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Improve efficiently soft-starter transients' immunity ByDelcho Penkov & Alain Côte Schneider Electric Summary Abstract ......................................................................................................... 1 Nomenclature.................................................................................................. 1 Introduction..................................................................................................... 2 Overwiew of SCR functionning and electrical transient issues.......................... 4 Case study...................................................................................................... 5 Modeling of the RVSS and case study power system in EMTP-ATP................ 6 Analysis of the thyristor turn on current transient.............................................. 7 Overview of the voltage transient during switching........................................... 9 Estimation of the risk of high current transient................................................ 11 Development of protection sizing tool............................................................ 12 Conclusion.................................................................................................... 14 Acknowledgements....................................................................................... 15 Appendices................................................................................................... 15 Vita................................................................................................................ 16 Improve efficiently soft-starter transients' immunity Abstract In this paper the authors present results of measurements and mathematical analysis on MV Silicon Controlled Rectifiers (SCR, Thyristors) for the purposes of the power electronics components protection during turn on. Current transient was identified as responsible for damaging soft-starters in field applications. This work is focused on the identification of the major parameters playing role in the current transient. Formulae for calculating the current rate-of-rise and risk identification procedure are derived. A simple tool for practical SCR transient protection design is described. Index Terms — Soft-starter, current transient, EMTPATP Nomenclature φ Phase shift between current and voltage, in ms. α Thyristor turn on delay with respect to voltage zero crossing, in ms. COM-POWER-WP--EN Rev1 | Improve efficiently soft-starter transients' immunity Introduction Silicon Controlled Rectifiers (SCR) or Reduced Voltage Soft-Starters (RVSS) are modern techniques used for smooth motor starting in MV power systems. Thus many papers on SCR design discuss motor or system protection issues like torque pulsations or harmonic reduction, however little is said about protection of SCR itself. Major electrical transient constraints on the semiconductors are overvoltages during switching off, and current rate of rise while turning on. For power systems with rated voltages of 5.5 kV and above the current transient may become important, and depending on the application, damage the semiconductors, some believe because long connecting cables are used. Since it is common to use one RVSS to start several motors sequentially, failure of the RVSS can lead to substantial production losses. Generally a 100 μH series reactor is likely to be sufficient. However, from an economical point of view and lack of space, it would be much better to determine a more rigorous way to size this reactor. Risk assessment is crucial, together with a clear explanation of the current rate of rise phenomenon. In this paper the authors investigate field measurements and mathematical models of the SCR in order to understand the mechanisms the current transient depends on. In a first step it came out that the transients depend on the immediate environment around the SCR including both upstream and downstream installation, and not only on the motor cable length. Further analysis helped us to build a mathematical constant parameters model in EMTP-ATP that reproduces accurately the system behaviour during thyristor turn on. This was important step since it allowed us to go further and by hand analysis establish a formula to calculate the current transient on turn on without performing a simulation. It allowed in-depth understanding of what the current transient was the most depending on. Consideration of the overall behaviour of the switching angle and motor acceleration during start made it possible to put forward recommendations to reduce the potential risk of SCR damage before installation of additional protection. Yet if this is not sufficient, calculation tool gives recommendation on the sizing of the protection reactance together with the expected current transient. The solution is generalised and user may account also for the installed protection capacitors. Unfortunately, due to a very high installation conditions dependency simple rule, just built on voltage/rated power/cable, is difficult to be formulated, given the necessity to make some preliminary calculations. Required input data concerns immediate upstream and downstream installation details, and how the soft-starter is set up. Practical tests confirmed the accuracy of the developed tool. Thus full SCR service continuity in optimized installation conditions will be ensured. The paper is organized as follows: Section II introduces the principles of the soft-starter functioning and the constraints it is exposed to. Section III is a brief overview of a field application where a soft-starter was damaged during motor start. Section IV presents the modelling of the soft-starter and the simplification assumptions that were validated by comparison with field measurements. Sections V and VI will describe the mathematical analyses made for deriving of the current rate-of-rise computation formula and estimation of critical transient voltage values. Section VII defines the critical moments (zones) during the motor start. Section VIII discusses the development of risk assessment tool capable of inductance sizing calculation. COM-POWER-WP--EN Rev1 | Improve efficiently soft-starter transients' immunity Improve efficiently soft-starter transients' immunity Overwiew of SCR functionning and electrical transient issues Thyristor Functioning Principles The SCR driven motor start is based on the use the motor is equivalent to variable impedance and of parallel thyristors connected in reverse parallel decreases with the acceleration of the motor. configuration to each other that are switched on The command signal (represented by α ) is also by a command signal. The command signal varied during the motor start. is intentionally delayed from the voltage zero- Globally the behavior shown in Fig. 2 is observed: crossing so that a smaller current is provided (ms) to the motor sufficient to start but lower than init = f (Veffinit) the rated starting current. The overall behavior is described in the Fig. 1. leff (% x Ir) (V,I) Vupstream leffinit = Veffinit.kd Rated current Veff (%) Rated voltage t(s) t(s) Ramp time Ithyristor Figure 2 – B asic evolution of main soft-starter depending variables. Figure 1 – Principle of controlled current in soft-starter. tcurrent_zero = α - φ t(s) Full wave voltage Veffinit Current zero time t(s) Current limit (1) Somewhere after passing in full-wave conduction of the thyristors a parallel by-pass contactor is The current through the thyristor stops naturally closed and RVSS stops. on zero crossing. The moment of zero crossing The user dependent settings are: depends on the phase shift between the current 1. initial voltage, in % of rated voltage and voltage. 2. ramp time (time to go to the current limit), in s This phase shift varies during the motor start as 3. current limitation, in % of rated motor current. Electrical transient switching constraints These are the surge voltage on switching off and current rate-of-rise on turn on. The surge voltage issue is solved by a parallel connected snubber, sized according to the expected overvoltage and k(V) 12 energy. This is a standard issue, scheduled during 4 the development of the soft starter. Fig. 3 shows 0 an example on a 6kV power system. The overvoltage on the thyristors goes up to 270 % of the peak rated single phase voltage. Connecting 2 or 3 thyristors in series reduces the overvoltage applied individually on them. Upstream voltage 8 -4 Voltage across the thyristor -8 -12 55 59 63 67 71 t(ms) : VP2F-VaP2F : VaP2F Figure 3 – M easurement of Voltage transient during a complete fundamental period. COM-POWER-WP--EN Rev1 | Improve efficiently soft-starter transients' immunity The current rate-of-rise issue differs because If it overpasses the thyristor limit (100-200 μA/s it depends on the installation conditions of the typically) the thyristor is damaged as well as the soft-starter. Its solving is not generalized but case softstarter itself. This is the subject of this paper. dependent. An example of current turn on rate of Fig. 5 shows a zoom on the current during this rise on 6 kV power system is shown in Fig. 4. transient: (A) (A) 1500 500 1000 400 500 300 0 200 Turn on current transient -500 -1000 -1500 55 100 0 59 63 67 71 t(ms) : IP1F -100 63 63.05 63.10 63.15 63.20 63.25 t(ms) : IP1F Figure 4 – Measurement of current through the thyristor during a complete fundamental frequency period. Figure 5 – C urrent transient on switching on of the thyristor. As it can be seen there is a high current transient In this paper the authors will focus on the main on turn on. parameters this transient depends on. Case study The problem of high current rate-of-rise emerged The power system is described hereafter: on a 6 kV power system in an oil refinery based in 1. Rated voltage of 6 kV Spain (Fig. 6). 2.30-40 m of 120 mm² cable upstream to Grid Power transformer the softstarter, 2 conductors per phase 3.320 m of 120 mm² cable downstream of the softstarter, 2 conductors per phase 4. 3.1 MW Motor. 6 kV bus The motor has been started several times before the soft-starter was damaged. Substantial Upstream cable Soft-starter Downstream cable Motor Figure 6 – C ase study power system. measurements on site, shown in Fig. 3 and 5 revealed high current rate-ofrise, over 170 A/μs whereas the thyristors were only able to withstand up to 150 A/μs repetitive rate-of-rise. After inserting a reactance of 100 μH in series with the softstarter the current rate-of-rise was measured as 40 A/μs during the current limitation period. The solution was very effective, however bulky. We focused our analysis on the identification of the origins of the problem. COM-POWER-WP--EN Rev1 | Improve efficiently soft-starter transients' immunity Modeling of the RVSS and case study power system in EMTP-ATP EMTP-ATP is a software package dedicated to 3.Cables were modeled in π, however in order to modeling of power system transients. avoid discharging of the immediate upstream It allows analysis of high frequency phenomena, of the RVSS cable capacitance into the i.e. switching transients, and was chosen as most downstream one, a different approach was adequate to the aim of our modeling. applied: the upstream and downstream cables Moreover EMTP-ATP allows in depth modeling have been considered as an equivalent cable of the power system together with suitable RVSS whose capacitances were placed on its ends. model, critical, since the analysis aimed to see The softstarter is placed along this single cable, the impact of the surrounding power system according to the real data. Its precise position on the semiconductors. does not have any impact on the current Please note that the modeling was focused on rate of rise since the cable capacitances are an accurate simulation of the transients during concentrated at the ends of this equivalent cable. switching on. At first, we modeled the complete power system using frequency-dependent cable Thus the resulting power system model was models and RVSS with its command circuit, greatly simplified as shown in Fig. 7. capable to represent the power system during the complete motor start. The comparison with real test measurements showed the very good Zcc Upstream cable Downstream cable Motor accuracy of the models. However, due to the very high number of setting parameters, such as the RVSS settings and motor, cable specifications, such approach was not applicable for large scale analysis on the current rate-of-rise, since it is difficult to establish, monitor and explore the very high number of various study cases it would require. Furthermore, indepth analysis Cupstream Cdownstream Figure 7 – Simplified power system model. (2) Cupstream = Csystem + Cprotection capacitors + Cupstream cable Cdownstream = Cmotor + Cdownstream cable showed that the current rate-of rise varies during The results obtained with this simplified model motor start, which requires simulation of were still precise (<5 % error) with respect to the complete process. With a timestep of 100 ns the measured values of current rate-of-rise, for an average of 15 s to be simulated, oscillation frequency and attenuation. the generated output files would have been Example curves are shown in Appendix C. difficult to handle. However this simplified model, built with only linear elements had another important advantage: We proceeded to simplification of the used models: it allowed clear analysis of the switching events. 1.The motor was implemented as series R-L fixed impedance with phase-to-earth parasitic capacitance. This assumption is valid since the transients on the thyristors are much faster than the speed variation of the motor shaft, responsible for the variation of it’s equivalent impedance (this is also stated in IEC 62271-100) 2.Power feed was assumed as source behind an equivalent short-circuit impedance (comprising the transformer), with phase-to-earth equivalent capacitance, including protection capacitors if any. COM-POWER-WP--EN Rev1 | Improve efficiently soft-starter transients' immunity Analysis of the thyristor turn on current transient As it was stated before the simplification of Thus in electrical terms this means that it may the power system model led to the possibility be summarized as a second order circuit of using simple mathematics in order to derive comprised of an inductor, capacitor and resistor, the behavior of the current in the first instants the latter providing the attenuation of the signal. after turning on.According to the measurements The estimation of their values will be given by (see Fig. 5) the current transient may be the mathematical analysis. approximated to a second order step response. Hypothesis 1.During switching on, due to the very high 2.During switching, again due to the very high frequency of the current transient (50-200 kHz) frequency, the motor is assumed as the upstream power circuit, except the a capacitor connected to earth, its equivalent connecting cable, is equivalent to a capacitor connected to earth. In fact, if this was not RL circuit having a very high value. 3.During switching on, the fundamental (50 Hz) the case, the current rate-of-rise will be current increase is neglected with respect to quite limited by the short-circuit equivalent the first quarter of the oscillation of inductance of the upstream circuit the transient current Equivalent circuit of the system during switching on The following parameters are defined: VC1, VC2phase to earth voltages at the moment of switching, upstream and downstream C1, C2equivalent capacitors of the power system upstream and downstream of to the soft-starter the soft-starter, the value being the sum of the upstream or motor equivalent The turn on of a thyristor is represented by capacitance and that of the upstream or the equivalent circuit in Fig. 8. downstream cable L R R, Lequivalent parameters of the connecting cable comprising both the upstream and downstream part, the resistance being VL C1 VC1 I VR C2 VC2 calculated at the presumed oscillating frequency of the current Figure 8 – Equivalent circuit for current transient analysis. COM-POWER-WP--EN Rev1 | Improve efficiently soft-starter transients' immunity Mathematical expression of the current rate-of-rise during switching on The following equation is derived from Fig. 8: R.I + L. The current rate-of-rise is calculated within 1 μs interval. Since the initial value of the current is zero, dI 1 1 + .∫I.dt + VC1 + C2 .∫I.dt + VC2 = 0 (3) dt C1 t=0 t=0 the current rate-of-rise 1 μs after turn on is equal From (3) the following expression of the current to the value of current at 1 μs which is given in (5). in the first moments after thyristor turn on is - ( VC1 t=0 + VC2 t=0) -10 -6/ T dI(t) = I(t) = .e .sin(w.10 -6) (5) w.L dt t=1µs obtained: I(t) = T= (VC1 t=0+ VC2 t=0 ) w. L Equation (5) allows the current rate-of-rise to be .e -t/T .sin(w.t) 2L R computed, once the power system is simplified (4) to the equivalent circuit of Fig. 8. Should any protection inductance be incorporated into 1 L w= R 2 4. 2L√ C the circuit, its value is to be added to the cable C1.C2 C= C1 + C2 It should be noted that the current rate-of-rise is Obviously from (4) the current transient depends The higher the rated voltage, the higher will be both on upstream and downstream circuit. the current rate of rise. For example, in a 6.6 kV However, as often in practical cases the upstream system it will be approximately twice as high as for cable is quite short, it is often said that the current a 3.3 kV system. There are two important variables transient is only dependent on the downstream that do not depend on the power system itself but cable. This is valid for the equivalent cable on the switching conditions. Those are the values inductance; however the upstream capacitance, of the upstream and downstream voltages on together with the one downstream will determine the capacitors. Their estimation requires the equivalent capacitance of the circuit and thus consideration of the transients on the voltages the frequency of the current transient. during switching off and on of the thyristors. inductance. proportional to the power system rated voltage. COM-POWER-WP--EN Rev1 | Improve efficiently soft-starter transients' immunity Overview of the voltage transient during switching A measurement of the voltage transient during The analysis of these measured voltages results in switching off and on is given in Fig. 9 the use of another equivalent circuit representing the power system between on-off switching. (V) 7000 5250 Downstream Voltage 3500 1750 0 -1750 -3500 -5250 -7000 60 61 62 63 64 t(ms) : VP2F : VaP2F Figure 9 – Measured Voltages on the soft-starter outgoing terminals during on-off switching. Frequency of the voltage transient The calculation of the transient voltage frequency Lm requires establishing the equivalent circuit of the Rm power system at the moment of switching off. Given the measured frequency of the transient voltage, 3-4 kHz, the following simplifying Csnubber assumptions are made: Cdownstream 1. The upstream circuit, including cable is represented by the short-circuit impedance of the power system, whose value is quite low compared to the one of the capacitors to earth. This assumption is valid when the transformer neutral earthing is made with small impedance, Figure 10 – E quivalent circuit for the voltage transient during switching off. The frequency of the voltage transient is therefore: Fdownstream_voltage= which is generally the case. 2. The cable impedance is negligible compared to that of the motor 3. The short-circuit impedance is negligible compared to that of the motor, thus the upstream circuit is considered to be directly earthed. According to the above assumptions, Leq= Lm + 1 2.�.√ Leq.Ceq 3 1 Lm = Lm 2 2 (4) Ceq= Csnubber + Cdownstream The calculated frequency is slightly higher than the real one because of the assumptions made for the short-circuit impedance of the upstream circuit. This will be accounted for in the next point. the following equivalent circuit for the voltage transient may be drawn: COM-POWER-WP--EN Rev1 | Improve efficiently soft-starter transients' immunity Consideration of the transient voltage value The transient voltage is the difference between In other terms, and with respect to the commutation the upstream and downstream phase-to-earth angle and the time interval between switching off voltage. Depending on the turn on instant, and on, the voltage is approximated as: the voltage across the thyristor will be different. Each side of the soft-starter should be considered individually. The upstream voltage value will be Vdownstream (pu of V(t)) 2 determined by the moment of switching on, i.e. t - period of downstream voltage oscillation 1 the delay given by the control circuit, (α). This value is easily estimated. The downstream 0.5 voltage is defined both from the commutation < t/2 moment and the transient evolution. The instantaneous fundamental frequency value of the downstream voltage is half the one on the other side, as shown in appendix A. Precise estimation of the voltage requires having the complete power system parameters, especially for the attenuation constant calculation. Current zero time Figure 12 – A pproximation of the downstream voltage value as function of current zero time. The value of the upstream voltage being always 1pu of itself, the voltage across the thyristor is therefore: Vth_turn_on This data is unavailable for many reasons. > 2.t t=α = (1+Vdownstream(α _ φ)).Vupstream t=α (6) Thus it is necessary to formulate a simplified method for the downstream voltage estimation. The next figure presents how its value may be approximated, of course in excess of the real one: (V,pu) Vreal t(s) -0.5 -1.0 -2.0 Vapproximated Figure 11 – Approximation of the downstream voltage evolution after turn off of the thyristor. COM-POWER-WP--EN Rev1 | 10 Improve efficiently soft-starter transients' immunity Estimation of the risk of high current transient The above equations and considerations allow the computation of the current rate-of-rise at each thyristor turn on. Yet this requires selection of particular moments when this calculation is critical for the estimation of the need of adding a protection reactor. First let’s have a look on the evolution of the turn on delay (α) and the current zero delay (φ) with respect to the voltage zero crossing: (ms) init = f (Veffinit) init Rated T(s) First danger zone Second danger zone End of ramp time Closing of bypass contactor Full wave voltage Figure 13 – Time variation of the control delay and current phase shift during the motor start. The critical instants during motor start are those where the current zero time is the smallest, in this case the voltage across the breaker would be at its potentially highest value. As it can be seen, there can be designated two critical zones: 1. First danger zone – it is the moment of from start to ramp end, where the control delay (α) will make a first brake, according to the requested current limitation, and slow its decrease, the current phase shift (φ) will continue decreasing with the acceleration of the motor 2. Second danger zone – the period after ramp end until going into full wave conduction. Current limitation means to maintain the current to the desired value. With the speed increase the current is getting smaller and the control angle has to be decreased. This increases in turn the current, much like a proportional control. The control angle decrease may lead to experience very high di/dt. Earlier it happens after the ramp end and higher is the current rate of rise. Between these two danger zones, the second one is potentially more critical. This is because of the certainty that during this period the current zero time will decrease, to values lower than half of the oscillation period (Fig. 12) and the voltage across the thyristor must be taken as 3 times the upstream voltage, (6). If this happens during the current limitation phase the control angle will be still relatively high, i.e. the voltage will be close to its’ maximum on turn on. Generally, in order to consider the worst case, the current rate of rise is to be calculated immediately after the ramp end.The estimation of the voltage constraint on the thyristor requires a preliminary estimation of the control delay and the current phase shift. The control delay can be derived from the required current limitation. First it is necessary to estimate the voltage rms value on the motor at ramp end: Vrmsramp_end = Imax Kd (7) Where: Imaxrequested current limitation, pu of rated current kdmotor starting current, in pu of the rated current The estimation of the control delay for a certain rms voltage at ramp end is made by dedicated algorithm, explained in Appendix B. The exact value of the phase shift can not be estimated with sufficient precision. This would require a close look on the motor equivalent parameters and speed evolution during start, which in turn is very load dependent. That is why it was preferred to use the stalled rotor phase shift. Parametric analysis on the phase shift impact showed that a higher power factor leads to a slightly higher di/dt (5-6 % over). Generally this should not play a role since selected reactor values will always be higher than the exactly needed, because choice is generally made among fixed by manufacturer values. Taking the immediate greater value will normally add additional security margin, far beyond 5-6 %. Of course, depending on the available reactor values, it may be sometimes important to increase the di/dt values by 5-6 % before going to selection. With the above assumptions, the ratio between the current rates of rise Zone2/Zone1 will be either 150 % or 200 %. COM-POWER-WP--EN Rev1 | 11 Improve efficiently soft-starter transients' immunity Development of protection sizing tool The above equations and considerations were Its’ application will ensure optimized installation implemented in a tool capable of calculating conditions for the SCR application as well as its the current rate of rise for the two designated service continuity. danger zones. Required Input Data Input data for the protection sizing tool. Designation Rated voltage Rated frequency Upstream capacitance Upstream cable material resistivity Upstream cable length Upstream cable relative insulation dielectric constant Number of cables per phase Downstream cable material Downstream cable length Downstream cable insulation dielectric constant Number of cables per phase Motor rated power Motor rated power factor Motor Starting power factor Motor Efficiency Motor Starting current RVSS Snubber capacitance Current limitation setting Thyristor current rate-of-rise limit Units kV Hz nF Ωm m Ωm m kW % x In nF % of In A/μs Results The case study data was entered for the estimation of the risk of current rate-of-rise and it’s evolution with the protection reactance. The next figure shows the results of calculation, sorted as: - Zone 1, when only danger zone 1 is Current rate of rise (A/µjjs) 300 because of propitious installation/setting/load 250 conditions 200 zone 2 is accounted, being more constraining than danger zone 1 Zone 1 Zone 2 350 accounted, danger zone 2 will not take place - Zone 2, (usual case), when only the danger Current rate of rise as function of installed protection inductance 400 Current limit set to: 380 % In Thyristor limit 150 100 50 0 0 10 20 30 40 50 60 70 80 90 Protection inductance (µjjH) Figure 14 – R esults of calculation of current rate-of-rise. COM-POWER-WP--EN Rev1 | 12 Improve efficiently soft-starter transients' immunity Discussion of the results The obtained results show that insertion of 100 μH inductance leads to 50 A/μs current rate-of-rise for danger zone 1, whereas the measured value was about 40 A/μs. Comparing the required inductance sizing for Zone 1 and on Zone 2, it may be seen that the required inductance is more than 5 times higher. This higher value will cost more because installation requirements will differ. Sometimes, in order to get rid of Zone 2 constraint, an earlier by-pass closing may be convenient. But this solution is not sure to be efficient. Also earlier by-pass closing is not really a solution; one may ask why we need a soft-starter if it is to not use it completely? An elegant solution in order to reduce current rate of rise would be to control α in a way that the current zero time remains higher than twice the voltage transient period. This will keep the current rate of rise at the smallest possible value. This will require signal processing of the upstream or downstream voltage oscillation immediately after the current interruption in the thyristor. The drawback of this solution is that it will not be efficient when the current limitation setting is very close to the minimum acceptable value, under which the motor will simply not start. In fact, reducing the current rate of rise requires increasing of the current zero time intervals that decrease the current rms value. Of course, in some existing installations over sizing the inductance may be the simplest and the most convenient solution. COM-POWER-WP--EN Rev1 | 13 Improve efficiently soft-starter transients' immunity Conclusion In this paper we presented in-depth analysis of the mechanisms and estimation of current rate-ofrise in MV soft-starter semiconductors. Based on field measurements and reasonable simplification assumptions a mathematical definition of the current transient immediately after the thyristors turn on was established. It showed that the current transient issues increases with the application rated voltage. Furthermore, soft-starter control analysis allowed defining two zones of major importance for correct sizing of protection solutions: one immediately after ramp end (beginning of current limitation phase) and another starting shortly after, until closing of the by-pass contactor. The second one requires greater value of the protection inductance. Also there were proposed partial solutions for decreasing the current rate of rise, to close earlier the by-pass contactor or to control the turn on delay (α). The most effective solution is sizing of the protection inductance by considering the second danger zone. All the considerations and mathematical formulae were implemented in a tool which was also presented and validated by comparison with field test measurements. This advancement will ensure that soft-starter installation conditions are optimized and safe for full SCR service continuity. COM-POWER-WP--EN Rev1 | 14 Improve efficiently soft-starter transients' immunity Acknowledgements Authors would like to thank Mr. C. Durand for his work on the simulation models, Mr. P.A. Claudel and Mr. R. Catalan-Herrero for the measurements they performed on site and Mr. R. Henri for his benefic contribution to the final version of this paper. Appendices Calculation of downstream voltage Vn = Va _ Ia.Zm = Vb _ Ib.Zm Zm Va Vn Vb Vc Figure A-1 – Equivalent circuit after current interruption in one phase. Ia = _Ib _ Ia = Va Vb 2.Zm (A-1) _ Vn = Va + Vb = Vc 2 2 Calculation of control delay as function of motor rms voltage Calculation of the control delay requires set up of Mathematically the rms value calculation is the limits of control angle variation. expressed as: Since the motor is isolated from earth, only control ϕ− delay < 2/3 of the fundamental half period is possible, so that there always at least two t V rms = 2 t thyristors conducting. With this assumption 0 α ϕ− ϕ+ t 6 t 6 sin( wt ) + T ϕ α 1 2 . sin( w.t − π ) 2 3 6 α+ + ∫ 0 + ∫ sin 2 ( wt ) + ∫ the voltage variation on one phase of the motor, for 6kV power system is given on the next figure: α− 6 2 ∫ sin ( wt ) + ∫ ϕ+ 2 ϕ + ∫ sin 2 ( wt ) + α− 6 t sin( wt ) + (A-2) T 6 t 1 2 . sin( w.t + π ) 2 3 6 t 2 2 + ∫ sin 2 ( wt ) α+ t 6 Where: t: period of the fundamental signal. (V) 6000 A dedicated calculation algorithm iterates on α Phase to neutral voltage 4000 2000 until the required value of the rms voltage is achieved. 0 -2000 -4000 -6000 0 10 20 30 40 50 t(ms) : X0001A : MOTA-N_MOT Fig. A-2 T ime variation of the phase to neutral motor voltage compared to the fundamental phase to earth voltage upstream of the soft-starter. COM-POWER-WP--EN Rev1 | 15 Improve efficiently soft-starter transients' immunity Comparison of measured and simulated waveforms (A) (V) 1500 Measured 1000 500 0 -500 -1000 -1500 0.05 Simulated 0.06 0.07 0.08 0.09 0.10 t(s) : simu_bpoil_v5. pl4 Fig. A-3 Comparison of line currents, simulated and measured. (A) 500 200 Measured 100 0 -100 -200 61 Simulated 61.5 62 Simulated Measured 0.06 0.07 0.08 0.09 t(s) : simu_bpoil_v5.pl4 : RVSSA-RVSS_A : RVSSA -RVSSA_A 400 300 10 7.5 5 2.5 0 -2.5 -5 -7.5 -10 0.05 62.5 63 63.5 t(ms) Fig. A-6 Comparison of phase voltages, simulated and measured. (V) 10 7.5 Measured 5 2.5 0 -2.5 -5 Simulated -7.5 -10 59 60 61 62 63 64 65 66 t(ms) : simu_bpoil_v5.pl4 : RVSSA-RVSS_A : simu_bpoil_v5. pl4 : RVSSA -RVSSA_A Fig. A-7 Zoom to Fig. A-6, during current zero in the thyristor. Fig. A-4 Zoom to Fig. A-3, thyristor turn on. (A) 1140 1120 1100 1080 1060 1040 1020 1000 980 64 Measured Simulated 65 66 67 68 69 70 t(ms) : simu_bpoil_v5.pl4 : RVSSA-RVSS_A Fig. A-5 Zoom to Fig. A-3, current crest values. Vita Delcho Penkov was born in Haskovo, Bulgaria. Alain Côte received his Electrical Engineering Hegraduated from Technical University of Sofia in degree from the National Polytechnic Institute 2002(MSC). In 2006 he received his PhD degree of Grenoble in 1983. He is currently working in ElectricalEngineering from the Institut National on electrical network analyses such as stability, Polytechnique deGrenoble (INPG). harmonic and over voltage studies. He is currently working for Schneider Electric as He has been personally involved in several Power Systems Engineer. Member of IEEE. instances of expertise on equipment failure or malfunctioning in different fields of industrial plants, particularly about transient phenomena. 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