Elsevier

Electric Power Systems Research

Volume 166, January 2019, Pages 223-231
Electric Power Systems Research

A thermal model for calculating axial temperature distribution of overhead conductor under laboratory conditions

https://doi.org/10.1016/j.epsr.2018.10.008Get rights and content

Highlights

  • Establishing model for axial conductor temperature calculation in laboratory.

  • Identifying non-weather related thermal parameters of different conductors.

  • Analysing change laws of non-weather related thermal parameters.

  • Measuring axial temperature of conductor by experiment platform.

  • Comparison of precision between thermal model and IEEE standard model.

Abstract

Most traditional thermal models of overhead conductor neglect the axial temperature distribution along the length of conductor. In order to provide a necessary foundation for calculating axial conductor temperature distribution in real weather conditions, a thermal model is proposed for the axial conductor temperature calculation under laboratory environment. This proposed model is established with the equivalent thermal network, and expressed as a nonlinear state-space equation. An identification method is presented to determine the conductor thermal parameters, which are non-weather related and hardly to be calculated theoretically. The interior-point algorithm is employed to optimize the objective function of parameter identification. The effectiveness of identification method and proposed thermal model are validated by experiment results. This study will provide the basic modelling principle, parameter identification method and conductor thermal parameters to develop the conductor thermal model under the real weather conditions in the future.

Introduction

In spite of temperature of overhead conductor can be measured directly by temperature sensors, or calculated indirectly from conductor tension or sag data, establishment of conductor thermal model is still a significant work since the thermal model can calculate conductor temperature under any specified current and weather conditions. For this reason, the conductor thermal model played a vital role to estimate dynamic thermal rating of overhead transmission line and increase power transfer capability in the last few decades [1], [2]. The conductor thermal model becomes more and more important, because it has been applied in electro-thermal coordination theory for enhancing the security and economic performance of power system [3].

Many works have been performed to develop the conductor thermal model with the theoretical and experimental analysis [4], [5]. On the basis of these studies, IEEE presented a thermal model that has now been accepted as a standard model [6]. With IEEE standard model, the conductor temperature can be calculated in both the steady-state and transient-state. To improve reliability of conductor temperature calculation, several probabilistic or intelligent algorithms, such as Monte Carlo simulation [7], [8], fuzzy algorithm [9], affine arithmetic [10] and nonlinear adaptive modelling technique [11], were developed with the IEEE standard model in the recent years.

However, the above-mentioned studies assumed overhead conductor is isothermal. In other words, the axial and radial temperature variation along the length of conductor was neglected. Since the diameter of conductor is much small than length of conductor, the radial temperature distribution can be neglected in most situations. But the temperature distributed along the energized conductor could be remarkable, because the weather conditions vary dramatically in spatial scale [12]. Even if the weather conditions do not change along the line, the axial temperature variation could be resulted by attachments of conductor, such as clamps, splice connectors and insulator strings [13], [14]. Furthermore, when the conductor is ruptured by fatigue or fretting, large temperature gradients will be generated on the surface of conductor [15].

Neglecting axial temperature of conductor brings three main problems in the power system. Firstly, the dynamic thermal rating would be difficult to estimate reliability due to the fact that the power transfer capability is essentially limited by the hotspot of conductor [16]. Secondly, the error of transmission line model is increased, because the line resistance and reactance change with the conductor temperature [17], [18]. Thirdly, the development of electro-thermal coordination theory is limited, since it is highly dependent on the dynamic thermal performance of transmission lines [19]. Therefore, it is necessary to establish a conductor thermal model that can be used to calculate axial temperature distribution. Especially, the processing of meteorology and transmission line thermal performance has been expected to be a standard feature of SCADA systems in the future [20]. Thus, establishment of such conductor thermal model is an inevitable requirement for the development of power system.

In order to establish the thermal model for calculating axial temperature distribution of overhead conductor, three major steps need to be implemented. Firstly, provide the mathematical expression of thermal model based on heat transfer analysis of conductor. Although some thermal analysis methods, such as finite element, finite volume and finite difference method [21], [22], can be used to simulate temperature field distribution, they are unsuitable for calculating axial conductor temperature in the actual projects, because of the huge computational cost and storage requirement. Secondly, determine the non-weather related thermal parameters of thermal model, such as heat capacity and axial heat conduction resistance of conductor. In order to determine these parameters in high accuracy, some laboratory experiments should be carried out under the natural convection condition and without disturbance of wind and solar radiation. Thirdly, apply the thermal model to calculate axial temperature distribution of conductor under real weather conditions. At this step, the weather related parameters in the thermal model should be determined considering the random variation of weather conditions. In addition, more affecting factors, such as longitudinal current, rain, fog and haze, should be taken account into the thermal model for further improving model reliability.

This study is aimed at implementing above first two steps, which are necessary preconditions to implement the third step. For this purpose, a new thermal model is proposed to calculate axial conductor temperature under the laboratory conditions, and an identification method is presented to determine conductor thermal parameters in the proposed model. Several laboratory experiments, performed with condition of natural convection and without disturbance of wind and solar radiation, demonstrate the effectiveness of the identification method and proposed thermal model. The work of this paper can be expected as a good foundation for calculating the axial temperature of conductor under real weather conditions in the future.

Section snippets

Conductor thermal model in IEEE standard

The overhead conductor temperature is affected by the wind speed and its direction, ambient temperature, solar radiation, and electric current of the conductor. In IEEE standard-738, the conductor thermal model can be expressed as a first-order differential equation [23]CdTcdt=qJ+qsqrqcwhere Tc is conductor temperature (°C), C is heat capacity of conductor (J/m °C). qJ and qs are, respectively, Joule and solar heat gains (W/m). qc and qr are, respectively, the convective and radiated heat

Principe of equivalent thermal network

In order to establish the thermal model considering the axial temperature distribution of conductor, heat balance of conductor is described by equivalent thermal network in this study. The equivalent thermal network is a thermal analysis method that has been widely used in temperature calculation of electrical equipment [24], [25]. Compared with other thermal analysis methods, such as finite element, finite volume and finite difference method, the equivalent thermal network has the advantages

Purposed thermal model

According to nonlinear systems theory [29], [30], the equivalent thermal network, essentially is a nonlinear multiple-input-multiple-output (MIMO) system and the axial temperature of conductor is both state variable and output of this MIMO system. Thus, a new thermal model, which expressed as following nonlinear state equation, can be proposed with (12) and Fig. 2.T˙C=ATC+BU+F(TC)

The vector TC in (21) is the state vector composed of conductor temperatureTC=[Tc,1Tc,2Tc,3...Tc,N]Twhere N is the

Objective function of identification

As mention above, it is hardly to calculate the thermal parameters Cm and Rdm with high precision, therefore these parameters should be determined by the parameter identification method. In order to identify the non-weather related parameters reliably, the parameter identification should be carried out under the natural convection condition and without disturbance of wind and solar. According to (19), the equivalent heat convection resistance Rc,i is affected by air density under the natural

Experimental setup

In accordance with Refs. [16], [17], an experimental platform was set up to verify proposed thermal model and identify its thermal parameters. Fig. 4(a) and (b) show the structure schematic and photo of experimental platform, respectively.

In this experimental platform, two steel frames with the dimensions of 2.0 m × 0.6 m × 0.8 m, are mounted on the ground and a steel beam with 3.5 m in length is fixed on top of steel frames. Four nylon wires with the 0.2 W/(m K) in thermal conductivity and 0.2 mm in

Validation of parameter identification

In order to identify the thermal parameters of proposed model, a series of experiments were carried out for 60 min. In these experiments, the current levels ranged from 200 A to 500 A with interval of 50 A, were loaded to the conductors, respectively. The ambient temperature during these experiments is about 25 °C.

Fig. 6 shows the measured temperature distribution of conductor ACSR 400/35 with the current of 400 A. It can be found that the conductor temperature, measured at each measuring point,

Conclusion

In this paper, a new thermal model is proposed with the equivalent thermal network to calculate axial temperature distribution of overhead conductor under the laboratory conditions. A parameter identification method, combining with the interior point algorithm, is presented to determine the non-weather related thermal parameters of conductor. Laboratory experiments indicate that the calculated accuracy of IEEE standard model is low in case of large axial temperature difference. Conversely, the

Acknowledgements

This work was supported by the ‘National Natural Science Foundation of China’, No. 51607091, ‘Fundamental Research Funds for the Central Universities’, No. 30916011334 and ‘State Key Laboratory of Smart Grid Protection and Control’, No. 2017002NR00013.

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