Dynamic adaptive space vector PWM for four switch three phase inverter fed induction motor with compensation of DC link voltage ripple

PEDS2009 Dynamic Adaptive Space Vector PWM for Four Switch Three Phase Inverter Fed Induction Motor with Compensation of DC – Link Voltage Ripple Hong Hee Lee Phan Quoc Dzung Le Dinh Khoa Le Minh Phuong NARC, Ulsan University, Korea hhlee@mail.ulsan.ac.kr Faculty of Electrical & Electronic Engineering HCMC University of Technology Ho Chi Minh City, Vietnam pqdung@hcmut.edu.vn Faculty of Electrical & Electronic Engineering HCMC University of Technology Ho Chi Minh City, Vietnam khoaledinh@hcmut.edu.vn Faculty of Electrical & Electronic Engineering HCMC University of Technology Ho Chi Minh City, Vietnam lmphuong@hcmut.edu.vn Abstract- This paper presents and analyses a new dynamic adaptive space vector PWM algorithm for four- switch three-phase inverters (FSTPI) fed induction motor under DC-link voltage ripple By using reasonable mathematical transform, Space Vector PWM technique for FSTPI under DC-link voltage imbalance or ripples has been proposed, which is based on the establishment of basic space vectors and modulation technique in similarity with sixswitch three-phase inverters This approach has a very important sense to solve hard problems for FSTPI under DC-link voltage imbalance, for example ensuring the required voltage for under modulation mode and over modulation mode and 2, extended to six-step mode The compensated technique also allows reduce the size of DC-link capacitors and the cost of the inverter Matlab/Simulink is used for the simulation of the proposed SVPWM algorithm under DC-link voltage ripple This SVPWM approach is also validated experimentally using DSP TMS320LF2407a in FSTPI-IM system The effectiveness of this adaptive SVPWM method and the output quality of the inverter are verified another our work [10], the adaptive SVPWM had been used for FSTIP under DC-link voltage ripple but in that proposed method, to simulate non-zero vectors in SSTPI we use the G G effective vectors V1' V 6' which lengths are equal the length of the G G shortest vector from V1 , V3 (Fig.4, 5) The content of this paper is aimed at presenting a dynamic adaptive SVPWM, that permit increase the maximum of fundamental of output voltage greater than one that be proposed in our work [10] and another paper [4,7], for FSTPI under DC – link voltage ripple This issue has not been approached in the above mentioned papers Keywords: Space vector Pulse-Width-Modulation, undermodulation, overmodulation, Four Switch Three Phase Inverter, Six Switch Three Phase Inverter, DC-link ripple I INTRODUCTION Nowadays, a few research efforts have been directed to develop power converters with reduced losses and cost for driving induction motors Hence, a reduced number of inverter switches is a promising solution Among them the four switch three phase inverter (FSTPI) (Fig.1) was introduced with four IGBT switches instead of standard six switches in a typical three-phase inverter (SSTPI) [1-3,8] Due to the circuit configuration, the maximum obtained peak value of the line to line voltage equal Vdc/2 so the voltage Vdc is about 600V In order to get a high dc-link voltage, in this paper authors use the single-phase diode rectifier and high dc-link voltage Fig.1 [7].The main drawback of FSTPI is the voltage ripple of DClink capacitors To ensure the quality of the output voltages of VSI, we must solve the mentioned above problem by using realtime compensation SVPWM technique when generating switching control signal in consideration of unbalanced DC-link voltages by direct calculation of switching times based on four basic space vectors in FSTPI In our work [9], the link between SVPWM for FSTPI and SSTPI have been done by using the principle of similarity and revealing complete solution for the PWM in the whole modulation index in case two DC-link voltages balanced In 399 Fig Circuit configuration of the FSTPI fed induction motors II ANALYSIS OF SPACE VOLTAGE VECTORS AND STATOR FLUX IN CASE OF DC LINK VOLTAGE RIPPLE According to the scheme in Fig.2 the switching status is represented by binary variables S1 to S4, which are set to “1” when the switch is closed and “0” when open In addition the switches in one inverter branch are controlled complementary (one switch on, another switch off), therefore: S1+S4 = (1) S3+S2 = Phase to common point voltage depends on the turning off signal for the switch: Va = 0; Vb = S1V1 + (S1 − 1) ⋅ V2 ; Vc = S3V2 + (S3 − 1) ⋅ V1; (2) V V (3) V1 = dc − ε Vdc ; V2 = dc + ε Vdc 2 Where V1, V2 voltage across the dc-link capacitors; V1+V2=Vdc 1 V ε = − the imbalance factor ; − ≤ ε ≤ 6 Vdc Combinations of switching S1-S4 result in general space G G vectors V1 → V4 (Table 1) Voltage imbalance in the DC link causes the space vector G G G G origin to shift along the V1 / V3 axis (Fig.3), with V1 and V3 no longer being equal in magnitude, as described in Table G In order to form the required voltage space vector Vref , we can use or vectors in one sampling interval Ts For three phase induction motors the stator flux linkage vector can be represented as follows [2, 4, 6, 9] : G G (4) Ψ = V (t )dt ∫ In case the motor is fed from a FSTPI inverter the flux linkage vector is: G G G (5) Ψ = t n ⋅ Vn + Ψ0 where n = ; tn : duration of Vn If the switching algorithms can ensure the best approximation by G G minimizing the discrepancy between vector loci Ψ and Ψ * , the stator voltage performance will be optimized This approach is used successfully for FSTPI in case of the balance in DC link voltage [9] S3 1 1 Vβ 2V2 V2 − V1 2V1 − V2 − V1 G V1 V1 + V2 G V2 − G V3 V1 + V2 G V4 G G G G G G G G G G V1' = a V1 ; V 2' = b V1 + V + c V ; V 3' = d V1 + V + e V 2 G G G G G G G G G G V 4' = f V ; V 5' = g V1 + h V + V ; V 6' = l V1 + m V + V1 2 G V2 G V3' G V4' − 2V1G/ V3 G V2' G V1' (V2 − V1 ) / O G V5' O 2V2 / G V1 ' G V6' G − (V1 + V2 ) / V4 Fig Voltage space vectors in the plan αβ Fig If PWM output voltages are synthesized without considering the non-ideal DC link conditions then unbalanced stator voltages will result, which causes large current variations and the deviation of real flux-linkage vector [4, 7] 400 (6) where the coefficients a,b,c,d,e are defined as follows: G G Case 1: DC-link voltage V1 < V2 ( V1 > V3 ) (Fig.3) a = G V Vα SVPWM method proposed in this paper is based on the principle of similarity of the one for SSTPI inverters, where plan αβ is divided into sectors (sector I…VI) and the formation of Vref is done similarly as for SSTPI in conditions of DC-link voltage ripples This facilitates the calculation of switching states for FSTPI and some developed modulation methods for SSTPI can be easily applied to FSTPI modulation method thanks to this proposed approach To simulate non-zero vectors in SSTPI, in this proposed G G method, we use the effective vectors V1' V6' , when the length of G G V1 + V3 the basic generated vector is equal ( ) (Fig.4, 5) Furthermore, when V1=V2, the same equations as in the case of balanced DC-link voltages are achieved [9] These modified vectors are formed as follows: V1 + V V − V1 ;b = l = ;c = m = ; d = g = 0; 2V 2 (2 V ) V2 V + V2 e = h = ; f = 2V1 2V1 TABLE COMBINATIONS OF SWITCHINGS AND VOLTAGE SPACE VECTORS S1 PEDS2009 III NEW DYNAMIC ADAPTIVE SVPWM APPROACH FOR FSTPI WITH COMPENSATION DC-LINK VOLTAGE RIPPLE CONDITION SVPWM proposed method for FSTPI in case of V1 < V2 (7) PEDS2009 G V2 β Vm _ max = (V1 + V2 ) / 3 (12) ⋅ (V1 + V2 ) TABLE VECTOR DURATIONS IN THE PROPOSED SVPWM METHOD G V3' G V4' − 2V1 / G V3 G V2' Vref (V2 − V1 ) / O' G V5' O Sector I T t x = tv ' = M s sin( π / − α ); π Ts t y = tv ' = M sin( α ) π t z = Ts / − t x − t y G V1' 2GV2 / V1 α G V6' G V4 [ ] a t x (1 − a ) + t y (1 − b − c − 0.5) + t z ; a+ f f t3 = t1 a t1 = tv1 = at x + bt y + t1; tv2 = 0.5t y ; tv3 = ct y + t3 − (V1 + V2 ) / Sector II [ SVPWM proposed method for FSTPI in case of V1 > V2 Fig G G Case 2: DC-link voltage V1 > V2 ( V1 < V3 ) (Fig.4) tv = bt x + dt y + t1; V + V2 V V − V2 a = ; ; b = l = ; c = m = 0; d = g = (2V ) 2V 2V V + V2 e= h= ; f = 2V1 tv = 0.5(t x + t y ); tv = ct x + et y + t3 (8) Sector III G To simulate zero vectors of SSTPI, we use the effective V0' : G G G (9) V0' ⋅ t z = V1 ⋅ t1 + V3 ⋅ t3 Where t1 and t3 are calculated by equations: ⎧ ft1 − at3 = 0; ⎨ ⎩t1 + t3 = t z (10) ty = 3 π tv1 = dt x + t1; MTs sin (π / − α ); MTs sin (α ); ] tv = et x + ft y + t3 A Under modulation (0 < M < Mmax_under) In this zone the required voltage space vector rotates in a hexagon The space vector modulation in this zone is based on the formation of three voltage vectors in sequence in one sampling interval Ts so that the average output voltage meets the requirement The calculations of the switching states in SSTPI and FSTPI are as follows for ½ Ts: [5] π [ a t1 = t x (1 − e − d − 0.5) + t y (1 − f ) + t z ; a+ f f t3 = t1 a tv2 = 0.5t x ; The basic vectors in each sector used to form the required space vector Vref is presented in Table tx = ] a t1 = t x (1 − b − c − 0.5) + t y (1 − e − d − 0.5) + t z ; a+ f f t3 = t1 a Sector IV [ ] a t x (1 − f ) + t y (1 − g − h − 0.5) + t z ; a+ f f t3 = t1 a t1 = tv1 = gt y + t1; tv = ft x + ht y + t3; tv = 0.5t y Sector V [ ] a t1 = t x (1 − g − h − 0.5) + t y (1 − l − m − 0.5) + t z ; a+ f f t3 = t1 a tv1 = gt x + lt y + t1; (11) tv = ht x + mt y + t3; tv4 = 0.5(t x + t y ) t z = Ts / − t x − t y where: tx - duration for vector Vx; ty - duration for vector Vy tz - duration for vector Vz; M – modulation index M = V*/V1sw (V* - amplitude of the required voltage vector, V1sw – peak value of six step voltage for balanced DC-link voltages ) The calculation results for the six sectors are shown in Table The pulse patterns for switching are presented in Fig.6 The proposed method ensures that these switching times are dynamically adjusted for each period Ts to compensate for the DC-link ripple The maximum obtainable output phase voltage Vm_max is defined as follows: 401 Sector VI [ ] a t x (1 − l − m − 0.5) + t y (1 − a ) + t z ; a+ f f t3 = t1 a t1 = tv = lt x + at y + t1; tv = mt x + t3; tv4 = 0.5t x For sector I, II, III For sector IV, V, VI PEDS2009 t x − t x1 t x = t x1 + ⋅ ( m − M max_ over1 ); M max_ over − M max_ over1 Similar to calculate ty,tz in this zone IV SIMULATION OF THE PROPOSED SVPWM UNDER DC-LINK VOLTAGE IMBALANCE OR RIPPLE Fig Pulse patterns for switching in the proposed method B Overmodulation in mode (Mmax_under ≤ M ≤ Mmax_over1) Similarly as for SSTPI, this mode starts when the required Vref goes beyond the circle inscribing the hexagon and reached its sides When sliding on the hexagon side (M=Mmax-over1) tz = 0: cos α − sin α Ts tx = ⋅ ; cos α + sin α (13) T t y = s − tx ; tz = As for the undermodulation effective vectors tX,Y and effective-zero vectors tz are formed from the two basic vectors When M = Mmax-under, values tx, ty, tz are defined as (11) In case of Mmax-under