The security region constraints of power systems cannot be approximated by a set of linear constraints in a general sense. The operational constraints of power systems, including security region constraints, are typically nonlinear and non-convex. However, in certain cases, linearization techniques can be used to approximate the nonlinear constraints of power systems with a set of linear constraints. For instance, for small deviations from the nominal operating point, the nonlinear constraints can be approximated by linear constraints using a Taylor series expansion. Moreover, linearization techniques can be used to obtain a linear approximation of the constraints around a particular operating point. However, these linear approximations may not hold true for all operating points, and they may not capture the full range of nonlinear behaviors of the system. Therefore, while linearization techniques can be useful to analyze the behavior of power systems, they cannot fully capture the nonlinearities of the system.

Power systems are complex nonlinear systems with a large number of interconnected components such as generators, transmission lines, transformers, and loads. The behavior of these components is governed by nonlinear physical laws, such as Kirchhoff's laws, which cannot be accurately represented by linear equations.

Furthermore, the security region constraints of power systems are typically related to the stability and reliability of the system. These constraints often involve nonlinear functions of the system variables, such as power flows, voltages, and frequencies, and they may depend on the operating conditions of the system.

I think if the changes of parameters are small ,the linearization can help and the error will be acceptable.

In the large variation of parameters ,a piecewise linearization may be help with a some extended mathematical operation.

thank you