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This study presents a bridgeless Cuk converter-fed brushless DC (BLDC) motor drive for an air conditioning system. A new approach of speed control of BLDC motor is proposed by controlling the voltage at DC bus using a single voltage sensor. The proposed drive utilises a bridgeless Cuk converter operating in discontinuous inductor current mode (DICM) for the power factor correction (PFC) and improved power quality (PQ) at the AC mains for a wide range of speed control. The bridgeless Cuk converter operating in a DICM gives an inherent PFC and requires a simple voltage follower approach for the voltage control. The bridgeless converter topology is designed for obtaining the low conduction losses and requirement of low size of heat sink for the switches. The proposed system is designed and its performance is simulated for an air conditioning system to operate over a wide range of speed control with near unity power factor at AC mains. Finally, the performance of the proposed drive obtained in simulation is validated with test results on a developed drive for its operation over a wide range of speed control with improved PQ at AC mains.