Mathematical Modeling of Multiple Capacitor Coupled Substations (CCS) Impact on Transmission Lines and Approaches for Ferroresonance Suppression

Rural electrification remains a critical challenge in achieving equitable access to electricity, a cornerstone for poverty alleviation, economic growth, and improved living standards. Capacitor Coupled Substations (CCS) offer a promising solution for delivering cost-effective electricity to these underserved areas. However, the integration of multiple CCS units along a transmission network introduces complex interactions that can significantly impact voltage, current, and power flow. This study presents a detailed mathematical model to analyze the effects of varying distances and configurations of multiple CCS units on a transmission network, with a focus on voltage stability, power quality, and reactive power fluctuations. Furthermore, the research addresses the phenomenon of ferroresonance, a critical issue in networks with multiple CCS units, by developing and validating suppression strategies to ensure stable operation. Through simulation and practical testing, the study provides insights into optimizing CCS deployment, ultimately contributing to more reliable and efficient rural electrification solutions.

Analysis of ferroresonance in a neutral grounding system with nonlinear core loss

The chaotic behaviour exhibited by a typical ferroresonant circuit in a neutral grounding system is investigated in this paper. In most earlier ferroresonance studies the core loss of the power transformer was neglected or represented by a linear resistance. However, this is not always true. In this paper the core loss of the power transformer is modelled by a third order series in voltage and the magnetization characteristics of the transformer are modelled by an llth order two-term polynomial. Extensive simulations are carried out to analyse the effect of nonlinear core loss on transformer ferroresonance. A detailed analysis of simulation results demonstrates that, with the nonlinear core loss model used, the onset of chaos appears at a larger source voltage and the transient duration is shorter.

Effect of power frequency excitation character on ferroresonance in neutral-grounded system

In most earlier ferroresonance studies the traditional excitation characteristic of iron core, in which the traditional excitation characteristic contains harmonic voltages or currents, has been used as if it were made up of pure fundamental voltage or current. However, this is not always true. In comparison with traditional excitation characteristics, this paper introduces the power frequency excitation characteristic of the iron core, which contains no harmonics. The power frequency excitation characteristic of iron core has been obtained by Elector Magnetic Transient Program, resulting in discrete voltage and current pairs. Extensive simulations are carried out to analyse the effect of power frequency excitation characteristic on potential transformer ferroresonance. A detailed analysis of simulation results demonstrates that with power frequency excitation characteristic of iron core inclusion at certain excitation voltage the ferroresonance may happen, conversely it may not happen with traditional excitation characteristic inclusion.

Dynamic analysis and fractional-order adaptive sliding mode control for a novel fractional-order ferroresonance system

Ferroresonance is a complex nonlinear electrotechnical phenomenon, which can result in thermal and electrical stresses on the electric power system equipments due to the over voltages and over currents it generates. The prediction or determination of ferroresonance depends mainly on the accuracy of the model used. Fractional-order models are more accurate than the integer-order models. In this paper, a fractional-order ferroresonance model is proposed. The influence of the order on the dynamic behaviors of this fractional-order system under different parameters n and F is investigated. Compared with the integral-order ferroresonance system, small change of the order not only affects the dynamic behavior of the system, but also significantly affects the harmonic components of the system. Then the fractional-order ferroresonance system is implemented by nonlinear circuit emulator. Finally, a fractional-order adaptive sliding mode control （FASMC） method is used to eliminate the abnormal operation state of power system. Since the introduction of the fractional-order sliding mode surface and the adaptive factor, the robustness and disturbance rejection of the controlled system are en- hanced. Numerical simulation results demonstrate that the proposed FASMC controller works well for suppression of ferroresonance over voltage.

Chaotic ferroresonance in a non-autonomous circuit

description of magnetization curve has important effect on ferroresonance. In most of earlier ferroresonance studies the magnetization curve is modelled as a 3rd or 5th order polynomial. However, it is not comprehensive. This paper investigates the chaotic ferroresonance behaviour exhibited by a non-autonomous circuit which contains a nonlinear flux-controlled inductance. The ferromagnetic characteristic of this nonlinear inductance represented by a magnetization curve could be expressed as an nth order two-term polynomial. By varying the value of exponent n, the circuit can assume a diverse range of steady-state regimes including fundamental and subharmonic ferroresonance, quasi-periodic oscillations, and chaos. A detailed analysis of some simulations demonstrates that the probability of chaos increases as the exponent of the magnetization curve rises. The effect of varying the magnitude of the source voltage on the chaotic behaviour of the circuit is also studied.

Effect of New Suggested Ferroresonance Limiter on the Stability Domain of Chaotic Ferroresonance in the Power Transformer with Linear Core Model

This Paper studies the effect of new suggested ferroresonance limiter on controlling ferroresonance oscillations in the power transformer. It is expected that this limiter generally can control the ferroresonance. For studying these phenomena, at first ferroresonance is introduced and a general modeling approach is given. A simple case of ferroresonance in a three phase transformer is used to illustrate these phenomena. Then, effect of new suggested ferroresonance limiter on the onset of chaotic ferroresonance and control of these oscillations in a power transformer including linear core losses is studied. Simulation is done on a three phase power transformer while one of its phases is opened, and effect of varying input voltage on occurring ferroresonance overvoltage is studied. Results show that connecting the ferroresonance limiter to the transformer exhibits a great controlling effect on the ferroresonance overvoltage. Phase plane diagram, FFT analysis along with bifurcation diagrams are also presented. Significant effect on occurring chaotic ferroresonance, the range of parameter values that may lead to overvoltage and magnitude of ferroresonance overvoltage is obtained, showed and tabulated.

Studying Effect of Magnetizing Curve Nonlinearity Index on the Occurring Chaotic Ferroresonance Oscillation in Autotransformers

This paper investigates the effect of iron core saturation characteristic degree on the onset of chaotic ferrore-sonance and duration of transient chaos in an autotransformer. The transformer chosen for study has a rating of 50 MVA, 635.1 kV, the magnetization characteristic of the autotransformer is modeled by a single-value two-term polynomial with q = 5, 7, 11. The core loss is modeled by a linear resistance and is considered a fix value for it. Simulation results are derived by using MATLAB software and nonlinear dynamics tool such as bifurcation and phase plan diagrams. It is shown settling down to the chaotic region is increased when degree of core nonlinearity is gone from 5 to 11.

Analysis of Chaotic Ferroresonance Phenomena in Unloaded Transformers Including MOV

We study the effect of a parallel metal oxide surge arrester on the ferroresonance oscillations of transformers. It is expected that the arresters generally cause ferroresonance drop out. Simulation has been done on a three phase power transformer with one open phase. Effect of varying input voltage is studied. The simulation results reveal that connecting the arrester to transformers poles, exhibits a great mitigating effect on ferroresonant over voltages. Phase plane along with bifurcation diagrams are also presented. Significant effect on the onset of chaos, the range of parameter values that may lead to chaos and magnitude of ferroresonant voltages is obtained, shown and tabulated.

Impacts of Water-Tree Fault on Ferroresonance in Underground Cables

Nowadays, more and more electrical power is being distributed to customers by underground cables rather than overhead transmission lines due to their advantage of providing better protection in inclement weather. They also have significantly reduced electromagnetic field emission because of their copper shielding. But underground cables have larger capacitance than transmission lines per unit. Thus, ferroresonance is more likely to occur in distribution systems using underground cables. Moreover, soil humidity at a depth of one meter remains 100 percent for most of the year, a factor that risks the occurrence of water tree (WT) in cables. Consequently, both ferroresonance and WT are prone to occur in underground cable systems. The objective of this paper is to determine the relationship between ferroresonance and water tree. A test system was designed to simulate and analyze ferroresonance in a cable system caused by single-phase switch and water tree. Eight scenarios of water tree were compared in the simulation. There sponses of ferroresonance are presented in this paper and two common patterns are observed from the simulation results.

Suppression of ferroresonance using passive memristor emulator

Power system inherently consists of capacitance and inductance in its components. Equipment with saturable inductance and circuit capacitance provides circumstances of generating ferroresonance, resulting in overvoltage and overcurrent in the connected system. The effects of ferroresonance result in insulation failure and hence damage to the equipment is unavoidable. Though many devices are proposed for mitigating such circumstances, a promising technology of using memristors may provide better performance than others in the future. A memristor emulator using the N-channel JFET J310 is used in this work. Unlike other electronic components that replicate memristor properties, the chosen memristor emulator is a passive device since it does not need any external power supply. Simulation and experimental results verify the design of a memristor emulator and the characteristics of an ideal memristor. Experimental results prove that the memristor emulator can suppress the fundamental ferroresonance induced in a prototype single phase transformer. The results of the harmonic analysis also validate the memristor performance against the conventional technique.

Ferroresonance at Open Phase Operating Conditions of Power Transformers

The reliability of electric supply to consumers is one of the most important factors that determine the requirements imposed on modem utility companies. This paper presents the results of investigation by computer software of the overvoltages resulting from a ferroresonance conditions in MV networks at open phase operating condition with and without connection to earth on source and load sides of distribution transformer. This overvoltage may reach 4.2 pu on one of the HV side of transformer unswitched phases. The results of the study show that ferroresonance overvoltage may be controlled by replacing fuses with circuit breakers on HV side to ensure switching-off all phases. Insertion of resistor or reactor in the neutral of source and loadsides of the transformer with 5% active load will help in suppressing overvoltages.

Analytical Approach for the Systematic Research of the Periodic Ferroresonant Solutions in the Power Networks

Ferroresonance is a complex and little known electrotechnical phenomenon. This lack of knowledge means that it is voluntarily considered responsible for a number of unexplained destructions or malfunctioning of equipment. The mathematical framework most suited to the general study of this phenomenon is the bifurcation theory, the main tool of which is the continuation method. Nevertheless, the use of a continuation process is not devoid of difficulties. In fact, to continue the solutions isolats which are closed curves, it is necessary to know a solution belonging to this isolated curve (isolat) to initialise the continuation method. The principal contribution of this article is to develop an analytical method allowing systematic calculation of this initial solution for various periodic ferroresonant modes (fundamental, harmonic and subharmonic) appearing on nonlinear electric system. The approach proposed uses a problem formulation in the frequency domain. This method enables to directly determine the solution in steady state without computing of the transient state. When we apply this method to the single-phase ferroresonant circuits (series and parallels configurations), we could easily calculate an initial solution for each ferroresonant mode that can be established. Knowing this first solution, we show how to use this analytical approach in a continuation technique to find the other solutions. The totality of the obtained solutions is represented in a plane where the abscissa is the amplitude of the supply voltage and the ordinate the amplitude of the system’s state variable (flux or voltage). The curve thus obtained is called “bifurcation diagram”. We will be able to then obtain a synthetic knowledge of the possible behaviors of the two circuits and particularly the limits of the dangerous zones of the various periodic ferroresonant modes that may appear. General results related to the series ferroresonance and parallel ferroresonance, obtained numerically starting from the theoretical and real cases, are illustrated and discussed.

基于谐波平衡法及Floquet理论的高速铁路10 kV供电系统铁磁谐振机理分析

高速铁路10 kV供电系统是含时变激励的非线性非自治系统,以至于该系统中必然存在丰富的复杂非线性现象。该文在考虑系统中磁饱和电感的非线性特性的基础上,构建系统数学模型,并基于谐波平衡法求解系统周期解的近似表达式,推导系统周期时变雅克比矩阵,以Floquet理论识别系统周期解的稳定性,揭示系统出现铁磁谐振时的物理机理,分析系统参数变化对系统产生铁磁谐振的影响,给出ATPDraw环境下的电路仿真结果。研究结果表明:系统铁磁谐振现象产生的机理是由于系统发生了鞍结分岔,且随着饱和相串、并联电容的变化,系统能够保持稳定运行的临界激励幅值Em会随之产生变化。另外,理论计算结果和ATPDraw仿真结果一致,表明采用谐波平衡法和Floquet理论可有效分析高速铁路10 kV供电系统中的铁磁谐振现象。

Mitigation of Transients in Capacitor Coupled Substations Using Traditional RLC Filter Techniques

This article presents an extensive examination and modeling of Capacitor Coupled Substations (CCS), noting some of their inherent constraints. The underlying implementation of a CCS is to supply electricity directly from high-voltage (HV) transmission lines to low-voltage (LV) consumers through coupling capacitors and is said to be cost-effective as compared to conventional distribution networks. However, the functionality of such substations is susceptible to various transient phenomena, including ferroresonance and overvoltage occurrences. To address these challenges, the study uses simulations to evaluate the effectiveness of conventional resistor-inductor-capacitor (RLC) filter in mitigating hazardous overvoltage resulting from transients. The proposed methodology entails using standard RLC filter to suppress transients and its associated overvoltage risks. Through a series of MATLAB/Simulink simulations, the research emphasizes the practical effectiveness of this technique. The study examines the impact of transients under varied operational scenarios, including no-load switching conditions, temporary short-circuits, and load on/off events. The primary aim of the article is to assess the viability of using an established technology to manage system instabilities upon the energization of a CCS under no-load circumstances or in case of a short-circuit fault occurring on the primary side of the CCS distribution transformer. The findings underscore the effectiveness of conventional RLC filters in suppressing transients induced by the CCS no-load switching.

Mathematical Modeling and Control Algorithm Development for Bidirectional Power Flow in CCS-CNT System

As the demand for more efficient and adaptable power distribution systems intensifies, especially in rural areas, innovative solutions like the Capacitor-Coupled Substation with a Controllable Network Transformer (CCS-CNT) are becoming increasingly critical. Traditional power distribution networks, often limited by unidirectional flow capabilities and inflexibility, struggle to meet the complex demands of modern energy systems. The CCS-CNT system offers a transformative approach by enabling bidirectional power flow between high-voltage transmission lines and local distribution networks, a feature that is essential for integrating renewable energy sources and ensuring reliable electrification in underserved regions. This paper presents a detailed mathematical representation of power flow within the CCS-CNT system, emphasizing the control of both active and reactive power through the adjustment of voltage levels and phase angles. A control algorithm is developed to dynamically manage power flow, ensuring optimal performance by minimizing losses and maintaining voltage stability across the network. The proposed CCS-CNT system demonstrates significant potential in enhancing the efficiency and reliability of power distribution, making it particularly suited for rural electrification and other applications where traditional methods fall short. The findings underscore the system's capability to adapt to varying operational conditions, offering a robust solution for modern power distribution challenges.

电容式电压互感器铁磁谐振试验测控装置

电容式电压互感器的铁磁谐振试验,需要对试验波形进行分析处理,人工处理比较繁琐,耗时较长。针对这一问题,本文介绍了一种电容式电压互感器铁磁谐振试验测控装置,可对短路开关进行控制,自动采集和分析试验波形,自动存储试验结果和波形数据,。将该装置用于实际电容式电压互感器进行铁磁谐振试验中,结果显示,测控装置比人工处理波形省去了人工处理波形的时间,提高了工作效率。

地铁供电系统直流母线电压谐振机理研究

地铁安全运行依赖于供电系统的稳定性和可靠性。随着行车密度的不断增大和新能源系统的高密度并网应用,地铁供电系统的电气特性时常会发生较大变化,不仅牵引侧可能出现类似线路短路的特殊负荷,且直流母线可能会产生谐振现象。为此,针对母线电压非线性振荡问题,文章首先建立了交流侧整流变压器电路的三阶非线性非自治状态方程的数学模型;然后通过增加一个时间维,将三阶非自治系统转换成四阶自治系统,利用数值分析的方法对系统的三维相图、相平面图、庞加莱映射图与分岔图进行探究;最后将仿真模拟得到的混沌波形通过24脉波整流后与现场实测振荡电压波形进行对比。结果表明,所得到的仿真波形与实录波形在幅值与频率上基本一致,从原理层面证明电网波动是引发地铁牵引供电系统非线性振荡的原因之一。

基波铁磁谐振理论分析及实验验证

基波铁磁谐振频繁发生于电力系统中,严重威胁电力系统的安全稳定运行。首先利用理论分析方法研究了典型铁磁谐振电路的基波铁磁谐振,用非线性曲线描述了非线性电感的饱和特性,并考虑了回路电阻对谐振的影响;在仅考虑基波分量的情况下,根据理论推导结果得出系统各参数对铁磁谐振的影响,并给出了各参数导致系统发生谐振的临界值求解方法;最后利用实验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:该方法能够很好地分析基波铁磁谐振及其影响因素,铁心损耗越小,电源电压越高,回路电阻越小,回路电容越小,系统发生谐振的可能性越大。

电磁式电压互感器的铁磁谐振仿真研究

在中性点不接地配电系统中,由于电磁式电压互感器(PT)励磁电感的非线性特性,会在一定条件下产生铁磁谐振,影响系统的安全运行。笔者以ATP-EMTP仿真软件对铁磁谐振及多种消谐措施进行了仿真分析和综合比较,结合仿真分析及实际工程应用情况,认为在众多消谐措施中PT一次侧中性点接消谐器和4PT接线方式是比较好的消谐方法。

变电站铁磁谐振仿真分析及抑制措施研究

以某110kV变电站为原型,在考虑了母线零、正序参数和进出线路几何参数情况下,利用ATP-EMTP电磁暂态仿真软件,对该变电站35kV侧由于出线单相接地引起的母线电压互感器的谐振情况及电压互感器一次侧中性点经非线性电阻接地,电压互感器开口三角短时投入阻尼电阻等措施的消谐情况进行了仿真计算。对母线上装设中性点接地的三相电容器组,采用电容式电压互感器等消谐方式的有效性进行了探讨。对谐振产生的原因和各种消谐措施的原理和消谐效果进行了分析比较。结合仿真结果和系统参数分析得出:单相接地故障消失时刻对于能否激发系统谐振起着关键性作用;电压互感器开口三角短时接入阻尼电阻和电压互感器一次侧中性点经非线性电阻接地2种措施消谐效果较为理想;H.A.Peterson的试验结论不能作为判断系统是否产生谐振的确切参数标准。