The aim of the security and stability control system (SSCS) is to maintain active power balance and frequency stability. For large SSCS, it is difficult to find the state space and the transition rates of the paths. The flat design yields more complex topology. Considering the random outages, the ultra-high-voltage dc (UHVDC) has more capacity levels and states. The existing evaluation cannot quantify the power balance capability of the SSCS. This paper newly quantifies active power balance capability of the multi-level SSCS with partial or complete outage of the UHVDC. An incidence matrix is proposed to describe the topology of the SSCS. A recursive solution to calculate the transition rates is proposed. The equivalent downward transition rate is newly defined. The increasable generation and the transition rates of the UHVDC at any initial state are newly included. The numerical analysis shows that the incidence matrix and recursive algorithm reduces the calculation effort for the practical SSCS with multi-level, redundancy component, and flat design. The active power balance capability of the SSCS is decided by the increasable power, the reduced generation and the downward transition rate.