Abstract: The optimal load dispatch of thermal units is an important model for the economic operation of the power system, and an essential teaching component in the foundational curriculum "Power System Analysis" for undergraduate students studying power systems. Typically, textbooks adopt the classical method based on the equal incremental cost principle to solve this problem, and explain the corresponding physical meaning in detail. Since the classical method is derived without considering the physical constraints of the upper and lower bounds of thermal power units, some textbooks augment this method by considering these constraints, that is, if the unconstrained optimal solution of a unit violates the upper (lower) bound constraints, the optimal solution corresponding to this unit will be constrained to the corresponding upper (lower) output bound, and then the other thermal power units will be re-dispatched according to the equal incremental cost principle. However, simple scenarios reflect that the supplementary content has a limited area of application. For this reason, this paper re-explores the optimal load dispatch of thermal power units, and presents sufficient and necessary conditions for the supplementary content to be applied. For undergraduate and postgraduate students, methods that consider the upper and lower bounds of the thermal units are proposed respectively, and strict theoretical derivations are performed. Theoretical derivations and quantitative simulation results illustrate that the supplementary method can be applied to most scenarios with few units, while it cannot be applied to cases with many units. Thus, the proposed method can be extended to scenarios with a greater number of units. This paper is expected to support the teaching process and the textbook re-editing of "Power System Analysis".