Apparatus and method for controlling a variable displacement compressor

A compressor with variable capacity has a control valve (CV) for controlling the displacement of the compressor. When the pressure in a discharge chamber (22) of the compressor (discharge pressure) equal to or higher than a predetermined threshold (L1), a controller (70) establishes a duty ratio a that is sent to the control valve (CV), to 0%, to limit the selling pressure. As a result, the compressor displacement is minimal and the discharge pressure is lowered. Therefore, the lines of an external coolant circuit does not receive an excessive load on the basis of a high discharge pressure. When the displacement of the compressor is minimum, the circulation of the refrigerant is stopped in the refrigerant circuit and containing the refrigerant, the lubricant circulates within the compressor.