Heating of Three-Phase Shielded Supply at Short Circuit

Abstract

Following the calculation of the mechanical forces acting on the shielded three-phase line published in [1] and [2], an algorithm describing numerical calculation of its temperature rise due to short-circuit currents is presented. Given are the equation for determining the electromagnetic sources of heating, heat transfer equation for propagation of heat in the line and another equation for a simplified calculation of the temperature rise of the line provided that the investigated temperature process is adiabatic. The methodology is illustrated with a typical example.Keywords: shielded three-phase line, three-phase short circuit, heating of three-phase line FORMULATION OF PROBLEMFeeding lines of high-power electrical rotating machines, transformers, arc furnaces and many other devices are highly stressed mechanically and thermally, in particular at short circuit. Mechanical stresses on these conductors can significantly be reduced using wires shielded with steel jackets, see [1] and [2]. On the other hand, the presence of shielding complicates local thermal situation; it reduces the possibility of transfer of heat from the conductor and, moreover, further losses by eddy currents induced in the shielding jackets are generated, representing additional sources of heat. The paper describes a method for calculation of heating of such a shielded conductor. The paper supplements the above works, as it describes the method of calculation of temperature rise of feeding lines. The results allow carrying out such a design of the line that is safe with respect to the thermal damage of its insulation. Consider a three-phase line represented by straight conductors X, Y, Z. The conductors can be either massive or created by electrically conductive ropes that are insulated and placed in the shielding steel jackets, see Fig. 1. The conductors are supposed to carry short-circuit currents. The aim of the paper is to investigate the volumetric Joule losses in the wires and shielding jackets and formulate an algorithm for calculation of their heating. Since the fault is a short phenomenon, the process of heating will be assumed adiabatic, i.e., heat is not transferred to the neighbourhood of the conductors. This assumption leads to higher temperatures than those actually occurring in the system. As information about heating serves for evaluating heat stress of the insulation system of the feeding line, the method provides safer values.The short-circuit currents in the conductors X, Y, Z are expressed by the following formulae:where A, B, C, T A , and T D are the parameters of the shortcircuit current. MATHEMATICAL MODELThe task can be solved with a sufficient accuracy as a weakly coupled electromagnetic-thermal problem. The electromagnetic phenomena are not tightly connected with the thermal effects and may be solved separately. Electromagnetic field in the feeding conductorsThe field in the conductors is quasistationary. With respect to a relatively low frequency, the skin effect in these conductors may be neglected. This f...

Bulletin of the Polish Academy of Sciences: Technical Sciences

“…The increase in the number of four-wire systems initiated development of mathematical description of power and currents [6,8,9], and allowed to come up with methods of designing compensators in such circuits [9][10][11][12][13][14].…”

Estudio del circuito simetrizador Steinmetz en sistemas con polución armónica

“…Así, en algunas ocasiones, para reducir el desequilibrio se recurre a los otros métodos mencionados (transformadores especiales o sistemas de equilibrado). Es común, para simplificar el estudio de estos métodos de simetrización, considerar ideal el transformador monofásico que alimenta la carga de tracción y representar dicha carga a partir de su impedancia equivalente a la frecuencia fundamental, Z L = R L + j•X L , la cual se determina con su demanda de potencia [6,8,14], Figura 2b. En general, la utilización de sistemas de equilibrado conectados junto a la carga monofásica consiste en la conexión de ciertas reactancias (normalmente una reactancia inductiva y una capacitiva) formando un triángulo con la carga monofásica.…”

“…En general, la utilización de sistemas de equilibrado conectados junto a la carga monofásica consiste en la conexión de ciertas reactancias (normalmente una reactancia inductiva y una capacitiva) formando un triángulo con la carga monofásica. Este conjunto, integrado por la carga monofásica y las reactancias simetrizadoras comúnmente es conocido como circuito Steinmetz el cual se muestra en la Figura 2c, [6,7,14,15]. En dicha figura se consideran todas las variables y componentes del circuito a la frecuencia fundamental.…”

“…El diseño del circuito Steinmetz se basa en la obtención de las reactancias que simetrizan la corriente consumida por la carga monofásica. En general, la obtención de expresiones analíticas que faciliten estos valores puede realizarse por dos procedimientos [6,14,15]. Así, partiendo de la hipótesis simplificativa del equilibrio de la tensión de alimentación, se pueden obtener expresiones sencillas del valor de estas reactancias.…”

“…En este punto, el diseño del circuito Steinmetz, es decir la determinación de las reactancias que simetrizan la corriente consumida por la carga monofásica o que anulan su factor de desequilibrio puede realizarse por dos métodos [6,14,15].…”