See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/252025894 Vector quantized spread spectrum Pulse Density Modulation for four level inverters Article · June 2011 DOI: 10.1109/ICIEA.2011.5975671 CITATIONS READS 8 127 2 authors: Biji Jacob M.R. Baiju College of Engineering Trivandrum Kerala public Service Commission 18 PUBLICATIONS 199 CITATIONS 111 PUBLICATIONS 2,090 CITATIONS SEE PROFILE SEE PROFILE Some of the authors of this publication are also working on these related projects: three dimensional svpwm and svpwm for DTC View project All content following this page was uploaded by M.R. Baiju on 31 July 2014. The user has requested enhancement of the downloaded file. Space Vector based Pulse Density Modulation Scheme for Two Level Voltage Source Inverter 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.