Recent research has applied semidefinite programming (SDP) to the optimal power flow (OPF) problem. Extending SDP formulations to include the ZIP load model, which consists of constant impedance, constant current, and constant power components, is necessary for many practical problems. Existing SDP formulations consider constant power components and can be easily extended to incorporate constant impedance components. With linear dependence on voltage magnitude, constant current components are not trivially formulated in a manner amenable to SDP. This letter details an approximate representation of ZIP loads in an SDP relaxation of the OPF problem.
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Molzahn et al. (2014) studied this question.
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