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Analytic Calculation of the DC-Link Capacitor Current for Pulsed Three-Phase Inverters
Folker Renken
Automotive Systems Powertrain Siemens VDO Automotive AG Siemensstraße 12 D-93055 Regensburg Phone: ++49 941 790 5385 Fax: ++49 941 790 90541 E-Mail:

Abstract - For pulsed three-phase inverters with symmetrical load the capacitor current inthe dc-link circuit is analytically calculated. These calculations can be applied for a constant dcvoltage as well as for sinusoidal modulated voltages and sinusoidal currents at the output. The additional load of the dc-link capacitor caused by harmonic currents of the filter circuit or by switching transitions of semiconductors is examined, too. At last, the calculations are examined by practicalmeasurements.

In figure 2 the pulsed control scheme of the three-phase inverter is presented. Above the three 120°-shifted sinusoidal control voltages us1, us2, and us3 are compared with a higher frequency triangle shaped modulation voltage um. If one phase of the sinusoidal control voltages is higher than the modulation voltage the high-side switch of this phase is turned-on. In the othercase the low-side switch of this bridgeleg is connected through. In this way the frequency of the
u um us1 us2 us3

I. INTRODUCTION Pulse inverters in uninterruptible power suppliers became generally accepted with the further development of disconnectible power semiconductors in the last years [1]. The dc-link capacitors contribute substantially to the volume, to the weight and to the costs ofthese inverters. For this reason the necessary expenditure of capacitors must be determined exactly to prohibit over design if possible. In most applications the dc-link capacitor effort is dependent on the load current. For pulsed three-phase inverters with symmetrical load the capacitor current in the dc-link circuit is analytically calculated. The power stage of the pulse inverter is presented inthe following figure.
iE Ld iCd uE Cd SL1 SL2 SL3 id SH1 SH2 SH3



uP1- G


uP2- G



uP3- G


iP1 LP1 iP2 LP2 iP3 LP3 uP1uP2uP3-

L1 L2 L3 CP1 CP2 CP3 Y

uP12 ud

uP12 G


ω1t -ud uP23 ud ω1t -ud uP31 ud ω1t -ud
90° 180° 270° 360°

Fig. 1: Power stage of a pulsed three-phase inverter

The power stage consists out of threeinverter-legs, an input filter circuit with dc-link capacitors and a three-phase filter circuit on the alternating voltage side. II. PULSE CONTROL SCHEME OF THE INVERTER For the calculation of the dc-link capacitor current, three sinemodulated phase voltages uP1-, uP2- and uP3- are assumed, whose fundamental part has the same amplitude and a phase shift angle of 120° to each other. Beyond that asymmetrical load with any phase shift angle ϕP1 as well as three-phase currents iP1, iP2 and iP3 at the output of the inverter are presupposed. The dc-link voltage ud at the dc-input of the inverter bridge is assumed as constant.

uP31 G

Fig. 2: Pulse control scheme of the three-phase inverter

triangle shaped modulation voltage um determines the pulse frequency of the inverter. Thefundamental frequency is given by the frequency of the control voltages. In the middle of the figure three half-bridge voltages uP1-, uP2-, and uP3- with the fundamental oscillation frequency are shown. The lower part of the figure shows the connected voltages uP12, uP23 and uP31 between the phases. It can clearly be seen - that with subtraction of the phase voltages during one period - two pulses areformed. These voltage waveforms at the load have approximately sinusoidal output currents in the individual phases of the inverter as consequence. For ideal sinusoidal phase currents the generation of the input current id in a three-phase inverter is presented in figure 3. The modulation factor amounts thereby to m = 0.8 and the fundamental phase shift angle is ϕP1 = 45°. Above the output voltages...