In this work, the Sub-Synchronous Control Interaction (SSCI) phenomena is investigated in an ac -dc system consisting of a Line Commutated Converter (LCC) connected to the series compensated ac side using the Generalized Nyquist stability Criterion (GNC). To do this, the impedance response of the LCC together with the ac filters looking from the Point of Common Coupling (PCC) bus is first obtained from an improved LCC analytical model. The ac system includes a transmission line model in series with the series compensation capacitor. The impedance frequency response of the ac network is then obtained by exciting an Electromagnetic Transients (EMT) model of the ac network (after isolation from the converter) with a multi-sine signal current signal and conducting a Discrete Fourier Transform (DFT) of the resulting voltage. With the impedance of both side available, GNC is employed to determine the Proposed "Harmonic Stability Margin (HSM)" index of the system. This is a measure of the propensity of the system to experience harmonic or sub-harmonic instability. The HSM is a function of the system parameters such as the controller gains, and especially has a linear relationship with Short Circuit Ratio (SCR). This allows easy determination of the critical SCR at the onset of instability from frequency response analysis at any other SCR value. The results are validated by EMT simulations.