【正文】 red as plex systems prising mechanical subsystems (rotor, hub, and gearbox) and electrical subsystems (converter/inverter, rectifier, and control) and loads. Failures in any of the subsystems can cause substantial financial loss. The problem bees more severe if the system is offgrid leading to unavailability of power. In light of this, there is a need for reliability evaluation of small WECS in order to determine a configuration that is efficient and reliable. Almost all mercially available small wind turbines are based on PMGs. The power conditioning systems (PCSs) for grid connection of the PMG based configuration requires a rectifier,boost converter, and a gridtie inverter. The reliability analysis of such PCS is greatly influenced by the operating conditions, ., covariates and therefore it is desirable to investigate the magnitude of their effects on the system reliability. Reliability calculation consider the voltage or current as a covariate for an electromechanical system [1], while the reliability of power electronic ponents is strongly influenced by the ponent temperature and variations [2]. Knowledge of the reliability of power electronic ponents is a key concern when differentiating between topologies. However, recent research intermittently endeavors to determine the reliability and advancement of the inverter rather than the PCS [2–4]. Most of the reliability calculations are 8 based on the accessible data provided by the military handbook for reliability prediction of electronic equipment which is criticized for being obsolete and pessimistic [5,6]. A parative reliability analysis of different converter systems has been carried out based on the military handbook by Aten et al. [6]。 systemsystemMT BF ?1? （ 21） tsystem systemeR ??? （ 22） . Reliability calculation for a PMG based SWT The reliability analysis for the PCS of the PMG based configuration is performed by the formulation described in Sections and . A Matlab program is developed which putes the ponent junction temperature using the conduction and switching loss formulations described in Section . After the determination of the failure rate for each ponent using (19), the program sums up the failure rates to evaluate the total system failure rates (20).The reliability of the system is obtainable once the system MTBF (21) is known. A brief schematic of the program and its operating procedure is given in Fig. 3. 5. Results The analytical calculations illustrated in the preceding section were carried out to determine the MTBF and consequently the reliability of a SWT configuration for a preassumed wind speed condition. The rated power for the wind turbine is assumed to be kW. The expected operating condition of the rated wind speed is considered as 13 m/s. It is assumed that the generator speed is proportional to the output voltage of the 3phase bridge rectifier which provides a rated 280 volt output at the rectifier terminal at the rated rotational speed. The switching frequency of the boost converter and inverter is considered as 20 kHz which is usual for 13 most of the practical applications [27]. In order to investigate the worst case scenario of the power loss in the numerical simulation study, the modulation index is assumed unity and the load current is assumed to be in phase with the output. A standard grid is considered which will reflect the optimum behavior as required by the optimum wind turbine operation. The analytical calculation is based on the data sheet on the EUPEC IGBT module FP15R12W1T4_B3 [28] and the parameters are provided in Appendix A (Table ). The results of the analysis following the procedure outlined in Section are presented in Table 1. It is well understood that small wind turbines and so as the PCSs need to be affordable, reliable and most importantly, almost maintenance free for the average person consider installing one. The calculation revealed that the PCS failure rate is 1:9009 10 5 and MTBF is 5:2607 104 h (6 years). As can be seen, the need of replacing the PCS corresponds to the MTBF value of 6 years leads to a more vulnerable system as pared to the life span of the wind turbine system, which is usually 15–20 years. Also from the financial standpoint, replacement of such a plex PCS is expensive and needs a highly skilled repair professional. Fig. 4 shows the reliability of the PCS for a period of 1 year (8760 h). The result reveals that the reliability of the PCS drops to 84% after 1 year and is less than 50% at 40,000 h ( years) as shown in Fig. 5, which is undesirable for a SWT turbine due to high maintenance and replacement costs. In addition, a reliable PCS is desirable by sacrificing a small percentage of the total system efficiency. The analysis thus helps to recognize that an optimum substitute PCS design is fundamental prior to operation of the small wind turbine system leading to a more robust system. The emphasis is then given to identify the most important subsystems in the PCS that is the least reliable. To achieve this objective, the MTBF of the bridge rectifier is decreased by 50% while the MTBFs of the boost converter and inverter are unchanged. In the same way, the effect of changes in the MTBFs for each of the boost converter and inverter on the systems reliability has been calculated and is presented in Fig. 6 along with the actual reliability of the system. It is observed from that the inverter is the dominating subsystem while, the boost converter has less significant effect than the bridge rectifier. It has been found in the literature that the inverter is the least reliable system [29]. Noheless, a higher reliability of the PCS is achievable by ch。 however, the calculated relia