Characterization of Harmonic Resonances in the Presence of the Steinmetz Circuit in Power Systems

Abstract

An electric power system is expected to operate under balanced three-phase conditions; however, single-phase loads such as traction systems can be connected, leading to unbalanced line currents. These systems are single-phase, non-linear, time-varying loads closely connected to the utility power supply system. Among problems associated with them, special consideration must be given to the presence of unbalanced and distorted currents (Barnes & Wong, 1991; Capasso, 1998; Hill, 1994; Howroyd, 1989; Marczewski, 1999; Qingzhu et al., 2010a, 2010b). These operating conditions damage power quality, producing undesirable effects on networks and affecting the correct electric system operation (Arendse & Atkinson-Hope, 2010; Chen, 1994; Chen & Kuo, 1995; Chindris et. al., 2002; Lee & Wu, 1993; Mayer & Kropik, 2005). The unbalanced currents cause unequal voltage drops in distribution lines, resulting in load bus voltage asymmetries and unbalances (Chen, 1994; Qingzhu et al., 2010a, 2010b). For this reason, several methods have been developed to reduce unbalance in traction systems and avoid voltage asymmetries, for example feeding railroad substations at different phases alternatively, and connecting special transformers (e.g. Scott connection), Static Var Compensators (SVCs) or external balancing equipment (ABB Power Transmission, n.d.; Chen, 1994; Chen & Kuo, 1995; Hill, 1994; Lee & Wu, 1993; Qingzhu et al., 2010a, 2010b). The last method, which is incidentally not the most common, consists of suitably connecting reactances (usually an inductor and a capacitor in delta configuration) with the single-phase load representing the railroad substation (Barnes & Wong, 1991; Qingzhu et al., 2010a, 2010b). This method is also used with industrial high-power single-phase loads and electrothermal appliances (Chicco et al., 2009; Chindris et. al., 2002; Mayer & Kropik, 2005). This delta-connected set, more commonly known as Steinmetz circuit, (Barnes & Wong, 1991; Jordi et al., 2002; Mayer & Kropik, 2005), allows the network to be loaded with symmetrical currents. Several studies on Steinmetz circuit design under sinusoidal balanced or unbalanced conditions aim to determine the reactance values to symmetrize the currents consumed by the single-phase load. Some works propose analytical expressions and optimization techniques for Steinmetz circuit characterization, (Arendse & Atkinson-Hope, 2010; Jordi et. al, 2002; Mayer & Kropik, 2005; Qingzhu et al., 2010a, 2010b; Sainz & Riera,