【正文】 e high reliability, attention should be focused on small WECS with straightforward but reliable PCS design that ensure easy maintenance and repair as well as less plexity in the control architecture for an optimum life. 4. Mathematical analysis A mathematical analysis of the power losses in the power electronics ponents, ., semiconductors (diodes/IGBTs) is required in order to plete a reliability analysis of the configuration. The losses for the power conditioning systems are strongly dependent on the voltage and current waveforms. Simplified analytical derivation of voltage and current equations associated with the individual semiconductor ponents are derived to determine the losses. The loss calculation presented in this investigation focus on the losses generated during the conduction and switching states of the semiconductors. Afterwards, the 10 mathematical analysis for reliability of the system is presented. . Loss analysis for a PMG based SWT For the 3phase diode bridge rectifier, the losses are calculated for a single diode from the known voltage and current equations. It is assumed that the current and voltage in the 3phase diode bridge rectifier are equally distributed in the diodes. Knowing the voltage and current for one diode, the losses can be obtained for all the diodes in the bridge rectifier. The conduction losses, DBdcdP, for the diode is expressed as dfoDBdcd IVP ?, （ 1） Under the assumption of a linear loss model for the diodes, the switching loss in each diode is given by [20] drefdcdrefdcSRWTDB dcd IIVVEfP,1,1, ??? （ 2） The total losses of the 3phase diode bridge rectifier, DBdcdP, for all 6diodes is given by DB DBsw tDB dc d tDB dswDB dcdDBdt PPPPP , 66 ???? （ 3） The conduction and switching loss of the Boost Converter (BC) is calculated by assuming an ideal inductor (LD) at the boost converter input. For a boost configuration, the IGBT is turned on for the duration d while the diode (D) conducts for the duration (1 d). The conduction current of the IGBT is the input current Idc1 while the inverter input current Idc2 is given by ? ?dII dcdc ?? 112 （ 4） The conduction loss for the diode and IGBT can be obtained by multiplying their onstate voltage and current with the respective duty cycle and is given by [21] ? ? ? ?dIrVIP dcdfdcBC dcd ???? 11o1, (5) ? ? dIrVIP dccecedcBC IGB Tcd ??? 101, （ 6） The mutation voltage and current for the boost converter is the DC link voltage, Vdc2 and input current to the converter, Idc1. The switching losses for a specific switching frequency, fSW of the diode and IGBT in the BC are given by [21] drefdcdrefdcSRswBC dsw IIVVEfP,1,2, ??? （ 7） ? ? I G B Tr e f dcI G B Tr e f dcO F FONSWBC I G B Tsw I IV VEEfP , 1, 2, ???? （ 8） The sum of (5)–(8) gives the losses of the BC as 11 ? ? ? ? ? ?BC I GB TSWBC I GB TcdBC dSWBC dcdBC I GB Tdt PPPPP , ????? （ 9） Most of the SWT systems integrate a single phase inverter for industrial as well as residential application. With the exclusion of snubber circuit, the inverter consists of four switches and four anti parallel diodes as presented in Fig. 1. The conduction losses of a diode and IGBT for the inverter can be expressed as [22], omfomdI N Vdcd IVMIrMP 02,1 c os821c os381 ?????? ???????? ?? ??? （ 10） omceomceI N VI G B Tcd IVMIrMP 02,1 c os821c os381 ?????? ???????? ?? ??? （ 11） An approximated solution for the diode and IGBT switching losses at an output current io is given by [21] ? ? I G B Tr e f OI G B Tr e f dcO F FONSWI N V I G B TSW I IV VEEfP , 2,1 1 ?? ? （ 12） drefOdrefdcSWIN V dSW I IVVfP,2,1 1?? （ 13） The total loss of the inverter is obtained as the sum of (10)–(13) ? ? I N V I GB TSWI N VdSWI N VI GB TcdI N VdcdI N V I GB Tdt PPPPP , ????? （ 14） The power loss of the conversion stage of the PMG based SWT is given by ? ? ? ?I N V I G B TdtBC I G B TdTDBdtP M Gt PPPP ?? ??? , （ 15） . Reliability analysis for a PMG based SWT Reliability is the probability that a ponent will satisfactorily perform its intended function under given operating conditions. The average time of satisfactory operation of a system is the mean time between failures (MTBF) and a higher value of MTBF refers to a higher reliable system and vice versa. As a result, engineers and designers always strive to achieve higher MTBF of the power electronic ponents for reliable design of the power electronic systems. The MTBF calculated in this paper is carried out at the ponent level and is based on the life time relationship where the failure rate is constant over time in a bathtub curve [23]. In addition, the system is considered repairable. It is assumed that the system ponents are connected in series from the reliability standpoint. The lifetime of a power semiconductor is calculated by considering junction temperature as a covariate for the expected reliability model. The junction temperature for a semiconductor device can be calculated as [24]： JAlossAJ RPTT ?? （ 16） losP is the power loss (switching and conduction loss) generated within a semiconductor device and can be found by replacing the losP from the loss analysis described in Section for each ponent. The life 12 time, ? ?JTL of a semiconductor is then described as ? ? ???????? ??JJ T