Development of high-power superconducting applications requires the accurate estimation of AC losses in the superconductor. In applications such as superconducting magnetic energy storage, the charge/discharge/persistent switching frequency of the coil, resulting from pulse width modulation control algorithms, is usually in the kilohertz regime. Therefore, a thorough investigation of the losses in the kilohertz regime of AC currents superimposed on large DC currents is essential in order to ensure the device stable operation at a predefined temperature. We describe here a unique experimental setup designed and built for characterizing AC losses in superconducting wires and coils under such special conditions. To minimize the eddy currents induced in the apparatus, a cryostat vacuum vessel was made of Delrin, an insulating synthetic polymer. The measurement setup allows driving DC currents up to 150 A and superimposed AC currents with amplitudes up to 10 Arms and frequencies up to 18 kHz. The system utilizes conduction cooling to reach a wide range of temperatures between 6 and 100 K and allows measurements of 10 cm long superconducting wires and coils with a diameter of 40 cm. The loss is measured by the electrical method, i.e., by direct voltage and current waveform measurement, achieving a resolution better than 100 nW. The system described here will assist in developing superconducting wires and coils for high-power applications.