For an alternating current transmission line, power flow through the line is proportional to the sine of the difference in the phase angle of the voltage between the transmitting end and the receiving end of the line. Where parallel circuits with different capacities exist between two points in a transmission grid (for example, an overhead line and an underground cable), direct manipulation of the phase angle allows control of the division of power flow between the paths, preventing overload. Quadrature boosters thus provide a means of relieving overloads on heavily laden circuits and re-routing power via more favorable paths.