سرکوب فرورزونانس در ترانسفورماتورهای قدرت با استفاده از تئوری آشوب

The main goal of this paper is the determination of the effect of the metal oxide varistor (MOV) on various ferroresonance modes including fundamental resonance, subharmonic and chaos mode which are generated in electrical power systems. Chaos theory is used for analyzing this effect. Also, the bifurcation, phase plan diagram and time domain simulation are used for this purpose. The proposed power system contains a no-load or lightly loaded power transformer. The magnetization curve of the transformer core is modeled by a single-value two-term polynomial. The core loss is modeled based on the flux of the transformer. The MOV modeled as a nonlinear voltage dependent resistance. The suppression effect of MOV on chaotic ferroresonance in power transformer is studied in this paper. The simulation results confirm that connecting the MOV to the transformer has a considerable suppression effect on ferroresonance phenomena.

The ferroresonance is a nonlinear resonance, which has result in multiple periodic and non-periodic modes in the system behavior. Considering system parameters and the initial condition of the ferroresonant circuit, it may settle to one of the following behaviors such as fundamental, subharmonic, quasi-periodic or chaotic resonances. Usually, the ferroresonance contains a nonlinear inductance and capacitances. The nonlinear inductance typically is a saturate magnetizing inductance of a transformer and the capacitance is a capacitive distribution cable or transmission line connected to the transformer. Ferroresonance phenomenon has been recognized and investigated in many papers as early as 1907 [1], [2], [3] and [4]. Isolated ferroresonant solutions in transmission lines have been investigated in [5], which presents the detailed analysis of the subharmonic mode of the ferroresonance and its sensitivity with respect to the length of the deenergised line. The study of the periodic ferroresonance in electrical power networks by bifurcation diagrams has been carried out in [6]. The analysis of the lightning-caused ferroresonance in capacitor voltage transformer (CVT) has been given in [7]. In the paper, a dynamic response to lightening and switching has been studied. So, the study investigates the effect of the lightning strike on a tower with a 132 kV CVT. The s-domain model of three winding transformer for modal analysis has been given in [8]. The influence of non-differential components to the power system small signal stability region has been studied in [9]. Considering the importance of the initial condition in the nonlinear systems, in [10], the impact of initial conditions on the initiation of the ferroresonance in the model of a 275 kV magnetic voltage transformer has been investigated. The transient response of a practical ferroresonant circuit has been studied in detail in [11]. The iterative approximation technique has been used for the determination of the transient response due to sudden application of a sinusoidal voltage. The analysis of subharmonic oscillations in a ferroresonant circuit with the focused on subharmonic (period-3) ferroresonant oscillations has been given in [12]. A novel analytical solution to the fundamental ferroresonance including power frequency excitation characteristic has been investigated in detail in [13]. A method of protecting the voltage transformer against ferroresonance overvoltages with a compact active load has been developed by [14]. The static VAR compensator (SVC) and the thyristor-controlled series capacitor (TCSC) analytical model, a systematical method for suppressing ferroresonance at neutral-grounded substations and the frequency response of the unfiled power flow controller (UPFC) has been simultaneously studied in [15]. A sensitivity study on power transformer ferroresonance in a 400 kV power system is presented in [16]. In that paper, the model of 1000 MV-400/275/13 kV power transformer has been described and the simulations have been compaired with field test results. The influence of supply, circuit and magnetic material parameters on the occurrence of the fundamental ferroresonance mode in a series inductance–capacitance–resistance (LCR) circuit with a nonlinear inductor has been discussed in [17] and [18]. The effect of the circuit breaker shunt resistance on the chaotic ferroresonance in voltage transformers has been studied in [19]. The suppression technique of the ferroresonance phenomenon in the coupling capacitor of the voltage transformer has been given in [20]. The impact of hysteresis and magnetic couplings on the stability domain of ferroresonance in asymmetric three-phase three-leg transformers has been discussed in [21]. Mitigating the ferroresonance of 161 kV electromagnetic potential transformers by damping reactors in gas-insulated switchgear has been presented in [22]. The frequency domain analysis of a power transformer ferroresonance has been studied in [23]. The aim of the current paper is to show the controlling effect of MOV on clamping the ferroresonance overvoltages and the application of MOV as a practical solution for protecting power transformers against ferroresonance overvoltages.

The dynamic behavior of a transformer in the case of occurance of ferroresonance has been studied including non-linearity in the core loss. Some modes of ferroresonance oscillation have been derived, and then it has been shown that the system greatly affected by MOV. The presence of the MOV results in clamping the ferroresonance in studied system. The MOV successfully limits the chaotic overvoltage to its marginal level. Therefore, in case of switching operation or phase opening causes ferroresonance oscillations in power networks, the transformer can be protected by using the MOV. It has been also shown that the core saturation plays a decisive role in determining the type of ferroresonance oscillations. The results show that a change in the value of the control parameter may originate different types of ferroresonance oscillations, MOV can clamp ferroresonance overvoltages, and the system shows a tendency to damp chaotic oscillations while saturation characteristic with lower knee point has been considered.