IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 42, NO. 8, AUGUST 2014
2117
Effects of DC Component in Asymmetric Fault Current on the Thermal Recovery Characteristics of an SF6 Autoexpansion Circuit Breaker Jun Min Zhang and Jiu Dun (Joseph) Yan
Abstract— A 2-D magnetohydrodynamic arc model is used to study the thermal recovery processes with long and short arc durations in an autoexpansion circuit breaker where a significant dc component in the fault current exists. The influence of the dc component on the pressure built-up in the expansion volume was first investigated and the thermal recovery characteristics compared with cases where asymmetry of the fault current is negligible. Results show that, in comparison with the cases of symmetrical fault current, pressurization in the expansion volume is largely determined by the arc energy in the second half cycle of fault current, which is significantly influenced by the dc component. The dc component affects evidently the arc temperature at the current zero point and leads to a reduction in the critical rate of rise of recovery voltage. Index Terms— Asymmetric fault, dc component, post arc current, SF6 circuit breaker, thermal recovery characteristics.
I. I NTRODUCTION
T
HE operation of a modern SF6 autoexpansion (also called self-blast) circuit breaker involves coupled physical, chemical, and fluid dynamic processes. It is well known that the performance of this type of circuit breaker depends on the arcing history because the formation of high-speed gas flow in the main nozzle during the period around the current zero is a direct result of nozzle ablation by arc radiation in the high-current phase [1]. Recently, there has been attempt to further increase the voltage and power ratings of this type of device due to its inherent advantages and strong market competition, but the task proves extremely challenging. Network faults, especially short circuit fault, are often asymmetric in their current waveform. The existence of a dc component not only changes the peak current of the fault current, but also alters the current zero point and arc duration, thus affecting the duration and severity of nozzle ablation. Although there have been numerous papers devoted to the simulation of the arcing process in autoexpansion circuit breakers [1]–[4] using given current waveforms, there has been
Manuscript received August 1, 2013; revised January 1, 2014; accepted June 13, 2014. Date of current version August 7, 2014. This work was supported by the National Natural Science Foundation of China under Grant 51177005. J. M. Zhang is with the School of Automation Science and Electrical Engineering, Beihang University, Beijing 100191, China (e-mail:
[email protected]). J. D. Yan is with the Department of Electrical Engineering and Electronics, University of Liverpool, Liverpool L69 3GJ, U.K. (e-mail:
[email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TPS.2014.2331974
no investigation in a systematic approach into the influence of the degree of asymmetry in the interruption capability of the breaker, especially the mechanisms through which difference in interruption performance from symmetric switching cases is made. It is therefore of interest to carry out such a study using an arc model that is verified and produces trustable results. There is a great demand for advanced high-voltage circuit breakers as a result of the rapidly development of economics in China. Proper computer simulation as a design aid tool is becoming more and more important in the manufacturing process. The breaking test of asymmetric short circuit current is required in the type test in any standards for ac circuit breakers, which has not been explicitly studied in details. Therefore, studying into the interruption process of asymmetric short circuit current will contribute to the knowledge and understanding of switching technology, leading to benefits of the manufacturing industry. An SF6 autoexpansion circuit breaker is different from the puffer type in that the upstream pressure is established as a result of nozzle ablation. However, they both have a very similar the period around the current zero where the arc is cooled down by strong convection and turbulent enhanced energy exchange in the radial direction of the arc column. It is commonly accepted to use the conservation equations of mass, momentum, and energy with appropriate boundary conditions as the arc model, which takes account of radiation transport, arc radiation induced inner wall ablation, turbulence enhanced momentum and energy transport, and the moving parts of the contacts, to investigate the behavior of the arc in the circuit breaker [5]–[7]. Computational fluid dynamic is employed to solve these conservation equations for arc modeling. Accurate prediction of the interruption capability of a circuit breaker is, however, hindered by our insufficient understanding in three aspects, deviation of the plasma state from local thermal equilibrium (LTE) and local chemical equilibrium (LCE), turbulence effect, and the determination of arc root, especially at low current. The LTE is usually assumed for the core of the arc column due to the frequent collisions between particles. The edge of the arc column is strictly speaking not in LTE. The thin non-LTE layer between the contact and the arc does not significantly affect the overall flow field and the arc column. Arc rooting is an extremely complex problem of 3-D nature and the mechanisms are not well understood. Therefore, they both are seldom considered in the arc model. The LCE is used to simplify the calculation
0093-3813 © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
2118
IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 42, NO. 8, AUGUST 2014
Fig. 1. Schematic view of arcing chamber: 1—static contact, 2—main nozzle, 3—auxilary nozzle, 4—moving contact, and 5—expansion volume.
Fig. 2. Mesh for the calculated gas flow field: 1—outlet, 2—inlet, 3—outlet, 4—main nozzle, 5—static contact, 6—moving contact, 7—expansion volume, and 8—transparent contact. TABLE I S OURCE T ERMS AND D IFFUSION C OEFFICIENTS
of the composition of mixture and the diffusion coefficient of the metal vapor [8]. Turbulence is an important mechanism for cooling the arc in the current zero phase and is considered for the investigation of thermal interruption capability. Previous studies show that the Prandtl mixing length model is able to represent the turbulent cooling effect in strong axial gas flow and to predict the critical rate of rise of recovery voltage (RRRV) after current zero [1], [9]–[11]. A symmetric arc current has been used in almost all previous investigations into the interruption process in highvoltage circuit breakers. There is very little systematic study on the gas flow field and interruption capability under asymmetric arc current conditions. Preliminary results on the arc characteristics have been reported recently under an asymmetric short circuit current [12]. This paper has substantially extended the range of the arc current and the arcing time and paid attention to both the arc behavior and thermal recovery at the current zero point. This paper is organized as follows. Section II starts with a description of the arc model with focus on the validity of the approach. Factors that affect the accuracy of the modeling results are analyzed and evidence given to verify the validity of the model. The submodels representing the important physical mechanisms are also given. This is followed by Section III where the geometry and operational conditions used in this paper are first given and results for different switching duties analyzed in detail. Conclusions are drawn in Section IV. II. A RC M ODEL Because there is a complex energy exchange process between arc plasma and SF6 gas around arc in the chamber during the interruption of an SF6 circuit breaker, the interactions of arc, gas flow, and electromagnetic field should be considered in the arc mathematical model. To describe the arc behavior in the chamber, a magnetohydrodynamic (MHD) model of arc is presented based on the Navier–Stokes equations combining with the Maxwell’s equations in this paper. For the arc model, following assumptions have been made. 1) The arc is axis-symmetrical and is described with 2-D cylindrical coordinate system. The arc burns between the static contact and the moving contact (hollow contact) (Fig. 1). A transparent contact (see the gray region labeled 8 in Fig. 2) is placed in the hollow contact to ensure the collection of electric current and axisymmetry during the whole arcing period, but has no effect on gas flow inside the hollow contact.
2) During the arcing period, the ablated polytetrafluoroethylene (PTFE) vapor, which is generated by the radiation of arc, adds mass, momentum, and energy to the gas domain, and makes the pressure increase in the expansion volume, and that can make the performance of flow field change in the chamber. Therefore, the ablation of PTFE nozzle is considered and the ablated PTFE vapor leaving the nozzle surface is as the increasing mass to influence on the source terms of conservation equations (Table I) in the model. The thermodynamic and transport properties of PTFE vapor are close to those of SF6 and we use the thermodynamic and transport properties of SF6 for the mixture of SF6 -PTFE vapor. The advantage of this approximation is that much computing time can be saved because no concentration equation for the PTFE vapor needs to be solved and there is little difference for this paper. The mixture of SF6 and PTFE vapor is assumed in LTE, the thermodynamic properties and transport coefficients given in [13] are used in our calculation. 3) Contact erosion is ignored due to the dual flow arrangement of the breaker where most of the metallic vapor is blown away from the contact gap and has little effect on the thermal recovery process of the breaker. 4) Radiation loss is considered by means of a semiempirical model [14], which calculates the net radiation loss per unit volume and time based on the concept of net emission coefficient (NEC). The model assumes a monotonic radial temperature profile. The maximum temperature is T m . The arc core is defined from the axis to the radial position of the 0.83 T m isotherm. The net radiation loss in the arc core is a function of temperature, pressure, and arc radius, which is defined as the radial distance from the axis to the 4000 K isotherm. The NEC data is taken from [15]. The 60% of radiation from the arc core is absorbed in the region between the core edge and the 4000-K isotherm, the remaining 40% of radiation escapes from the arc and reaches the inner surface of the nozzle [16] causing radiation induced nozzle ablation.
ZHANG AND YAN: EFFECTS OF DC COMPONENT IN ASYMMETRIC FAULT CURRENT
5) During the period around the current zero, the arc is cooled rapidly by the strong gas flow from the upstream where the pressure is relatively higher. Turbulent cooling is substantial in this period. Two of the most popular turbulence models, the Prandtl mixing length model and the κ–ε model, have been studied for turbulent arcs. A comparative study of the two models to gas blast arcs demonstrates the superiority of the Prandtl mixing length model [17]. Thus, the Prandtl mixing length model is adopted for this paper by setting the turbulent Prandtl number at unity. The mixing length for turbulent momentum transfer lm is given by lm = R 1/2 c( 0 4K (1 − ρ/ρ4K )2r dr ) , where R4K is the arc’s radius of 4000-K isotherm. ρ and ρ4K are the gas density at r and at 4000 K, respectively. c is a turbulence parameter, a value of 0.3 is used following [1]. The Navier–Stokes equations modified to consider ablated nozzle vapor, Lorentz force, Joule heating, and radiation loss as additional source terms in a cylindrical coordinate system can be written as [18], [19] ∂(ρφ) + ∇ · (ρVφ) − ∇ · (∇φ) = S (1) ∂t where φ, , and S are the dependent variable, diffusion coefficient, and source terms, respectively, which are listed in Table I for the conservation equations. ρ is the density of gas. V is the velocity vector. In Table I, u and v are the velocity components of gas in axial and radial direction, respectively, h is the enthalpy, μl and μt are, respectively, the molecular and turbulent viscosity, kl and kt are, respectively, the molecular and turbulent thermal conductivity, c p is the specific heat capacity at constant pressure, P is pressure, Fx and Fr are Lorentz force in axial and radial direction, respectively, m is the mass of ablated PTFE vapor entering the nozzle, and its calculating method is given in [20], in the energy conservation equation, Q = Se −Un , Se = σ E 2 is Joule heat power, σ is the electrical conductivity, E is the electrical field, Un is the net emission radiation loss, and Q m = mhv , h v is the energy of PTFE vapor at 3400 K, which is equal to 11.9 MJ/kg. The Lorentz force and the electrical field can be solved from the following equations: ∇ · (σ ∇ϕ) = 0 E = −∇ϕ j = σE Bθ = (μ0 /r ) Fx = jr Bθ ;
(2)
(3) (4) r
jx r dr 0
Fr = jx Bθ
(5) (6)
where ϕ is the electrical potential, jr and jx are the radial and axial current density components, respectively, Bθ the selfinduced magnetic field, and μ0 is the magnetic permeability of free space. III. R ESULTS AND A NALYSIS The thermal interruption process with and without dc component (namely asymmetrical and symmetrical short-circuit
2119
current) has been studied in a high-voltage SF6 autoexpansion circuit breaker. The parameters of the circuit breaker are as follows: 1) rated voltage of 40.5 kV; 2) rated breaking short circuit current of 31.5 kA; and 3) initial absolute pressure P0 of 0.6 MPa in the interrupter filled with SF6 at temperature T0 of 300 K. The schematic diagram of the interrupter is given in Fig. 1, where its mechanical compression chamber connected the expansion volume via a valve is not shown. The grid system for the flow field is shown in Fig. 2. There are altogether 10 thousands cells for the whole flow field domain. The cell size is about 1 mm × 1 mm, which is adaptive for the accuracy of calculating results following a sensitivity study with doubled cells. In Fig. 2 and Table I, r and x represent the radial and axial directions, respectively. The pressure at the flow outlet is set to 0.6 MPa. The calculation domain of electric field, which is rectangular, as shown in Fig. 1, is larger in the radial direction than the flow field domain given in Fig. 2. The boundary in the r-direction is varied until its further extension hardly affects the calculated electric field within the flow field, and ∂ϕ/∂r = 0 is assumed along the boundary. The potential of moving contact is set at zero, and that of fixed contact is iteratively solved until the current is equal to the given value. The electrical conductivity inside the contacts is set to 106( m)−1 and the electrical conductivity of rest region where electrical conductivity is zero is set at 10−3 ( m)−1 for calculated convenience. Once the potential distribution is known, the electric field is calculated. Then, the Joule heating power, the current density in the arc, and the Lorentz force can be easily determined. In the simulation, the velocity of the moving contact is that provided by the manufacturer. The arc current is the rated short-circuit current. Four typical cases, namely, a long arc duration of 19.5 ms and a short arc duration of 12 ms, have been computed under the rated short-circuit current with and without dc component. For the long arc duration case, in the presence of a dc component, the time span in the second half cycle of the current is more than 10 ms with an increased peak current (57 kA). For the short arc duration case with dc component, the time span in the second half cycle is
