# Effect of Harmonics on Ferroresonance in Low Voltage Power Factor Correction System--A Case Study
## 1 Introduction  
Due to the increasing number of nonlinear loads, current and voltage harmonics are becoming more common in power systems [1, 2]. Nonlinear loads inject current harmonics into the power system, resulting in voltage harmonics at the system impedances [2, 3]. The distorted voltage affects all linear and nonlinear loads connected to the power system. In general, current and voltage harmonics cause various problems ranging from minor to severe. For power systems to function properly, voltage and current harmonics must be limited. Limits are defined by standards, grid codes, and regulations in each country [4, 5]. The limits define the maximum voltage and/or current harmonics for public distribution systems, but each industrial facility is responsible for the limits within the facility [6]. Numerous examples from industry show that compliance with limits within the industrial facility does not guarantee elimination of problems associated with harmonics. Current and voltage harmonics cause numerous problems such as increased losses on busses, lines, and electrical machines [7], reduction in power factor, overheating and/or complete damage to conventional PFC devices, reduced efficiency, audible noise, undesirable operation of protective devices, difficulties with sensitive devices, parallel and series resonances [8, 9, 10, 1, 1], etc. Moreover, rare and dangerous phenomena due to harmonics may occur in practice, which are not reported in the literature. In this paper, an example of such a phenomenon, a three-phase ferroresonance of the detuned reactor triggered by switching on the capacitor stage of the automatic detuned PFC system in an industrial plant with high harmonic content, is analyzed. Ferroresonance is a rare nonlinear phenomenon in which energy oscillates between a capacitive element and a nonlinear inductive element that alternately goes into saturation. During ferroresonance, high voltages and currents with abnormal waveforms and harmonic content occur [11; 12]. Ferroresonance can be triggered by a variety of transient events that cause the system to jump from a stable steady state to the ferroresonant steady state. The phenomenon of ferroresonance is complex to analyze and predict due to its nonlinearity and sensitivity to small changes in the system parameters and initial conditions [13]. As a result, repeatability in simulations and experimental studies is rare [14]. Numerous examples of ferroresonance in practice have been reported [12; 15; 16; 17], while the electrical system configurations in which ferroresonance may occur are identified as follows: [18; 19]: (a) voltage transformer energized through the grading capacitance of open circuit breakers, (b) voltage transformer connected to an ungrounded neutral system, (c) capacitor voltage transformer, (d) power transformer supplied accidentally on one or two phases, (e) power transformer, fed through a long transmission cable with low short-circuit power, (f) power transformer connected to a compensated transmission line connected in series, (g) power transformer connected to a de-energized transmission line running in parallel with an energized line, and (h) inductive neutral networks. However, the ferroresonance triggered by the three-phase opening/closing of the circuit breaker is extremely rare [20; 21]. Recent studies are concerned with modeling phenomena [22; 23; 24], protective measures to prevent the occurrence of ferroresonance [25; 26; 27], reporting of new cases [28; 29] and types of ferroresonance [30]. This paper analyzes the three-phase ferroresonance of the detuned reactor of the PFC system in an industrial plant, which is triggered by the switching on of the capacitor stage and affected by harmonic distortions. To the best of the author's knowledge, this phenomenon has not yet been reported in the literature. Automatic detuned PFC systems are used for reactive power compensation in systems with high harmonic content [31].