scheme. reference space vector to generate switching vectors for two level voltage source inverters in the proposed scheme. The m-axis is placed along the A-phase axis of the induction motor. The resolved components Vm and Vn are III. THE PROPOSED SPACE VECTOR PULSE DENSITY obtained from instantaneous values of three phase control input V , V and V . MODULATION SCHEME a b c The scheme (Fig.2) consists of two Sigma-Delta A. Principle of the proposed scheme Modulators, one each for m and n components of the input Fig. 2 represents the proposed Space Vector Pulse Density reference space vector. Each sigma-delta modulator consists of Modulation Scheme. In the first block, the instantaneous values a difference node, a discrete time integrator, a quantizer in the of three phase reference voltages Va, Vb, Vc are converted into forward path and a digital-to-analog converter (DAC) in the reference voltage space vector Vref. The voltage space vector feedback path. The quantizer consists of two parts, m-n frame represents the combined effect of the three reference phase component to three phase reference voltage converter and voltages at a particular instant. Fig. 3 shows the voltage space Space Vector Quantizer. All these blocks are implemented vectors of a 2-level voltage source inverter. It has eight inverter using digital signal processing scheme. voltage vectors (V to V ) which divides two dimensional 0 7 The difference between reference space vector Vref and vector space into six sectors 1 to 6. analog estimate of quantizer output vector Sa is integrated to obtain error vector Ve in sigma-delta modulator. The error vector Ve is quantized to obtain switching vectors S. The m-n frame components of error vector Ve is converted back to three

1228 2011 6th IEEE Conference on Industrial Electronics and Applications phase signal using following relations for quantization in the which sampled error vector Ve exists is determined from the proposed Space Vector Quantizer. Principle of proposed Space instantaneous amplitude of the three-phase signals Va’, Vb’ Vector Quantizer is explained in detail in next subsection. and Vc’ corresponding to Ve. The algorithm to find out The output switching vector S is converted to its analog voronoi region and corresponding assigned code word is given equivalent value (Sa) in Į-ȕ frame components by digital to below. analog converter in the feedback path. The sector in which the sampled reference space vector is located is determined for If (Va’* Vb’ *Vc’ > 0 ) finding out the optimum switching sequence. Selection of And { if (Va’ > 0) Voronoi Region – A, Vector V1 – 100 optimum switching sequence is described in subsection C. The elseif (Vb’ > 0) Voronoi Region – C, Vector V3– 010 proposed scheme uses only instantaneous reference phase elseif (Vc’ > 0) Voronoi Region – E, Vector V5 – 001 } amplitudes to obtain switching vectors without using lookup Else If (Va’* Vb’ *Vc’ < 0 ) table and timer. And { if (Va’ < 0) Voronoi Region – D, Vector V4 – 011 elseif (Vb’< 0) Voronoi Region – F, Vector V6 – 101 B. Proposed Space Vector Quantizer elseif (Vc’ < 0) Voronoi Region – B, Vector V2 – 110 } The error vector Ve, obtained by integrating the difference between reference space vector Vref and analog estimate of The codeword (code vector) assigned to the seven voronoi quantizer output vector Sa, are random in nature with varying regions in the proposed Space Vector Quantizer corresponds to amplitude and phase. The error space vector can be mapped as the actual inverter voltage space vectors. The generations of a point in two dimensional vector space region of 2-level switching vectors to the inverter directly from the code vectors inverter. These instantaneous random error vectors can be using the instantaneous reference phase amplitudes without quantized by the principle of vector quantization. The vector using lookup table and timing calculations, results in faster space of two-level inverter is divided into seven Voronoi implementation in DSP. regions, named A to G as shown in Fig. 4. The Voronoi regions are selected with two-level inverter voltage vectors as their C. Selection of Optimized Switching Sequence centroids. The two-level inverter voltage vectors are therefore The proposed Space Vector Pulse Density Modulator has to taken as the codewords (Code Vector) of these Voronoi select output vector S that is adjacent to the reference space V regions. All the error vector e falling in a specific Voronoi vector Vref. If difference between reference space vector Vref region can be quantized to the corresponding codeword and quantizer output vector S is too large, error vector Ve may (inverter voltage vector). The eight codewords are coded using jump to a region which is not adjacent to the reference space 3 bits (000 to 111) which are the actual two-level inverter vector Vref, resulting in selection of code vector from that voltage vectors. region. The selected code vector could be a non-adjacent to the

For quantizing the error vector Ve, it is converted into three instantaneous reference space vector. This leads to direct phase signal (Va’, Vb’ and Vc’) at each sampling instant. If the polarity reversals in the inverter line to line voltages [17]. Such resultant Space Vector of Ve is less than 30% of DC link polarity reversals are undesirable because of increased over- voltage stresses they invoke at the load terminals. Since the voltage ( | Vref | < 0.3*VDC ), the voronoi region G and code word 000 is assigned. If the magnitude of error vector is selection of vectors from non-adjacent sectors is very low, greater than 30% of DC link voltage, voronoi region A to F in replacing such vectors by zero vectors will not affect modulator performance significantly [17]. To find out whether the error vector Ve lays near to the reference space vector Vref, the sector in which the original reference space vector Vref located is determined. The sector of the voltage reference space-vector is identified from the instantaneous amplitude of the three phase input reference signal. The combination of voronoi region of error vector Ve and the sector of voltage reference space-vector Vref is used to determine actual switching vector. To reduce the inverter switching losses, minimum switching sequence is done by assigning zero vectors appropriately. Selection of switching vectors V0 through V7 at any sampling instant is determined according to the optimum switching sequence determined by the combination of the reference space vector’s sector and the integrated error vector’s voronoi region. For example, consider the case reference space vector Vref is located in sector 1, and then the nearest inverter voltage vectors are V1, V2 or V0. If the error vector Ve is located in the Voronoi regions A or F, then switching vector V1 is assigned. On the other hand, if the integrated error vector Fig. 4 The Voronoi regions A to G corresponding to the Vector Quantization Ve is located in the Voronoi regions B or C, then switching regions of 3ĭ input control signal. vector V2 is assigned.

2011 6th IEEE Conference on Industrial Electronics and Applications 1229 Whenever the reference space vector crosses a voronoi proposed scheme is Pulse Density Modulated wave where region, the error vector Ve may be too large. If the error vector density of the pulses are changed resulting in switching Ve is too large, it may be located in voronoi regions D or E, frequency variation. In SVPWM pole voltage switches at even if the reference space vector Vref is in sector 1. Under constant frequency and pulse width is varied according to the these conditions zero switching vectors (V0 or V7) is assigned control signal Fig. 6(b). In Random PWM switching frequency to avoid polarity reversal in the inverter line to line voltages. is varied randomly with duty ratio proportional to the control Selection of zero switching vectors V0 [000] or V7 [111] signal Fig 6(c). depends on the previous switching vector to minimize the The pulse density property of the proposed scheme is inverter switching losses. If the error vector Ve was in voronoi region A or C (corresponding to switching vectors 100 or 010) further illustrated with the time scale expanded three pole in the previous sampling instant, then the zero switching voltage waveforms given in Fig. 7(a). Upper three traces in Fig. vector V0 [000] is assigned. On the other hand if the error 7(a) are the three pole voltages (VAO, VBO , VCO) for the proposed scheme with modulation index m= 0.8. Time scale vector Ve was in voronoi region B or F (corresponding to switching vectors 110 or 101) in the previous sampling instant, expanded waveforms of the marked area in the upper three then the zero switching vector V7 [111] is assigned. There by traces are shown in lower three traces obtained using DPO3000 series oscilloscope. It can be seen from Fig. 7(a) that the width ensuring the switching of one inverter leg only. Similarly all the cases switching vectors are selected. of each pulse is equal to sampling time but the density of pulses are varied according to the V/f control scheme. This will change the effective width of pulses and resulting in the IV. EXPERIMENTAL VERIFICATION OF THE PROPOSED variation of switching frequency. The time scale expanded SCHEME three pole voltage waveforms of Random SVPWM is given in The proposed scheme for two-level inverters is Fig. 7(b). The switching frequency is varied randomly with implemented for 11.5 kVA two-level inverter driving a 2 HP width of pulses in Random SVPWM is varied in wide range three phase induction motor using the dSPACE DS 1104 RTI resulting in minimum pulse width problem. platform (Fig. 5). Results are taken with V/f control for The switching frequency in the proposed scheme is not different modulation indices covering different speed ranges constant but varies randomly as seen from Fig. 6 (a) and 7(a), including over modulation conditions. The results of proposed since it is Pulse Density Modulation strategy. Variable scheme are compared with SVPWM and random PWM switching frequency results in spreading of the harmonic schemes under identical conditions. spectrum. In Fig.8 the voltage spectra of A-phase Pole voltage The Induction motor Pole voltages (VAO) and Phase (VAO) for the three schemes are compared for modulation index voltages (VAN) of the proposed scheme, SVPWM and 0.8 obtained experimentally using DSO. Fig.8(a) shows pole Random PWM for modulation index 0.8 are shown in Fig. 6(a), voltage spectra of the proposed scheme at average switching (b) and (c) as upper and lower traces respectively. From pole frequency 5 KHz. The spectra of the proposed scheme do not voltage (VAO) waveform of the proposed scheme in Fig. 6(a), have any prominent harmonic spikes. Due to the inherent it can be noted that the pole voltage remains positive VDC property of over-sampled Sigma Delta Modulator, low during positive peak and zero during the negative peak of the frequency switching noises are spread over a wide bandwidth fundamental sinusoidal signal. The value of the pole voltage [8] in the proposed scheme. The switching frequency used in varies rapidly between VDC and zero with approximately zero the SVPWM scheme is 2.5 KHz, hence prominent switching mean during the zero crossover of the fundamental sinusoidal noise are present at 2.5 KHz and its harmonics as shown in signal. The average in each sampling period of the pole voltage Fig.8(b). In Random SVPWM scheme with average switching tracks the analog control input. The Pole voltage of the frequency 2.5 KHz, low order harmonics are significant as seen from Fig.8(c). The switching frequency harmonics are 20 to 15 dB less in the proposed scheme in the audible frequency range compared to SVPWM and Random SVPWM. Hence tonal acoustic noise emitted from ac motors operating with a carrier frequency in the audible range can be substantially reduced in an inexpensive manner by using the proposed scheme. Fig. 9 show the comparison of Total Harmonic Distortion characteristics of the Proposed scheme, SVPWM and Random PWM schemes with different modulation indices for the Pole Voltage evaluated experimentally. It shows Total Harmonic Distortion of the Proposed scheme is much less than SVPWM scheme and comparable with the Random PWM scheme for all modulation indices.

Fig. 5. Three-phase Two-level Voltage Source Inverter with Induction Motor.

1230 2011 6th IEEE Conference on Industrial Electronics and Applications Fig.6(a). Upper trace: Pole Voltage (VAO) and Fig.6(b). Upper trace: Pole Voltage (VAO) and Fig.6(c) Upper trace: Pole Voltage (VAO) and Lower trace: Phase voltage (VAN) for the proposed Lower trace: Phase voltage (VAN) for the SVPWM Lower trace: Phase voltage (VAN) for the Random scheme with modulation index m=0.8. . scheme with modulation index m=0.8. . SVPWM scheme with modulation index m=0.8. Scale : X-axis: 5ms/div; Y-axis : 50 V/div Scale : X-axis: 10ms/div; Y-axis : 50 V/div Scale : X-axis: 10ms/div; Y-axis : 50 V/div

Fig.7(a). Experimental waveforms of three pole voltages (VAO, VBO, VCO ) for Fig.7(b). Experimental waveforms of three pole voltages (VAO, VBO, VCO ) for the proposed scheme with modulation index m= 0.8. Time scale expanded the Random SVPWM scheme with modulation index m= 0.8. Time scale waveform of three pole voltages of marked area in the top waveform is given expanded waveform of three pole voltages of marked area in the top in the bottom traces. X-axis: 1ms/div; Y-axis : 50 V/div waveform is given in the bottom traces. X-axis: 1ms/div; Y-axis : 50 V/div

Proposed scheme m=0.8 SVPWM scheme m=0.8 RPWM scheme m=0.8

0 0 0

Fig.8(a). Experimental Pole voltage (VAO) spectrum Fig.8(b). Experimental Pole voltage (VAO) spectrum Fig.8(c). Experimental Pole voltage (VAO) for the proposed scheme with modulation index for the SVPWM with modulation index m=0.8. spectrum for the RPWM with modulation index m=0.8. Scale : Y-axis : -40 ~ 40 dB, 10 dB/div; X- Scale : Y-axis : -40 ~ 40 dB, 10 dB/div; X-axis : 0 m=0.8. Scale : Y-axis : -40 ~ 40 dB, 10 axis : 0 ~ 50 KHz, 5 KHz/div ~ 50 KHz, 5 KHz/div dB/div; X-axis : 0 ~ 50 KHz, 5 KHz/div

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