Power supplies for parallel operation Power supplies

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Nelson Townsend
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1 Power supplies Power supplies for parallel operatio U 1 2 U Parallel operatio of switchmode power supplies Techical details for passive curret-sharig The aim of operatig switchmode power supplies (SMPS) i parallel is to icrease output power by icreasig the output curret. How this ca best be achieved by usig the passive curret-sharig method is described i the followig article. By Marti Rosebaum U 1 = U + U E1 U 2 = U + U E2 U = U + U E a N a1 Fig. Bild Characteristic Keliie ( weiche lies ( soft Keliie ) characteristics ) vo parallelgeschaltete of switchmode power Schaltetzteile. supplies operated i parallel. U E SMPS SNT 11 SMPS SNT 22 SMPS SNT a1 U 1 a2 U 2 a U a2 There are two methods of realisig parallel operatios that coform with today s stateof-the-art techology. Firstly, usig active curret-sharig (cotrolled load-sharig) ad secodly, usig passive curret-sharig. Active curret-sharig measures the output curret of each power supply ad adjusts the output voltage of each idividual SMPS to produce uiform curret distributio. This method has the advatage of esurig very exact cur- SMPS SNT 1 1 SMPS SNT 2 2 SMPS SNT Bild Fig. 2. Symmetric Symmetrische cablig Verkabelug is a basic requiremet ist eie Voraussetzug for usig für die Parallelschaltug switchmode power vo supplies Schaltetzteile. i parallel. a Verbraucher Load ret-sharig ad costat loadig of the SMPSs operated i parallel. The disadvatages are the eed for additioal compoets ad higher costs. By compariso, i the case of passive curret-shar ig, the curret is distributed as uiformly as possible via a "soft output cha racteristic (Fig.1) for each SMPS. This approach has the advatages of eedig less switchig techology ad allowig for parallel use of a almost ulimited umber of SMPSs. The somewhat more iaccurate curret distributio must be see as a disadvatage. Passive curret distributio -the basics Some importat details o passive curret-sharig follow, based o the assumptio that the followig requiremets have bee met. R i + 2 x a U Fig. Bild Equivalet Ersatzschaltug circuit der diagram parallelgeschaltete use Schaltetzteile of switchmode power for parallel supplies. idetical switchmode power supplies are used i parallel. Each switchmode power supply is symmetrically cabled to the load (Fig. 2) 1. 1 = U + U E1 (R i + 2 ) a = U + U E2 (R i + 2 ) a = U + U E3 (R i + 2 ) a3.... = U + U E (R i + 2 ) a The followig equatios for the switchmode power supplies form the basis for calculatig parallel operatio. Requiremets for parallel operatio of switchmode power supplies: 1 = 2 = 3 =... = ad a = a1 + a2 + a a This gives rise to the followig equatio system for the SMPSs operated i parallel.

2 Power supplies for parallel operatio Power supplies P amax(rl) 132 W Fig. 4. Maximum load output i relatio to wire (The diagrams show i Figures are available upo request for all switchmode power supplies with passive curret-sharig desiged for parallel operatio purchased for example from the compay MGV Stromversorguge ( mω 5 = U + U E1 (R i + 2 ) a1 = U + U E2 (R i + 2 ) a2 = U + U E3 (R i + 2 ) a3... = U + U E (R i + 2 ) a After a umber of simplifi catios, various equatios for the SMPSs operated i parallel ca be deduced with the aid of this equatio system. But fi rst of all, the defi itio of the mea value of the settig toleraces: = 1 i=1 U Ei Voltage at load: = U + R i + 2 a (1) Based o equatio (1), the equivalet circuit diagram for the SMPSs used i parallel ca be costructed as show i Fig. 3. t is amazig that this results i such a simple equivalet circuit diagram (ECD) for a parallel coectio. The ECD cosists of oly three elemets. O the oe had, it is made up of two voltage sources with parameters that are easy to ascertai. Added to these is a resistace, which ca also be simply calculated based o the power supply s iteral resistace, the wire resistace (load wire) ad the umber of switchmode power supplies i parallel coectio. By goig a step further ad addig together the two voltage sources, oe arrives at a equivalet circuit diagram for a real equivalet voltage source cosistig of a ideal voltage source ad iteral Curret at the kth switchmode power supply (1 < k < ): ak UEk UEM 1 = + R + 2 R i L Accuracy of the curret-share at the kth power supply (1 < k < ): a (2) 6 A Fig. 5. Maximum available curret that ca be draw from the parallel series i relatio to wire amax(rl) mω 5

3 Power supplies Power supplies for parallel operatio 24,2 A 24 23,8 Fig. 6. Load voltage i relatio to load curret at Ua(a, 18 mω) 23,6 23,4 23, , A 6 a ak UEk UEM = a ( R i + 2 ) (3) Aalysig equatio (2) more closely, it will be oted that the secod part of the sum represets the share of curret i the case of equal curret distributio across the parallel coectio. t is therefore logical that the fi rst part of the sum represets the deviatio from this uiform curret distributio. By calculatig the deviatio as a proportio of the curret produced by a SMPS i the case of uiform curret-sharig, oe arrives at the deviatio i percetage terms (equatio (3)). t is iterestig to ote the factors affectig this percetage deviatio. For istace, the curret share becomes more exact as the load curret (see Fig. 7), iteral resistace ad wire resistace icrease. Furthermore, the accuracy of the curret share also icreases, the earer the settig tolerace moves towards the mea value of the tolerace of adjustmet. The maximum curret that ca be draw from the parallel coectio (assumig U E1 > U E ad a1 = 1N) is: a max = N ( U E1 ) (4) R i + 2 The maximum curret that ca be draw from the parallel series is reached whe the switchmode power supply with the highest oload-operatio (i this case, SMPS 1 is assumed to have the highest o-load-operatio) draws the rated curret. The total output curret of all other SMPSs is therefore always lower, or ot more tha the rated curret of oe SMPS (Fig. 1). The maximum load output i relatio to the wire resistace whe drawig the maximum curret amouts to: [ ( )] ( ) P max = U + U R + 2 R a E1 N i L UE UEM N 1 Ri + R 2 L (5) Calculatio example demostratig applicatio of the derivative formulae The followig switchmode power-supply data are assumed for the purpose of this example: Nomial voltage: U = 24V Rated curret of oe SMPS: N = 2A teral resistace of the SMPS: R i = 17.5mΩ Switchmode power supplies used i parallel: = 3 Settig toleraces of the three power supplies: U E1 = 5mV, U E2 = -1mV, U E3 = - 3mV Mea value of settig tolerace: = 1/3 (5mV 1mV - -3mV) = 3.33mV

4 Power supplies for parallel operatio Power supplies 5 % a1 1 ak a2 a A 6 a Fig. 7. Percetage curret-share i relatio to the load curret at Determiatig the level of wire resistace based o the maximum available output that ca be draw off by the load, applyig cocrete values (see also Fig. 4) P a max = [ ( )] = ,5 V 2 A 17, mω+2 14 mv 6 A ,5 mω+2 (5a) The resistace ca be read off o the diagram show uder Fig. 4 at the poit where the output reaches its maximum. the case of this sample calculatio, resistace is reached at about 18mΩ. All further calculatios will be based o this optimal wire Maximum curret which ca be draw from the parallel coectio, applyig cocrete values: amax = 14 mv 6 A ,5 mω + 2 R Accordig to Fig. 5, the maximum curret that ca be draw from the parallel supplies, takig ito accout the resistace, amouts to about 57.5A. This fi gure is equivalet to 95.8% of the 6A that are theoretically possible. The load voltage i relatio to the load curret at a resistace of = 18mΩ (Fig. 6) is calculated as the result of: L (5b) 4 mm2 3 Fig. 8. Cross-sectio of the wire i relatio to its legth for A(l) m 3

Power supplies Power supplies for parallel operatio Abbreviatios used A Wire cross-sectio R i teral resistace of the SMPS ECD Equivalet circuit diagram Load-wire resistace (go-adi dex umber retur

5 Power supplies Power supplies for parallel operatio Abbreviatios used A Wire cross-sectio R i teral resistace of the SMPS ECD Equivalet circuit diagram Load-wire resistace (go-adi dex umber retur lead) ak Percetage deviatio of the SMPS Switchmode power supply curret share at the kth Output voltage of the SMPSs SMPS operated i parallel a Load curret Output voltage of the th amax Maximum available load SMPS curret U E put voltage a Output curret of the th SMPS Mea value of the settig usig parallel operatio toleraces N Rated output curret of a U Nomial ope-circuit voltage SMPS U Actual ope-circuit voltage of κ Electrical coductivity the th SMPS k dex umber U E Settig tolerace of the output l Wire legth voltage for the th SMPS Number of SMPSs operated i (calculated as the ope-circuit parallel voltage mius rated voltage) P amax Maximum load output Marti Rosebaum Qualified egieer was bor i Coburg. After traiig as a power-plat electroics egieer ad gaiig two years skilled experiece i this field, he studied electrical egieerig at Coburg Polytechic, specialisig i Electrical Power-Techology. After completig his studies, he supervised a research project at Coburg Polytechic o the subject of verterfed asychroos machie. Sice October 1997, he has bee active for the compay MGV Stromversorguge, both developig stadard switchmode power supplies ad realisig customised solutios. marti.rosebaum@mgv.de = 24.33V 17.83mΩ. a Percetage curret-share (based o a/) of the three power supplies i parallel series i relatio to the load curret at resistace: a1 = 2.617A/a a2 =.748A/a a3 = 1.869A/a Fig. 7 illustrates clearly the iterrelatio betwee the curret share ad the load curret. The zero-percet lie o the vertical axis of the diagram correspods with a uiform curret share, meaig that each switchmode power supply is providig the same curret. Very small load currets lead to extremely ufavourable curret distributio. As a rule, this does ot however preset a problem, as i such case the idividual SMPSs are operated far below their rated output. From a load curret of about 25A upwards, the divergece i the curret shares is uder 1% ad at the maximum level of available curret, eve lower tha 5%. As far as the user is cocered, it is ot so much the resistace that is of iterest as the cross-sectio measuremet of the wire that should be used i relatio to its legth i order to realise a This ca be calculated usig the well-kow formula for wire resistace: = 1 (6) κ. A Preparig a diagram based o this equatio ca help to determie relatively quickly ad simply the required cross-sectio of the wire at a give legth, based o the assumptio of maximum available output. The diagram show i Fig. 8 must be qualifi ed by poitig out that the cross-sectio of the wire is subject to a miimum value (curret carryig capacity of cables i accordace with the relevat regulatios). view of the miimal cross-sectio measuremets, it will ot be possible to realise resistace i the case of every applicatio. However, care should by all meas be take to esure symmetrical cablig of the idividual switchmode power supplies.

Determining the sample size necessary to pass the tentative final monograph pre-operative skin preparation study requirements

Determining the sample size necessary to pass the tentative final monograph pre-operative skin preparation study requirements Iteratioal Joural of Cliical Trials Paulso DS. It J Cli Trials. 016 Nov;3(4):169-173 http://www.ijcliicaltrials.com pissn 349-340 eissn 349-359 Editorial DOI: http://dx.doi.org/10.1803/349-359.ijct016395