【正文】 ration can significantly increase the reliability. In addition, fans inside the inverter have a limited lifetime and deserve special attention [12]. Nevertheless, there are other aspects (. humidity, modularity, and packaging) that also require special attention beyond the technical improvement and are not a part of this present study. 3. Failure modes of small wind turbine systems The need for long term field data is of great importance to the evaluation of technical and economical performances. Long term failure and reliability data for wind turbine subsystems are readily available because of the significant (and growing) number of wind turbines of various age, type and location in existence across the world. This information facilitates the identification of the most probable failure subsystems in WECS, and allows optimization of the design features as well as system configuration. A review has been conducted for the failure distribution of SWT subsystems. Data published by The Scientific Monitoring and Evaluation Programme (WMEP) in Germany [16], Elsfork, Sweden [17], and Landwirtschaftskammer, SchleswingHolstein, Germany (LWK) [18] are presented in Fig. 2 along with the large wind turbine data provided by DOWEC project in Netherland [19]. In the review, mechanical subsystems consist of drive train, gears, mechanical brakes, hydraulics, yaw system hubs, and blade/pitch while, the generator, sensors, electric system, and control system prise the electrical subsystem. The distribution of the number of failure depicted in Fig. 2 shows that the sum of the failure rates of the electrical related subsystems is higher in contrast to the mechanical subsystems. A pletely reverse portrait exists for large wind turbines where the failure mode is principally dominated by the mechanical subsystems. Indeed, the electric and control system posed of power electronic ponents is an integral part of any PCS which not only dictates the performance but also bear a major fraction of the overall cost for a small WECS. As a whole, in order to ensure 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