As shown in Figure, the receiving end current is equal to the sending end current, i.e., IS = IR. The series voltage VQ is injected in such a way that the magnitude of the injected voltage is made proportional to that of the line current. Furthermore, the phase of the voltage is forced to be in quadrature with the line current. We then have,(10.20)
The ratio λ/X is called the compensation level and is often expressed in percentage. This compensation level is usually measured with respect to the transmission line reactance. For example, we shall refer the compensation level as 50% when λ = X /2. In the analysis presented below, we assume that the injected voltage lags the line current.
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