Comparison of Linear and Conic Power Flow Formulations for Unbalanced Low Voltage Network Optimization

Applications of optimization models for electricity distribution networks

“…The voltage‐dependency of the power consumption is modeled in various ways, including constant‐impedance models (Sharma et al, 2015), ZIP models (Gutierrez‐Lagos & Ochoa, 2019; Meng et al, 2018), and CVR factor models (Jha et al, 2019); Y. Liu et al (2019b) even include harmonic components in a constant‐impedance model. Demand response : Other control schemes directly change the load demand. This can include guarantees that the total demand within a given time period is not changed, that is, it is only shifted around within that period (Sharma et al, 2015), or that it is not excessively concentrated (Sharma et al, 2015), or that the demand is at most reduced to a guaranteed level (Vanin et al, 2020). Switches : Switches naturally appear as part of network reconfiguration problems, which are not very common in the literature on unbalanced OPF.…”

“…Several approaches exist to deal with this: some authors relax the integer variables as continuous ones (Bazrafshan et al, 2019; Sharma et al, 2015), with additional penalty terms for deviations from the discrete values (Nguyen et al, 2019) or a heuristic for mapping to a higher or lower discrete value (Gutierrez‐Lagos & Ochoa, 2019). Other authors approximate or relax the network model and solve the mixed‐integer problem directly (Jha et al, 2019; Vanin et al, 2020).…”

“…More situation‐specific objectives have also been used, including: Minimizing unbalance through the sum of squares of the negative sequence voltage magnitude at each bus (Araujo et al, 2013; J. Wang et al, 2019); Minimizing harmonics through the sum of squares of harmonic voltage magnitudes (J. Wang et al, 2019); Minimizing PV curtailment (M. Z. Liu et al, 2020; Nguyen et al, 2019; Ricciardi et al, 2019); Minimizing the number of curtailed loads (Vanin et al, 2020); Maximizing EV charging, inversely weighted by the charge level of the individual EVs (Richardson et al, 2012). Maximizing welfare in markets with distribution marginal locational pricing (Bai et al, 2018; Y. Liu et al, 2018; these references do not include an unbalanced model). …”

“…• Demand response: Other control schemes directly change the load demand. This can include guarantees that the total demand within a given time period is not changed, that is, it is only shifted around within that period (Sharma et al, 2015), or that it is not excessively concentrated (Sharma et al, 2015), or that the demand is at most reduced to a guaranteed level (Vanin et al, 2020). • Switches: Switches naturally appear as part of network reconfiguration problems, which are not very common in the literature on unbalanced OPF.…”

“…Gurobi (Carquex et al, 2018;Göl & Abur, 2014) CPLEX (Jha et al, 2019;Ricciardi et al, 2019) (Vanin et al, 2020) (M. Z. Liu et al, 2020;Teimourzadeh et al, 2019) CPLEX, Ipopt and Mosek (Vanin et al, 2020) (Akhijahani et al, 2019;Chen et al, 2016) Gurobi (Vanin et al, 2020)…”