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Power quality (PQ) issues are direct consequences of integrating power electronics components and non-linear loads into microgrids. These issues can also be triggered by an unbalanced loading in the microgrid. Certainly, they affect the daily operation scheduling of the microgrid. This paper proposes an optimal harmonic power flow (OHPF) framework for the daily optimal scheduling of a grid-connected microgrid, which is constructed by combining the optimization formulation and harmonic power flow (HPF). Within the framework, PQ is evaluated by observing three indices including voltage magnitude, voltage total harmonic distortion (THD V), and voltage unbalance factor (VUF). A non-iterative mitigation scheme based on demand side management (DSM) is proposed to avoid PQ indices violations and is integrated into the optimization formulation part of the OHPF as a set of load constraints. The proposed constraints allow a flexible combination of different DSM actions including load shedding and interphase load transfer (ILT). Furthermore, the constraints to limit voltage magnitude, voltage THD, and VUF are integrated into the formulation in the form of penalty functions. The software implementation of the proposed OHPF involves Julia-based JuMP.jl and Gurobi solver for optimization part and OpenDSS for harmonic load flow part. The effectiveness of the proposed framework is tested using a modified IEEE 37-bus feeder for different load fluctuations, which allow different combinations of PQ indices violations. The assessment involves both normal and intentional islanding conditions. The results demonstrate that, under different random events, the proposed framework can avoid the violation of PQ indices limits in most cases without adding an excessive computational burden to the original optimization and harmonic load flow algorithms. • Power quality-constrained scheduling framework for a grid-tied microgrid is proposed. • Power quality disturbances are avoided by a set of DSM constraints. • DSM is designed to enable a flexible combination of load shedding and transfer. • Case studies are applied to the modified IEEE 37-bus feeder. • The DSM effectiveness is influenced by the tightness of the load deviation limit. [ABSTRACT FROM AUTHOR]