Space ector (PWM) Digital Control and Sine (PWM) Pulse Width Modulation modelling, simulations Techniques & Analysis by MATLAB and PSIM (Powersys) Tariq MASOOD.CH Dr. Abdel-Aty Edris Prof. Dr. RK Aggarwal Qatar Petroleum (Manager Power Delivery R & D) University of Bath Dukhan Qatar EPRI USA Bath _ UK Prof. Dr. Suhail A. Qureshi Prof. Dr. Abdul Jabber Khan Yacob Y. Al-Mulla University of Engineering & Technology Rachna College of Engineering &Technology IEEE Chair Lahore Pakistan Gujranwala Pakistan Doha Qatar Author contact Details: Email: maaat 00@ ieee.org Ph:: 00974 560 75 7;; P.O Box 000 5 Dukhan Qatar Abstract --- previous work conducted in the STATCOM/SC (FACTS Devices) control domain with degree of precision and how to lead & Lag compensator will be implemented as control passageway to address power quality issues too. In this paper we have emphasized methodically the relationship between sinusoidal Pulse width modulation and Space vector modulations. The relationship involved the fundamental perception to create holistic approach for the new pacesetters for today. All the relationship provided Bidirectional Bridge for the transformations between carriers based frequency and space vector pulse width modulations. It is also reflected all the drawn conclusions are independent load type. Therefore both methods have been discussed along with their viability in power system control. Introduction:- For long period carried-based PWM methods [] were widely used in the most applications. The PWM modulation has been studied extensively in the last decade. Hence, the main objective of PWM over here to achieve following objective considerably. wide linear modulation range. less switching loss. less total harmonic distortion in the spectrum of switching waveform 4. and easy implementation and less computational calculations With the emerging technology in microprocessor the S PWM has been playing pivotal and viable role in power conversion. It is using space vector concept to calculate the duty cycle of the switches which is imperative implementation of digital control theory of PWM modulators. The comprehend relationship in between S PWM and Sine PWM render a platform not only to transform from one to another but also to develop different performance PWM modulators. However, many attempts have been made to unite the two types of PWM methods [4],[5]. Furthermore, the S pulse width modulation technique has been used in [6],[7].. Characteristics of Six-step voltages source inverter. Purpose of Pulse width modulation. oltage source inverter (SI) and its operation stages with respective digital phenomenon stagewise 4. Switching characteristics 5. Modelling of space vector with MathCAD 6. Determine the switching time of each transistor at each operation sector ( S to S6) 7. Switching Time table at Each Sector ******************. Characteristics of Six-step voltages source inverter This is called the six-step inverter, because it comprises with six "steps" in the line to neutral (phase) voltage waveform. Harmonics of order three and multiples of three are absent from the line to line and the line to neutral voltages and consequently, absent form the current Output amplitude in a three-phase inverter can be controlled by only change of DC-link voltages (). Purpose of Pulse width modulation The major contribution of the PWM in power system conversion/delivery as bulleted below:- Control of inverter output voltages And reduction of Harmonic components
sequence as shown below in the matrix. Figure : Pulse width modulation waveform Figure : waveforms of gating signals switching sequence, line to negative voltages for six-step voltage source inverter Figure A: Pulse width modulations SI inverter out put voltage when control > tri A0 dc/ when control < tri A0 - dc/ Control of inverter output voltages PWM frequency is the same as the frequency of tri Amplitude is controlled by the peak value of control. Fundamental frequency is controlled by the frequency of control. What is modulation index (M). dc.( ) control peak of A0 m ------------- () tri Where, ( A0 ) : Fundamental frequency component of A0 underlying issues of PWM implementations o Increase in power loss due to high switching operation PWM frequency. o Reduction of Available voltages o EMI problems due to high-order harmonics. oltage source inverter (SI) and its operation stages with respective digital phenomenon stagewise B. Space vector PWM Switching Sequence Three phase two level PWM inverter as shown in figure : the switch function is defined by where I a, b,c, denotes E/ at the inverter output (a, b c) with reference to point N 0 denotes E/ and N is the neutral point of the bus [9]. SWi, the upper switch SWi+ is on and bottom switch SWi- is off. SWi 0, the upper switch SWi+ is off and bottom switch SWi- is on. S, S, S5 are opened the binary equation [--] and the bottom switches will be remained closed. S4, S6, S switches are opened the binary equation will be [000] and to upper switches will be remained closed. Both conditions the voltages will be zero 0 7 0 These switches are in operation with following stages Figure : Three-phase voltage source inverter A. Gating signals, switching sequence and line to negative voltage. Six-step (SI) operation
Stage # Output three phase voltages Stage # Stage # PWM frequency signal and control voltage signal Stage # 4 IGBT discontinuous mode of operation and output voltages after conversion Stage # 5 Stage # 6 Output voltages IGBT without compensations
Six inverter voltages vectors for six step voltages source inverter operation sequence as Tabulated below. oltage Switches Binary sequence sequence 5-6- -0-6-- -0-0 -- --0 4 --4 0--0 5-4-5 0-- 6 4-5-6 0-0- Table ; switching operation sequence with respective switches state (NO/NC) Normal open/normal close ab bc ca an bn π msinωt + 6 bn cn msinωt + cn an msinωt + 5π 6 π ----------------------- (5) ---------------------- (6) --------------------- (7) C. Carrier Based pulse Width modulations The universal representation of modulation signals are vi ( ( i a, b, c) For three phases PWM carrier will be as mentioned: vi ( ui( + ei( Where ei( is the injected harmonics and ui( is the fundamental signals. These are three-phase symmetrical sinusoidal signals. ua() t msinωt ---------------------------- () π ub() t msinωt + 4π uc() t msinωt + --------- --- --- () ---------- (4) Line-to-Line voltages ( ab, bc, ca) and line to neutral voltages (an, bn, cn) -line to line voltages Sine PWM output line-to-line voltages -Amplitude of line to line voltages (an, bn, cn) --Fundamental frequency component is (ab) 4 ( ab ) ( rms) π ------------------------------ (8) 6 0.78 π --Harmonics Frequency components (ab)h :: amplitudes of harmonics decrease inversely proportional to their harmonics order 0. 78 ( ab ) h ( rms) -------------------------------- (9) h Where h 6n+ and (n,, ) -Phase-voltages an () t [ msin ωt+ ei() t ]---------------------- (0) π bn () t msin ωt ei() t + + --------- () 4π cn () t msin ωt ei() t + + --------- ()
Line to neutral phase voltages after conversion Where ei( is injected harmonics and "m" is the modulation index an an bn cn ------------ () bn an + bn cn ------------- (4) cn an bn + cn ------------ (5) in the linear modulation range the output line-to-line voltages are equal or less then the dc-bus voltage. However the possible modulation index m max in the linear range, and we have umin ( ei( umax ( Where u min min( ua(, ub(, uc( ) and u max max( ua(, ub(, uc( ) it is clear that the ei( harmonics did not appear in the line-to line voltages. Therefore ei( is usually called the zero sequence signal. Hence it can be calculated. ei ( ( ua( + ub( + uc( ) ------- (6) ei( 0 yields sinusoidal PWM. In the linear range from the equation (4), (5) ui < we have m max and the maximum line to line voltages are when the m > the over modulation will occur. ei ( 0 Non-sinusoidal PWM occurs, when ei( is the suitable such as ei( m/6sin(w all the tops of ui( cut by ei(. m max, and maximum line to line voltages reach in linear range. Therefore the different ei( leads to different carrier pulse width modulators for three phase converters. 4. Switching characteristics:- PWM scheme can be divided in two operation modes. [],[] Continues pulse width modulation for the u ( < ei( < u ( ( m ) min max therefore each carrier signal period, each output of the converters legs are switching between the positive or negative rail of the DC-link. Discontinues pulse width modulations for the discontinues width modulation scheme, in the linear modulation range, the zero-sequence component ei( u ei( u max (... or ( min in each carrier cycle, one modulation signal will be equal to +- and the corresponding leg tied to positive or negative trail of the Dc-link with out switching action. Thus from average compare with continues PWM schemes to discontinues schemes can reduce the average switching frequency by % and cause less switching loss. Pulse width modulation methods and degree of freedom The way of assignment of the voltage vector to converters has the degree of freedom. Utilizing of property makes it possible to realize flexible controls [8]. a. Basic switching vectors & Sectors b. 6 active vector Axes of a hexagonal DC link voltage is supplied to the load Each sector ( to 6): 60 degree c. Two zero vector (0, 7) at origin No voltage is supplied to the load (7, ) (0, 000) Figure ; Basic switching vectors and sectors Comparison between sine wave PWM and space vector pulse width modulation.
Space vector PWM Sine waver PWM Generates less harmonics distortions Generates high harmonics distortions Provides more efficient use supply of voltages Provides Less efficient use supply of voltage Locus of reference vector is the inside of a circle with Locus of reference vector is the inside of a circle with radius of radius of oltage utilization: space vector PWM time sine wave 5. Modelling of space vector with MathCAD d. Step # determination of d, q, ref and angle (a) e. Step # determination of time duration T, T, T0 f. Step # determination of switching time of each transistor (S to S6) A. Step # Coordinates d-q Power transformation in the principle ways :abc to dq values refer to figure q : 0 + bn cos ( 0) cn cos ( 0) q 0 q : an + bn q 0 α atan q : α 0. d q d q : d 0 0 65.58 ref : d + ref 65.58 q cn an bn cn Figure : space vector calculation Figure : voltage space vector and its components in (d,q) d, q, ref Line_oltage : 400 an bn cn 0 d : an bn cos ( 60) cn cos ( 60) d 668. d an : bn cn d 0 Figure 4: space vector Locations
( π α ) sin T Tz α sin( π ) sin( π α ) T Tz α sin( π ) T 0 Tz ( T+ T ) ------------------ () ------------------- () Figure 5: Time Duration Calculations T z : 57 0.996 56.77 50 sin π α ref a : a 0.996 T : T z a 400 sin π ( ) sin α T 0.05 T : T z a T 7.487 0 ( ) sin π T 0 : T z T + T T 0.577 0 b. Switching time duration at any sector [T,T,T0] Figure 6: Time Duration Calculations T 0 B. Step # Determination of Time duration [T,T,T0] a. Switching time duration at sector # ref T 0 dt + T+ T T dt + Tz 0dt -------- (7) T+ T Tz ref ( T + T ) ------------ (8) ref Tz... and... α Where, fs ---------- (9) And 'fs' is the fundamental frequency cos( α) Tz ref sin( α) cos( π ) + T T vdc 0 sin( π ) ----- (0) where,0 α 60 Tz ref π n T sin α + π Tz ref π sin π α Tz ref π n sin π cos α cos π sin α T Tz ref n sinα + π Tz ref n n cosα sin π + sinα cos T0 Tz T T Where " n " through 6 (that is, sector to 6) 0 α 60
6. Determine the switching time of each transistor at each operation sector ( S to S6) Figure 0; S PWM switching patterns at sector # 4 Figure 7; S PWM switching patterns at sector # Figure ; S PWM switching patterns at sector # 5 Figure 8; S PWM switching patterns at sector # Figure ; S PWM switching patterns at sector # 6 Figure 9; S PWM switching patterns at sector # 7. Switching Time table at Each Sector Sector Upper switches Lower switches (S4, S6, S)
4 5 6 (S, S, S5) S T+T+T0/ ST+T0/ S5T0/ S T+T0/ ST+T+T0/ S5T0/ S T0/ ST+T+T0/ S5T+T0/ S T0/ ST+T0/ S5T+T+T0/ S T+T0/ ST0/ S5T+T+T0/ S T+T+T0/ ST0/ S5T+T0/ S4 T0/ S6T+T0/ ST+T+T0/ S4 T+T0/ S6T0/ ST+T+T0/ S4 T+T+T0/ S6T0/ ST+T0/ S4 T+T+T0/ S6T+T0/ ST0/ S4 T+T0/ S6T+T+T0/ ST0/ S4 T0/ S6T+T+T0/ ST+T0/ conf. Rec IEEE-IAS Annual Meeting seattle, 99 pp. 00-009. [8]. Tatshito Nakajima, Hirokazu Suzuki. Multiples Space vector control for self commuted power converters. IEEE Trans. On power delivery, vol., No. 4, October 998. [9]. Keliang Zhou and Danwei Wang Relationship between space-vector modulation and three-phase carrier-based PWM: a comprehensive analysis. IEEE Trans. On Industrial Electronics vol. 49, no., February 00. Acknowledgement:- I do appreciate for the powersys - France Management and technical team for their technical support and assistance to accomplish this project. powersys France has render full support with their software PSIM 7.0 latest version for the period of two years to analyse the viability of PSIM in digital control system. References:- []. T.M.Rowan, R.J.Kerman and T.A.Lipo, 'operation of naturally sampled current regulators in transition modes', IEEE Trans. Ind. Applicat., vol., pp. 586-596, July/Aug. 987. [].. Kaura and Blasko, "New method to extend linearity of sinusoidal PWM in the over modulation region," IEEE Trans. Ind. Applicat., vol., pp. 5-, sept/oct. 996. []. S.R Bowes, "New sinusoidal pulse width modulated inverter," proc. Inst. Elect. Eng. ol., pp. 79-85, 975. [4] J. W. kolar, H. Ertl and F.C Zuch Minimizing the current harmonics rms value of three-phase PWM converter system by optimal and suboptimal transition between continues and discontinuous modulation, in proc IEEE PESC 9, June 99, pp.7-8. [5]. D. Jenni and F. Wueest, Minimization parameters of space vector modulations, in proc. 5 th European conference power electronics and applications, 99, pp.76-8. [6]..Blasko, analysis of Hybrid PWM based spacevector and triangle-comparison methods, IEEE Trans. Ind. Applicat, vol., pp 756-764, may/june 997. [7]. D.G.Holmes the general relationship between regular-sampled pulse-width modulation and space vector modulation for hard switched converters in