With the advancement in computations and the introduction of renewable energy sources, flexible demands can play the main role in load frequency control. Some industrial and domestic loads can provide synthetic inertia that aids the natural inertia provided by conventional generators. This enhances small signal stability performance, as the total system inertial would be larger. The load frequency control (LFC) system with flexible demand-side control capability, in general, forms a time delay system. In this paper, a new approach to analyse the stability of the LFC system with controllable loads and communication delay is proposed by transforming the transcendental characteristic equation to a nonlinear equation in the complex frequency domain. The marginal frequencies are used to determine the DM. The sweeping test, together with the binary iteration algorithm, is implemented to find these marginal frequencies, yielding accurate DM computation. The method offers advantages in terms of accuracy and easy implementation. The paper also examines the influence of the flexible demand response on frequency stability as the flexible load participation factor is increased beyond 0.2. As the flexible demands participation factor is increased beyond 0.2, the stability of the system becomes delay-dependent.