A CCC has superior commutation ability when compared to a line commutated converter used in a conventional HVdc system. This paper models the commutating and post commutation period of the converter circuit in theoretical style, and formularize the commutation and extinction equation with mathematical treatment. The equations express the relations among firing angle, overlap angle, effective margin angle, state variables and converter parameters, and compose nonlinear simultaneous equations. The fine CCC commutation characteristics are shown by using the equations to several commutation capacitor configurations, The authors propose the predictive firing angle calculation method for the constant margin angle control (A gamma'R) operation of a CCC-HVdc system as the practical application of the obtained equations. The obtained equations cannot be solved algebraically for their complexity, then convergence calculations of numerical analysis are assessed, but it is hard to secure the derivation to the various operating conditions. The authors propose to apply an approximate polynomial equation from the off line calculated characteristics to achieve the firing angle predicting equation, The design index for approximation polynomial of A gamma'R is presented to make the polynomials to low order. The suitability of the proposed predictive A gamma'R is studied with simulations by applying it to the converter controller and it can make the most of the CCC availability.