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  Pspice Analysis of Parallel Operation of Two IGBT Inverters Miroslav Lazić, Boris Šaši ć , Dragana Petrovi ć  and Dragan Staji ć    Abstract  — Two full-bridge inverters are connected in  parallel in order to increase power of a programmable AC source. Lossless current sharing by adding balancing inductors was investigated. Effects of IGBT parameter tolerances and temperature variations were analysed through ORCAD 9.2 PSPICE (including Monte Carlo analysis). It was found that manufacturing tolerances of balancing inductors have greater effect on the current sharing than IGBT parameter variations. Adding the inductors in series with both power rails, positive and negative, of the bridges reduces required inductance and improves current sharing. Results of the analysis will be used to  build an experimental circuit. Keywords  — Programmable AC Source, Current Sharing, Inverter Bridge. I.   I  NTRODUCTION   Current Sharing Analysis of Parallel operation of two H-Bridges in ADC Accessory are represented in this  paper. Main goal of this analysis was to improved manufacturing efficiency by increasing power of the  power electronics equipment (used in the magnetron sputtering applications for thin film deposition of semiconducting materials). II.   R  EQUIREMENTS   The existing system consists of a standard high power DC source followed by a full bridge inverter  .  The inverter is capable of generating unipolar and bipolar pulses of various frequencies and duty cycles. An example of unipolar and bipolar outputs is shown in Fig. 1. Fig. 1. Examples of output waveforms Output power can exceed 10kW, with very wide,  process dictated, ranges of output voltage and current – up to 1700V and 300A. Frequencies of interest are in a very wide range of 50Hz to 25kHz. A dedicated digital circuit is used to control the output in response to the system requirements. In order to increase power, while avoiding major redesign and introducing risk to the established manufacturing process, it was decided to parallel two inverter stages. Requirement for current sharing was determined to be within 15%, not a very strict requirement. Due to the complexities of digital control and utilized digital feedback loop compensation, standard current sharing schemes were not deemed practical, due to the implications on project timing and risk assessment. It was decided that a simpler approach is analyzed – a  possibility of driving both inverters with identical drive signals and adding series inductors in line with the two  paralleled inverters. Sensitivity analysis to temperature changes (affecting IGBT parameters), inductance values and tolerances and, finally, sensitivity to combined effects was the critical part of the project. III.   S IMULATION M ODEL   Initial circuit, as modeled in PSpice is shown in Fig. 2. The model includes some of the relevant parasitic elements, values of which were estimated based on the existing inverters. Q1Q2Q3Q4Q5Q6Q7Q8V1V2V3V4V5V6V7V8RLVDC   Fig.2. Initial simulation model IGBT parameters suitable for PSpice simulation model are listed in Table I. The two bridges use IGBT modules SEMIKRON SKM400GB176D.The modules are built  based on INFINEON part number SIGC186T170R3. After longer research and communication with INFINEON's applications engineers it was found that adequate replacement, for which simulation models are available is EUPEC's (formerly SIEMENS and now acquired by INFINEON) part number BSM150GB100D. After running Monte Carlo analysis and varying for IGBT parameters and operating temperatures, the obtained results were expectedly poor, as shown in Table II. For brevity, results for only two switches, in identical  positions, are shown. Simulated load current is 200A. As we are using computer-generated random numbers for the analysis (the random number seed), it is important to note that, in reality, these are pseudorandom numbers, due to the deterministic nature of the computers. If the seed number is repeated, identical random numbers will  be repeated as well. For multiple trials, different random number seeds were used, as presented in the Table II. The Table II lists only the worst case current through the switch for each set of simulations. Highlighted are the worst case deviations. Ideally, current through each IGBT would have been 100A – large deviations from the ideal 33  Proceedings of Small Systems Simulation Symposium 2012, Niš, Serbia, 12th-14th February 2012  number prove the need for forced current sharing. TABLE I. IGBT  MODEL PARAMETERS Model Parameters   Symbol   Value AREA (area of the device)  A 1.858 cm2 AGD (gate-drain overlap area)  A GD  1.4823 cm2 KP (MOS transconductance) K   p 3.54 A/V2 KF (triode region factor) K  f   CGS (gate-source capacitance  per unit area) C  GS  10.7 nF/cm2 COXD (gate-drain oxide capacitance per unit area) C  OXD  59.3 nF/cm2 VT (threshold voltage) V  T  5.8 TAU (ambipolar recombination lifetime) Τ    8x10 -6  cm WB (metallurgical base width) W  B  36.7385x10 -3  cm  NB (base doping)  N  B  0.1651x10 14 /cm 3  TABLE II C URRENT SHARING OF THE ORIGINAL CIRCUIT  No. Seed number ICQ2 (A) ICQ6 (A) min. max. min. max. 1 default 86.5 130.1 68.7 109.1 2 100 109.5 122.7 76.2 89.5 3 1000 92.6 126.4 72.5 101.1 Figure 3 shows four current sharing inductors added to each leg of both paralleled inverters. The results for added 10µH inductance are summarized in Table III. The inductance was selected based on the excellent results (5% deviations) when temperature effects on IGBT  parameters are neglected. Q1Q2Q3Q4Q5Q6Q7Q8V1V2V3V4V5V6V7V8RLVDC   Fig. 3. Model with current sharing inductors   TABLE III C URRENT SHARING WITH 10 µ H  BALANCING INDUCTORS  No. Seed number ICQ2 (A) ICQ6 (A) min. max. min. max. 1 default 102.6 126.5 88.4 96.2 2 10000 102.3 120.6 78.1 96.5 3 30000 107.7 124.7 74.1 91.2 The results indicate that, when IGBT parameters are taken into account, achieved results are modest, at best. IV. V ARIATIONS OF K  EY P ARAMETERS   It is obvious that seed number also plays significant role in the final outcome. Of course, this is little related to the actual operation of the circuit and warrants a closer look. Table IV summarizes I CQ2 -I CQ6  values for different seed numbers. TABLE IV D EPENDENCE OF CURRENT IMBALANCE ON SELECTED SEED NUMBER Seed number I CQ2 -I CQ6  (A), max.  No inductors 10uH inductors, default 61.24 22.14 10 41.91 28.08 100 46.57 33.78 1000 31.6 27.05 10050 48.18 36.50 It is interesting to note that selected seed number has much larger effect on the circuit without balancing inductors then on the one with 10uH inductors. Relative to the load current of 200A, worst case imbalance is 36.5A, or 18.2%. Q4Q2Q8Q6V11V12V15V16RL1VDC   Fig. 4. Simplified circuit So far, adding balancing inductors to decouple the two inverter bridges did not result in significant improvements. Further improvements were investigated. It was found that adding balancing inductors in series with emitters of the IGBTs with grounded emitters (low 34  Proceedings of Small Systems Simulation Symposium 2012, Niš, Serbia, 12th-14th February 2012  side switches Q2, Q6, Q3 and Q7) has significant effects. Rather than running the initial model (Fig. 1) and change inductor values, the schematic was simplified in order to minimize convergence errors. Only IGBTs connected in  parallel are shown. The simplified circuit is shown in Fig. 4 and summary results in Table V. TABLE V C URRENT SHARING WITH BALANCING EMITTER INDUCTORS Added inductance ICQ2 (A)   ICQ6 (A)  1uH 111.4 87.5 5uH 108.4 90.5 10uH 105.6 93.2 20uH 103.2 95.8 The table outlines worst case results of several simulations with different inductance values and seed numbers. Upon examination of results, and comparison with those shown in Tables III and IV, improvements are significant, deviation from ideal current sharing is less than 7%. It is interesting to note that adding the same inductor values into the collector circuits does not yield any improvements. One example of simulation resulsts are given in Figure 5. econg example can be seen in Figure 6 (illustrates simulation results ICQ2-ICQ6 for L3=L4=L5=L6=10uH and Iload=50A). Figure 5: Differences in collector currents between Q4 and Q8 Figure 6: Differences in collector currents between Q2 and Q6 V. I  NDUCTOR T OLERANCES   The paper further discusses analyses for various duty cycles and load currents, finding and addressing the worst case scenario. Final inductance value of 70uH is identified as acceptable, and analyzed for the manufacturing tolerances. Table VI summarizes worst case analysis, combining effects of IGBT parameter variations and inductor tolerances. TABLE VI C URRENT SHARING RELATIVE TO 70 U H  INDUCTOR TOLERANCES 20% 10% 5% 3% 1% I CQ2avg / I CQ6avg  1.45 1.22 1.13 1.11 1.08 I CQ4avg / I CQ8avg  1.33 1.17 1.12 1.09 1.07 Here we are looking at ratio of currents through IGBT’s in identical positions. 5% tolerance allows meeting the requirement for current sharing within 15%. VI. P RACTICAL O BSERVATIONS Based on the previous analyses the following observations can be made: 1. The very basic current balancing scheme with one  balancing inductor per H-bridge was evaluated against somewhat more complex scheme using two inductors per  bridge, one in the upper leg and one in the lower leg of each paralleled bridge. The latter was proved to be more effective and results in significantly smaller required inductance 2. Variations of IGBT parameters have much lesser effects than balancing inductor tolerances. 3. Tolerances of the balancing inductors should be within ±5% (from each other) in order to ensure current sharing within 15%. 4. It is desired to have IGBT parameters vary within 10% (DEV=10% and LOT=5%). This combined with inductor tolerances of DEV=10% results in adequate current sharing. It proved difficult to obtain exact  parameter distributions from component vendors and it may be impossible to establish any type of control over the parameters, however, manufacturer's applications engineers feel that normal distribution falls well within the desired tolerances. 5. Inductor values of 70uH are adequate for switching frequencies of fs≥1kH z. For low switching frequencies inductor values need to increase (inversely proportional increase seems like a reasonable approximation). 6. It is important to reiterate that a. Simulations did not take into account positive temperature coefficient of chosen IGBTs. It was assumed that there is a fixed difference in Vces due to temperature differences: this is the worst case and in practical circuit Vces of the two IGBTs operating at different temperatures will tend to drift toward each other minimizing the difference and improving current sharing.  b. Snubber circuits were not simulated due to convergence problems. Resulting reduction in current rise time (di/dt) is neglected, which again results in somewhat worse current sharing than could be expected in a  practical circuit. c. Analyses were performed with duty cycle of D=0.8 and D=0.1. Presented results are given for the worse of the two cases (constant D=0.8), which again may lead to somewhat exaggerated imbalances. 7. In summary, the proposed current balancing scheme uses two inductors, one in the upper and one in the lower leg of the H-bridge. Target current sharing can be achieved by using reasonable inductance of 70uH, assuming IGBT parameter values variations of 10% or less and inductor tolerance of ≤5%.   35  Proceedings of Small Systems Simulation Symposium 2012, Niš, Serbia, 12th-14th February 2012  VI. C ONCLUSION   In order to achieve significant increase in output power of the high power programmable waveform AC source, without major redesign effort, it was decided to connect two inverter bridge circuit in parallel. Given sufficient  power reserve, current sharing requirements were set at 15% over the range of output loads. Computer simulation and Monte Carlo analysis was used to determine the worst case operating conditions and determine minimum required inductance value and tolerance. The basic lossless current sharing scheme, by using one inductor per inverter bridge was compared with the concept using two inductors, one in positive and the other one in negative leg of each paralleled bridge. The latter was proved to be more effective requiring significantly smaller required inductance. Adding inductors in series with IGBT emitters further improves current sharing, albeit at added cost and complexity. Variations of IGBT parameters have less effect on the current sharing than tolerances of added inductors. Tolerance of ±5% is sufficient to allow current sharing within 15%. An experimental circuit is currently being built for laboratory and field evaluations. R  EFERENCES   [1] Chibante, R., Araújo, A., and Carvalho, A., “A Simple and  Efficient Parameter Extraction Procedure for Physics Based IGBT  Models”, Proceedings of 11th International Power Electronics and Motion Control Conference (EPE-PEMC'04). Riga, Latvia 2004. [2] Protiwa, F.-F., Apeldoom, O., and Groos, N., “New IGBT Model For Pspice”, Proc. of the Fifth European Conference on Power Electronics and Applications, September 1993, Brighton, UK, Vol. 2, pp. 226-231. [3] -, Semikron, “ SKM400GB176D ”,  Datasheet [4] -, Infenion, “ SIGC186T170R3 ”, Datasheet [5] -, Eupec, “ BSM150GB100D ”  , Datasheet [6] -, Cadence, “ Pspice Manual ”,  Orcad 9.2 36  Proceedings of Small Systems Simulation Symposium 2012, Niš, Serbia, 12th-14th February 2012
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