In this study, a $CO_2$ air-conditioning system was investigated with different types of electrically driven compressors, parallel flow type gas cooler, four-pass type evaporator, internal heat exchanger integrated with accumulator, and electric expansion valve. The experimental study was conducted under various operating conditions (ie., different rotational compressor speeds, air inlet temperatures and air velocity coming into heat exchangers). The experimental results showed the cooling capacity was 3.5kW at $35^{circ}C$ ambient temperature when the vehicle was idle (ie., the worst condition for cooling off the gas cooler). In terms of performance effect of the compressor, the e-RP model had a slightly better cooling capacity and coefficient of performance than the e-GR model under the same test conditions. An experimental equation for optimum cooling-performance control was also suggested based on the results. A high-pressure control algorithm for the super critical cycle was determined to achieve both maximum cooling performance and efficient energy consumption. The results from the experimental equation coincided with those of previous experimental studies.