Calculation of Harmonic-constrained Low Voltage Dynamic Operating Envelopes

Dynamic operating envelopes (DOEs) establish the feasible range of import and export values for prosumers, moving away from static limits and thereby making it possible to free up more network capacity. With the growing penetration of distributed energy resources (DERs) in low-voltage (LV) distribution networks, methods to quantify DOEs are becoming increasingly important. DERs are also sources of harmonics that until now have been neglected in studies on DOE quantification. We present a non-linear, three-phase harmonic optimal power flow model defined in the current-voltage variable space. The model calculates both export and import DOEs in a real-world LV feeder and representative 906-node LV network. We also examine the impact of non-static DER power factors, the use of root-mean-square (rms) voltage limits in the optimization, and the role of considering harmonic injections. Results illustrate scalability of the developed model and show that considering harmonics reduces DOE export values. The decrease does not occur only because of reaching the total harmonic distortion (THD) limit but also because of a more appropriate representation of rms voltage and current values. Conversely, DOE import values increase under the detailed harmonic model, highlighting potential for higher network imports.These findings provide practical insights for system operators. Incorporating harmonicaware DOEs can improve near real-time network utilization and enable effective management and optimization of active endusers’ DER portfolios.