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In our world of today developing incredibly fast, load frequency control (LFC) is an indispensable and vital element in increasing the standard of living of a country by providing a good quality of electric power. To this end, rapid and notable development has been recorded in LFC area. However, researchers worldwide need for the existence of not only effective but also computationally inexpensive control algorithm considering the limitations and difficulties in practice. Hence, this paper deals with the introduction of (1 + PD)-PID cascade controller to the relevant field. The controller is simple to implement and it connects the output of 1 + PD controller with the input of PID controller where the frequency and tie-line power deviation are applied to the latter controller as feedback signals also, which is the first attempt made in the literature. To discover the most optimistic results, controller gains are tuned concurrently by dragonfly search algorithm (DSA). For the certification purpose of the advocated approach, two-area thermal system with/without governor dead band nonlinearity is considered as test systems initially. Then single/multi-area multi-source power systems with/without a HVDC link are employed for the enriched validation purpose. The results of our proposal are analyzed in comparison with those of other prevalent works, which unveil that despite its simplicity, DSA optimized (1 + PD)-PID cascade strategy delivers better performance than others in terms of smaller values of the chosen objective function and settling time/undershoot/overshoot of the frequency and tie-line power deviations following a step load perturbation.