Analyzing the stochastic behavior of ferroresonance initiation regarding initial conditions and system parameters

Power quality and power disturbances are the most important increasing factors throughout electrical networks. Ferroresonance as one of these disturbances can cause quality and security problems. This paper analyzes the stochastic behavior of ferroresonance as a nonlinear resonance phenomenon of the erratic nature and difficult prediction. Furthermore, the impact of different parameters on the initiation of ferroresonance is investigated. It is illustrated that a small change in the initial conditions leads to a large difference in the long-term behavior of the system, and this makes the future of the system unpredictable. Based on the stochastic behavior of ferroresonance some papers took different parameters into account and attempted to identify the basins of attraction for different ferroresonance regions. Here, according to real condition it is illustrated that these basins are highly depending on the initial conditions and there are no transparent boundaries for them. Also, by changing different parameters and initial conditions, the probability degree of ferroresonance initiation is calculated and depicted. Moreover, the impact of source angle on the ferroresonance initiation is investigated.     

铁磁谐振仿真模型的改进

在中性点绝缘的复杂电网中,因系统突发单相接地故障而激发的铁磁谐振现象经常出现,利用MAT-LAB内建的仿真工具实现了由于电压互感器非线性励磁电感和系统对地电容匹配而引起的铁磁谐振暂态过程的数字仿真,并分析比较了各种不同消谐方法的作用及效果.     

Electromagnetic transient study on flexible control processes of ferroresonance

Ferroresonance, which is a common phenomenon in power systems, have threatened the security of power systems for a long time. Although several ferroresonance suppression measures have been applied in power systems, ferroresonance still occurs occasionally. In this study, a flexible control strategy to control different ferroresonant modes is proposed. The behavior of a typical ferroresonant circuit acquired from a ferroresonance testing system to obtain the electromagnetic transient and control details of the control method is also investigated. The key parameters in the control module are determined, including the switching frequency and the coefficients of the proportional–integral (PI) controller. Then, six typical ferroresonant overvoltages are selected as control systems using the proposed method. Given the effect of a damping resistor and fully controllable power electronic switches with a gate signal controlled by a proportional–integral (PI) control system, these six typical ferroresonant overvoltages can all be suppressed in 0.12 s to the non-ferroresonant state after the controller is activated. The electromagnetic transients, including the essential system state quantity transients in the control process, are also investigated. At last, a laboratory prototype is implemented, and the experimental results show that the proposed method is useful for ferroresonant overvoltage control.     

Damping effect of load on the ferroresonance phenomenon in power networks

A generalized approach to the ferroresonance phenomenon, occasionally resulting from power transformers connected to transmission systems, is given. The effect of the transformer load current on the ferroresonance phenomenon at different load power factors is studied. A second-order equation determining the value of the critical load impendance at any load power factor is derived. Also, the effect of the transmission line parameters and the saturation degree of the transformer magnetization characteristic on the value of the critical load current and hence on the ferroresonance phenomenon is shown.     

消除中性点接地系统铁磁谐振新方法

由于母线PT励磁特性的非线性,铁磁谐振频率发生在中性点接地变电站的空母线上。本文提出了一种抑制这种现象的方法。在铁磁谐振可能发生之前,同时将数个并联的电阻投入PT二次星形侧;一段时间之后,逐一切除这些电阻,以防再次激发铁磁谐振。电阻值和电阻的个数通过EMTP模拟确定。利用EMTP模拟结果很容易绘制电阻－电压－频度图（R－V－F图）,这种图能直观地显示电阻值变化时对谐振抑制效果的影响 。该方法的优点之一是R-V-F科能够很容易地选择消谐电阻;之二是不需要关注谐振的性质,是基波谐振还是分次谐波谐振。基于上述原理,利用PC机、开关卡、可控硅和电阻等,开发了消谐器,并在一110kV变电站成功进行了试验。     

Lightning arrester failure and ferroresonance on a distributionsystem

Since 1987 the Upper Peninsula Power Company (UPPCO) has been experiencing a large number of lightning arrester failures on a portion of their distribution system in southern Marquette County, Michigan, USA. It was in the area of the US Navy's extremely low frequency (ELF) antenna, where the distribution system had been reconfigured so that the transformers were connected line-to-line in order to eliminate interference from the antenna. A study determined that the system was susceptible to ferroresonance during single line faults under lightly loaded conditions and that the overvoltages experienced could be causing the lightning arrester failures. This conclusion was further strengthened by a statistical study which compared the actual number of failures to an expected number of failures, given the systems loading condition and fault rate     

铁磁谐振过电压原因分析及预防

对铁磁谐振产生的危害、原因、条件、现象及运行中发生铁磁谐振如何处理进行了阐述：并结合产现场实际发生的一次铁磁谐振现象,分析了具体原因,并制定了切实可行的防范措施。     

General method of finding initial conditions

A general way of finding the initial conditions appearing in systems described by ordinary differential equations is given. The proposed method is based on control theory and graph analysis, and works for both linear and nonlinear systems. It permits an investigation of the initial conditions induced by any one or more of the following: (1) step inputs; (2) impulse inputs; and (3) jumps of system parameters caused by some external effect other than the primary input     

Fast ferroresonance suppression of coupling capacitor voltage transformers

This paper describes a procedure for fast suppression of the phenomenon of ferroresonance in coupling capacitor voltage transformers (CCVT) without major change in the CCVT design. It is shown that it is possible to adjust parameters of the secondary overvoltage protection and the filter circuit so that the ferroresonance can be cleared in a very short time interval. The study cases reported in this paper show that ferroresonance is effectively cleared within two cycles. An implementation of metal oxide varistors (MOV) as part of passive ferroresonance protection is also addressed. The Electromagnetic Transients Program (EMTP) is used for modeling transients and fine-tuning the ferroresonance suppressing circuit. The studies are conducted on the Trench TEHMP161A CCVT.     

小波-PSO在电力系统铁磁谐振研究中的应用

随着电力系统的发展和非线性元件在电力系统中的广泛应用,铁磁谐振给电网和用电设备造成危害问题变得较为突出.由于铁磁谐振检测,既需要检测突变点,又需要进行分频,但是进行小波变换时选择合适的小波基比较困难.将利用小波变换检测铁磁谐振波形的奇异点,从而判断谐振的发生时刻;然后利用粒子群优化算法(PSO)求解非线性铁磁谐振电路方...     

Determination of initial conditions in active RLC networks

A new method is described of determining the initial values of state variables in active RLC networks. This method utilizes neither the conservation principle of charges and fluxes nor the theory of distributions. An RLC active network is assumed to be formed at t = 0 by joining or disconnecting the elements that are contained in it, this operation being performed by the use of a set of switches. The new method is based on the consideration of switches as independent sources, and the state equations are extended to cover this situation, and their solution at t = 0⁺ gives the initial conditions that have been sought. Further, the new method is applicable to any state-space formulation techniques used.     

On initial conditions,generalized functions and the Laplace transform

This note exposes the mathematical setting of initial value problems for causal time-invariant linear systems, given by ordinary differential equations within the framework of generalized functions. We show the structure of the unique solutions for such equations, and apply it to problems with causal or persistent inputs using time-domain methods and generalized Laplace and Fourier transforms. In particular, we correct a widespread inconsistency in the use of the Laplace transform.     

Performance of metal-oxide arresters exposed to ferroresonance inpadmount transformers

Ferroresonant overvoltages have been recognized as a threat to arresters installed on underground distribution systems. Extensive tests have been performed to evaluate the thermal and electrical performance of MOV arresters exposed to this duty. Arrester discharge currents were found to be small and arrester heating is slow. The eventual temperature rise and the potential for thermal instability depends greatly on the type of arrester. Arrester designs which promote better heat dissipation to the ambient are shown to reach an acceptable steady-state temperature when exposed to ferroresonance of indefinite duration     

基频铁磁谐振的理论及仿真研究

基频铁磁谐振频繁发生于电力系统之中,严重威胁电力系统的安全稳定运行.本文利用理论分析方法研究了典型铁磁谐振电路的基频铁磁谐振,用非线性曲线表达式描述非线性电感的饱和特性,并考虑了回路电阻对谐振的影响,给出了求解各参数导致系统发生谐振的临界值的方法,并利用实验的方法验证了理论分析中电源电压对铁磁谐振影响的正确性.研究结果表明:该理论分析方法能够很好地分析基频铁磁谐振及其影响因素,为合理设计电力系统参数提供有力的依据;铁芯损耗越小,电源电压越高,回路电阻越小,回路电容越小,系统发生铁磁谐振的可能性越大.     

矩阵分解原理在电力系统铁磁谐振中的应用

阐述了铁磁谐振等效电路及其数学模型,以矩阵分解技术为工具得到了电路消除谐振的条件,在不同的初始条件下对电路进行模拟仿真.结果表明,消除谐振的条件可以用分解矩阵的HURWITZ条件来决定,并用数值模拟进行验证,结果正确,说明唯一稳态消谐法的有效性.     

Study of the periodic ferroresonance in the electrical power networks by bifurcation diagrams

The principal contribution of this article is to determine the existence zones of the various periodic ferroresonant modes (fundamental, harmonic and subharmonic) intervening in the electrical power network. The bifurcation diagrams are used for this purpose. To be able to plot a bifurcation diagram of a particular solution, it is initially necessary to locate this solution and then to follow it according to a bifurcation parameter. The developed computation code, resulting from the implementation of the Galerkin method jointly with the pseudo-arclength continuation method, has proved to be a powerful and reliable tool to construct these bifurcation diagrams. Indeed, it enables the electrical power network operators to better understand the problems of the phenomenon which had been observed in its network and to foresee new ferroresonance cases.Applied to the single-phase ferroresonant circuits, both series and parallel, we have been able to easily calculate the existence zones of these modes, as well as the stability limits of the system on ranges of broad variation of the parameters.Several results obtained numerically by software MATLAB, as from the real cases, are presented and commented upon.     

断路器非全相操作引起铁磁谐振的验算分析

结合电力行业标准ＤＬ／Ｔ６２０－１９９７对变压器装调中性点间隙保护的有关规定和要求,以枫树坝电厂２号主变压器中性点出现不接地运行过程中,高压侧断路器操作机构故障所引起的主变压器事故为实例,对断路器因操作机构故障出现非全相动作或严重不同期所引起的基频、分频及高频铁磁谐振进行验算。分析过程对变压器有关断路操作引起铁磁谐振的核算和中性点间隙保护的选择有指导价值。     

Analysis of lightning-caused ferroresonance in Capacitor Voltage Transformer (CVT)

Power networks contain capacitances and inductances that can saturate, presenting opportunities for ferroresonance to occur. Most power equipment is designed through linear theory but ferromagnetic materials are highly non-linear and when they resonate, the non-linearity produces currents and voltages that are larger than usual. Ferroresonance is a complex, non-linear electrical phenomenon. It can cause dielectric and thermal problems through overvoltage, an intrinsic phenomenon present in all networks. A network dynamic response to lightning and switching will be energy storage and release. The transfer of energy will propagate an overvoltage through the network and damage substation equipment when lightning strikes near the substation. Application of conventional mathematics is inappropriate to ferroresonance study in which actual events are simulated. Lightning strikes that occurred near a substation and that led to explosion of CVTs have been reported, so this study investigates the effect of a lightning strike on a tower with a 132 kV Capacitor Voltage Transformer (CVT). Alternative Transient Program (ATP) was used for the simulation which duplicated the lightning-strike effect that causes a CVT to explode.     

Fuzzy理论在电力系统铁磁谐振研究中的应用

根据电力系统铁磁谐振的模糊性,应用Fuzzy理论对电力系统发生铁磁谐振的可能性、影响因素及防止措施进行了研究.这种新方法对补充和完善铁磁谐振问题的研究具有重要的意义.     

Solving the ferroresonance problem when compensating a DC converterstation with a series capacitor

When a DC link feeds into an AC power system where the short circuit ratio is low or very low, the AC voltage requires some form of supplementary control. The concept of a series capacitor located between the AC system and the DC link has been an attractive consideration but is susceptible to ferroresonance between the series capacitor and the converter transformers, Using DC link controls judiciously, it is shown that any onset of ferroresonance can be eliminated. Benefits to series compensating a DC converter are presented