Power System Security is broader. Power system steady state, transient stability, planning,etc all comes within security study of power system
Power system Security is Broader. And stability is the part of security or can say initial security is maintain the stability.
Security is defined as the ability of a power system to withstand sudden disturbances. This requires that sufficient generation and transmission resources are available to meet projected needs plus reserves for contingencies. Thus, security implies that the power system will remain intact even after outages or equipment failures.
Power system stability is the ability of an electric power system, for a given initial operating condition, to regain a state of operating equilibrium after being subjected to a physical disturbance, with most system variables bounded so that practically the entire system remains intact.
Thus, it is not logic to compare between them to decide which one is broader. Each of them can cause a problem to the other. A security problem can cause a stability problem and vice versa.
In my opinion, this question is a trap. We cannot say which topic is broader because they are not in the same dimension. However, for the same reason this question is valuable to be discussed. Basically, "security analysis in a power system" is used a static method to ensure healthy of a system from defined N minus contingencies. This is quite difference from a study in dynamic model under "power system stability".
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