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Abstract
Optical fiber composite low voltage cable (OPLC) is an optimal way of connecting the smart grid with the load. In this paper, the field distribution of temperature and stress is simulated by applying the finite element method. At the overload condition, the fiber unit’s temperature rises to 59°C that generates the strain of 387 µε. This strain and temperature together result in the additional attenuation of 0.053 dB/km in the optical fiber. Temperature and strain are termed as the major contributing factors towards the attenuation in the optical fiber as temperature caused 16.03% while strain caused 80.56% of the total loss.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Smart grid integrates the communication network with the power distribution network that allows the grid to control and communicate simultaneously by using smart meters. Electricity and information network are the two important parts of services provided to the end-users that were provided separately by the power companies and telecommunication companies in a traditional manner. A smart grid made it possible to provide electrical power and information technology under the same platform as the distribution system more efficient and robust. In a smart grid this efficient and robust network links the smart grid with the smart meters installed at the user’s end through a cable that can transmit electrical power and information simultaneously. This is made possible by using the Power Fiber to the Home (PFTTH). PFTTH realizes the transmission of electricity and information in the same cable that not only serves the purpose of transmitting the electricity but also meet the multiplicity requirements of the users including the demand-side response (DSM), advanced metering infrastructure (AMI), the electricity time of use pricing (ToU) and application of Internet of Things (IoT) [1]. Liu Jianming proposed the multi-utility services platform for the smart grid that includes the concept of PFFTH and the cable that he proposed was Optical fiber composite low voltage cable (OPLC) which was based on the concept of PFTTH [2]. Optical fiber composite low voltage cable is capable of serving the purpose of communication between the grid and the load [3]. In optical fiber composite low voltage cable, the power conductors and optical fiber run together in the single cable, having the functions of delivering electrical power as well as perform the communications that serve as a means of shifting the load towards off-peak hours that is the main feature of smart grid. The OPLC cable is established on the impression of power fiber to the home (PFTTH) having dual purposes of transferring electrical power and carrying out communication from the grid to the load [4,5]. The OPLC cable is designed to use in the distribution network operating at a voltage of less than 1 kV that can connect the smart meters with the substation of the smart grid [6]. Significant support is attained by the OPLC from the management in China to be mounted in the distribution systems. After the installation of optical fiber ground wire (OPGW) and optical fiber-composite PVC insulated drop wire OPDV, OPLC is now the upcoming project to be carried out in China [7,8].
In submarine cable, the optical fiber performs the function of analyzing the thermal field inside the cable, a lot of researchers worked on analyzing the electrostatic field along with temperature increase in the cable [9]. Electrical and thermal field analysis is conducted by Dmitriev using the finite element method [10]. Sun researched optimization of the structure of optical fiber composite low voltage cable to minimize the temperature increase inside the cable to decrease the attenuation level in the fiber, in this study the main focus is given to minimize the temperature by using the structural optimization technique by using Comsol simulation. [11]. Optimal selection of material used as a heat resistant layer is carried out by Ahsan, in the study the optimal heat resistant layer is chosen so that the temperature and strain can be minimized by using coupled equations [12]. Temperature monitoring technology is used by Yuqing to carry out the condition monitoring of optical fiber composite low voltage cable (OPLC) [2]. In the study Yuqing used distributed fiber Raman scattering temperature measure technology. In preceding studies, the research work related to the temperature field inside the cable along with the electrical field distribution and monitoring the working conditions had been done by most of the researchers [13]. Simulation work has been reported by Wang, in which he used 2-D Comsol simulation by using the electromagnetic wave analysis technique to measure the attenuation as the thermal stress is increased on the fiber but due to the absence of experimental setup the analysis was not enough to associate the attenuation loss caused by temperature and stress [14]. It is an important research aspect to analyze and assess the causes that can influence the working of the OPLC cable before installing the cable in the distribution network. In this paper two significant factors, temperature and strain are being analyzed that play a major part in attenuation in optical fiber in the working condition of OPLC. In this paper we have addressed three novelties. First, the three phase OPLC cable is simulated for the first time by considering the temperature increase along with the stress field distribution inside the cable. Second, the attenuation is related with the increase of temperature and strain inside the cable as the current begin to flow. Third, the strain is termed as the most influential factor in causing the attenuation that is helpful in the future research in the designing the OPLC cable.
The simulation for thermal field distribution and stress field distribution is being done by applying the finite element method (FEM) in COMSOL Multiphysics software. The OPLC is then placed in the experimental setup to examine the upsurge in thermal field and strain in the cable at optical fiber by using Brillouin optical time-domain analysis (BOTDA). Further, the attenuation in the optical fiber is also being monitored and analyzed separately due to temperature and strain to declare the most significant factor that causes the attenuation.
2. Problem formulation
The OPLC is deliberately constructed to perform the purpose of transferring electrical power and carrying out the communication together in the same cable as the power conductors and the optical unit runs together. The escalation of current originates the upsurge in temperature that initiates the stress to be created inside the OPLC cable. The first hurdle is to precisely examine the temperature and strain distribution on the optical fiber in the working condition of the cable. The second problem is to analyze the attenuation loss that occurs as the temperature and strain increase in the cable. The third problem is to identify the factors that contribute more towards the attenuation.
The first problem is solved by integrating the study of a magnetic field, heat flow in solids, and solid mechanics. The flow of current generates the heat inside the cable that is being analyzed by using the first law of thermodynamics. The stress produced as the temperature is increased is solved by using the structural mechanics module. The second problem is being solved by experimentally analyzing the attenuation that occurs as the current flow in the conductor. The third problem is to analyze the factors that contribute to the additional attenuation in the optical fiber that is solved by adding the additional attenuation caused by temperature and strain separately and compared with the total additional attenuation that occurs in the OPLC cable to get the percentage contribution from these two factors.
3. Structure and materials of OPLC
OPLC cable comprises three-phase conductors with the neutral and optical fiber unit stranded together in the single cable. Depending upon the distribution networks there are several structural types of OPLC cable having single-phase and three-phase conductors [15]. The structure discussed in this paper is a three-phase cable having neutral and optical fiber run along one another. The exterior insulation layer is Polyethylene (PE) with a thickness of 5 mm. Each conductor strand has a diameter of 1.684 mm having insulation of PVC with a width of 1.224 mm. The optical unit comprises the insulation material as TPE. OPLC-VV-0.6/1kV-4×16+GT-24B1.3 is shown in Fig. 1.
The properties of materials including the thermal conductivity along with density, thermal expansion coefficient, and heat capacity coefficient are listed in Table 1.
Table 1. Material's Properties
4. Modeling of temperature and stress in OPLC
The upsurge of temperature and stress is being examined by creating the cable’s model in COMSOL Multiphysics as the AC flows in the conductors [16]. In earlier studies, to simulate problems involving the temperature distribution, ELEFANT 2D used by researchers. In COMSOL, to analyze the heat distribution, magnetic field module equations are coupled with the heat equations in solids to calculate the escalation of temperature in the cable as the AC flows in the conductors. Stress distribution inside the cable’s structure is being analyzed by coupling the equations used in the study of structural mechanics that allows the calculation of stress in the cable that is generated due to the temperature increase. As the magnetic field is applied, the AC flows through the conductor [12]. The current is produced by the magnetic field density and ampere’s law gives the mathematical relation as in (1).
In the above relation in (1), J is termed as current density, while H is termed as the magnetic field density. The mathematical relation between electric field intensity and current density is provided by ampere’s law. To produce the current density, an electric field is generated in COMSOL by using (2).
In the above mathematical relationship, E is termed as the electric field intensity, while σ is termed as the electric conductivity, and B is taken as the density of magnetic flux. Je is termed as the density of electric current that is applied externally. Electromagnetic waves generated by electric fields are used to produce the current. In the simulation model only resistive losses are taken into account and neglecting the hysteresis losses to produce the heat in the conductor as in (3) [17].
For the calculation of heat transfer, thermodynamics first law is applied to execute the simulation. The heat equation is changed in a way as we have used temperature instead of energy and is given in (4).
Here Cp is termed as specific heat capacity with the units as J/kg.K, T is termed as temperature having unit as kelvin K, ρ is the density kg/m3, q is termed as the heat flux having units of W/m2, τ is termed as the tensor for stress having units of Pa, p is termed as the pressure with the unit of N/m2, ε is the tensor for strain that is further used in the study of solid mechanics for analyzing the stress field inside the cable. The rate of change of density is given in (5).
It is stated by the heat conduction equation that the temperature gradient and heat flux are proportional as in (6) [17].
In the above relation, the k is termed as the thermal conductivity (W/m×K). Putting the above equations in (4), the equation gets shortened as (7).
In the above heat Eq. (7), resistive losses due to the electromagnetic field are given as (8).
In the result of escalation of temperature in the cable due to the flow of current, the insulation layers also expand in every direction causing the external pressure within the insulation layers that results in the deformation. The value of heat transfer coefficient “h” is taken as 5 W/m2K. The enlargement of insulation layers due to temperature rise causes the generation of stress field that is analyzed by coupling the strain tensor equations in the simulation.
The OPLC cable is modeled in COMSOL Multiphysics. The geometry of the OPLC cable is exported in COMSOL after being built in AutoCAD. The studies of the magnetic field and heat transfer in solids are interconnected to get the thermal field distribution inside the cable during the working condition. The mesh is applied to the cable structure and the meshing of the cable is shown in Fig. 2.
4.1 Temperature field distribution in OPLC
In OPLC cable the alternating current is generated by using the magnetic fields and heat generated due to the flow of current is transmitted to outer layers to establish the equilibrium. The conductors have the PVC insulation allows the maximum limit of the temperature increase to 70°C. A temperature of 70°C is attained by giving the current density of 4.88 A/mm2. An upper limit of normal operating conditions made the temperature increase at the optical unit became 54.2°C. For the overload current, a 10% increase in temperature at the conductors is simulated, 77°C is termed an overload current that is being attained by inserting the current density of 5.23 A/mm2. In OPLC cable the materials having different thermal conductivity makes the uneven temperature distribution inside the cable shown in Fig. 3.
4.2 Stress field distribution in OPLC
The upsurge of the temperature in the cable results in the generation of stress fields within the insulation layers that are further analyzed by integrating the study of solid mechanics with heat flow in conductors in the COMSOL. The finite element method is used to solve the strain tensors as the cable’s insulation layers enlarge because of their thermal expansion coefficients. Later strain and the young’s modulus of the materials are used to calculate the stress. This stress is responsible for deforming the optical fiber [18]. The stress distribution in the optical unit of OPLC cable is shown in Fig. 4. At the current density of 4.88 A/mm2, the optical fiber unit’s temperature rise to 54.2°C and the stress at the optical fiber reaches 2.57×107 N/m2. This stress along with the temperature is held responsible for the attenuation in the optical fiber [19–22].
5. Experimental analysis
The strain experienced by optical fiber is calculated by applying the Brillouin optical time-domain analysis (BOTDA). BOTDA uses frequency shift to measure the rise in temperature and strain in the optical fiber that occurs during the current flow in cable in real-time. In BOTDA analysis two light signals termed as probe and pump are inserted from each end of the fiber and as the temperature and strain in the path of the fiber increased the difference in the frequency of the inserted light waves is recorded. The frequency shift has a linear relationship with the increases of strain and temperature that is being used by the BOTDA to sense the increase in strain and temperature. It is expressed as (9).
Here, Cε is the strain coefficient MHz/µε, CT is the temperature coefficient MHz/°C, νB and vB0 are the fiber Brillouin frequency shifts, Δε, and ΔT is termed as the change in strain and temperature respectively. The values of strain coefficient Cε and temperature coefficient CT is taken as 0.052 MHz/µε and 1.089 MHz/°C respectively. To calculate the stress, a strain is put in (10). In (10) E is termed as the young’s modulus.
In the experiment setup, three experiments are performed. The first experiment is conducted on the OPLC cable to analyze the rise of strain and temperature when the current density is enlarged in the cable along with the additional attenuation due to the upsurge of temperature and strain. The attenuation caused in the experiment conducted on OPLC cable is due to the combined effect of increase in temperature and strain. To separately identify and analyze the effect of attenuation caused by temperature and strain, two further experiments are conducted on bare optical fiber. The second experiment is conducted on bare optical fiber to analyze the additional attenuation with the rise in temperature and third experiment is conducted to analyze the additional attenuation with the rise in strain. These three experiments are conducted to analyze the attenuation caused by temperature and strain separately. The attenuation caused by temperature and attenuation caused by strain are added together and compared with the attenuation occur in actual OPLC cable to see the percentage attenuation caused by each factor.
5.1 Analysis of attenuation due to temperature in a bare fiber
In the optical unit of OPLC, the single-mode optical fiber G.652D is used to carry out the communication purpose. In the experimental setup, the additional attenuation in G.652D is analyzed for the temperature range from 20°C to 100 °C. For transmission of the light, the Keysight DFB 81663A light source is used as an input source. The short term stability of the light source is 0.003 dB that helps to analyze the smallest attenuation. The input power of the light source is 10 mW. The wavelength used to transmit light is 1550 nm. To measure the output power a power energy meter PM320E is used. 1 km long fiber is placed inside the temperature controller. The stability of the light source is monitored for 30 minutes. After that, the temperature is increased beginning after 20°C to 100°C having a step size of 10°C. To analyze the attenuation loss of optical fiber, the experimental setup is shown in Fig. 5.
5.2 Analysis of attenuation due to strain in a bare fiber
In the experimental setup, the additional attenuation caused by the strain in the optical fiber G-652D is analyzed. The fiber is linked with the fiber connectors and the fiber is connected between the fixed and movable ends, the movable end is controlled by a high precision displacement stepper motor. The fiber connectors are linked with the BOTDA to examine the strain at fiber in real-time. The spatial resolution of BOTDA is set as 0.5 m. The experimental setup is shown in Fig. 6. 300 meter long optical fiber is used to analyze the attenuation due to strain. The connected fiber is first linked to the BOTDA and the strain in the fiber is analyzed by running the analysis in BOTDA. The movable point is adjusted in a way that there is no strain present in the fiber. It is important to reduce all the strain in the fiber before starting the experiment as the presence of strain can play the part in extra attenuation. As the strain becomes zero in the fiber, the point is taken as the reference. The fiber is then linked to the input source and output measuring meter and displacement platform are moved to give 100 µε per step, attenuation data is analyzed up to 1000 µε.
5.3 Temperature and strain in OPLC
The OPLC cable is injected with the current in the conductors during the experiment. The current is generated by the facility containing the current inducing transformers, the facility has a maximum power output of 480 KVA and can generate the maximum current of 4000 A. The conductors are connected with the bus-bars to inject the current into the conductors. The current that streams in the conductors triggered the temperature increase inside the cable, the temperature sensors inserted inside the cable are used to measure the increase in temperature. The rise in temperature results in the increase in the strain at the optical fiber that is measured by using BOTDA. The length of the cable is 100 meters that are used in the experiment. The data of temperature in real-time is saved by using data acquisition module. The optical unit of OPLC cable consists of 24 strands of optical fiber that are being utilized for two purposes, one set of fibers is to measure the strain by using the BOTDA analyzer and another set of fibers is to analyze the additional attenuation in fiber as the current runs in the conductors. The platform for experiment is shown in Fig. 7.
One end of single-mode fiber is linked to the light source and another end is linked to the energy meter. The stability of the light source is measured for the first 30 minutes and data is recorded to use for the reference value as there is no increase in strain and temperature. The second set of fiber is connected to the BOTDA, one end is connected to the probe light and another end is linked to the pump light. In the start, BOTDA got the reference value of frequency shift as there is no current in the cable. The current is then inserted into the cable and the temperature inside the cable is monitored. The experiment results showed that the current density of 5.00 A/mm2 caused the overload condition as the conductor’s temperature to reach 77°C. As the temperature becomes stable the frequency shift is recorded to get the value of strain and the data from power energy meter is saved to get the additional attenuation.
6. Results
6.1 Analysis for temperature and strain escalation in OPLC
At the start of the testing, no current is injected into the cable and the strands of optical fiber in the cable were linked with the light source, energy meter, and BOTDA. After getting the data of light source and BOTDA frequency shift, the current of 20 A is inserted in the cable, a current is injected with a step size of 20 A in the cable as the maximum temperature at the current-carrying wire reached up to 77°C. The temperature at conductor and fiber at increasing levels of current densities are contrasted with the simulation results and shown in Fig. 8.
For the conductors with PVC insulation, the over-load current of 5.00 A/mm2 caused the increase of temperature to 77°C. In the experimental setup the 100 m long cable is used. Starting 10 m is comprised of optical fiber and at the ending point 10 m is optical fiber connected to BOTDA. At increasing current levels, the frequency shift is shown in Fig. 9.
The frequency shift is used in (9) to get the strain and (10) to get the stress. The Cε is the strain influence coefficient taken as 0.052 MHz/µε, CT is the temperature influence coefficient taken as 1.089 MHz/°C and E is termed as the young’s modulus of fiber taken as 71e9 Pa. The values of strain influence coefficient Cε and temperature influence coefficient CT is calculated by using temperature and strain increase experiments in our previous research [12]. The strain at increasing current density is given in Table 2. The BOTDA analyzer gets the data at the step size of 0.1 m at each point (14) is used to get the value of strain along the length of the fiber. For the starting 10 m, the fiber doesn’t face any temperature or strain increase because it is out of the cable. The temperature data is recorded through the thermocouple sensors placed inside the cable that leaves the equation with one unknown variable that is the strain.
Table 2. Strain at increasing current levels
The strain attained from the simulation and experiment are compared and graphically present with the increase of current density in Fig. 10. The increasing trend of both experiment and simulation is similar but the results of the experiments are a bit higher due to the increased temperature of fiber in real-time results shown in Fig. 8. The maximum value of strain is taken as in the optical unit the fibers are twisted along the length of cable that makes them face variation in temperature distribution in the cable.
The strain attained from the simulation and experiment are compared and graphically present with the increase of current density in Fig. 10. The increasing trend of both experiment and simulation is similar but the results of the experiments are a bit higher due to the increased temperature of fiber in real-time results shown in Fig. 7. The maximum value of strain is taken as in the optical unit the fibers are twisted along the length of cable that makes them face variation in temperature distribution in the cable.
The additional attenuation that occurs in the optical fiber is measured by using the power energy meter. The stability of the power source is tested for 30 minutes and as the light source became stable the transmitted light power is taken as the input power Pin. As the temperature became constant in the cable, at each current density, the transmitted power of light source decreased at the output end. This decreased power is taken as the output power Pout and attenuation is calculated by (11). The light source is set on a wavelength of 1550 nm. The fluctuations that occur in the light source are in the transmitted power and these fluctuations are the reason for an error of +0.003 dB in the recorded data and are shown in Fig. 11.
6.2 Analysis for the attenuation caused by temperature and strain in a bare fiber
The attenuation caused by temperature is experimentally analyzed by putting 1 km long optical fiber in the temperature controller having silicon oil in it. The free space in the temperature controller allowed the oil to expand freely without exerting any external stress. Optical fiber is linked with the input source and the other end is connected with the power energy meter. The controller’s temperature is set to 20°C and recorded the stability of the light source, as the light source becomes stable the value of the input power is taken as the reference. The temperature is then increased to 100°C having 10°C as step size. At 100°C, the additional attenuation becomes 0.015 dB/km, shown in Fig. 12.
The attenuation caused by strain in optical fiber is experimentally analyzed by attaching the fiber to immovable support and another end to a mobile point. The experiment starts with 0 strain and goes up to 1000 µε with the step size of 100 µε. The attenuation caused by strain increased linearly, the strain of 500 µε caused the attenuation of 0.051 dB/km and 1000 µε caused the attenuation of 0.108 dB/km as shown in Fig. 13.
6.3 Discussion on results
The optical fiber unit runs along with the conductors in OPLC. As the current is injected into the cable the temperature begins to increase as well as the strain. These two factors turn out to be the important factors that contribute to the additional attenuation. The rise in the temperature at the conductors elevates the fiber’s temperature along with the strain that is calculated by using the finite element method. The simulation results provide the limit of current density for maximum operating conditions of the cable that is further used in an experimental setup to avoid the insertion of large currents that can damage the optical unit in the cable while experimenting. In the experimental setup the current density is increased by observing the temperature of the conductor, the current density of 5.00 A/mm2 caused the conductor’s temperature to rise to 77°C and the temperature at fiber unit becomes 59°C.
The upsurge in temperature caused the increase of strain at the fiber that causes the additional attenuation. The additional attenuation caused by temperature is due to the extrinsic absorption of OH- ions present in the optical fiber and attenuation caused by strain is due to the fluctuation of the refractive index along with the photo-elastic effect that reduces the transmitted light power. The change of attenuation observed in the OPLC cable is due to both temperature and strain but the contribution from each factor was unknown that is further clarified in this paper that strain contributes more than 80% of additional attenuation loss. The contribution of temperature and strain in attenuation is given in Table 3.
Table 3. Additional Attenuation by Temperature and Strain at Increasing Current Density
While experimenting, the temperature sensors are inserted in the OPLC by cutting the insulation layers, the OPLC cable is positioned again in the original form. The insertion of these sensors allows some of the heat to slip through the cut points into the surrounding air. The leakage of this heat is the reason that simulation results are a bit greater. The OPLC is 100 m long, in the optical unit of OPLC there are 24 strands of optical fiber that are fused with one another in such a way that the optical fiber length inside the OPLC became 1 km, in this way the attenuation analyzed in the optical unit is measured in dB/km. The attenuation in the OPLC cable is due to both temperature and strain but it is not clear that which factor is contributing more towards the attenuation. To separate the contribution of temperature and strain towards the attenuation, experiments are performed by applying temperature and strain separately and results of additional attenuation are added from temperature and strain, these results are then compared with the total additional attenuation. The results showed the negligible difference between the attenuation that occurs in OPLC cable and the sum of attenuation by temperature and strain, which confirms that temperature and strain are the two major factors that contribute to the additional attenuation. The results showed that strain is the prominent factor in attenuation in optical fiber communication. Temperature is the other factor that also contributes to attenuation. The additional attenuation observed by the temperature at 69°C contributes 16.03% of the total additional attenuation observed in OPLC cable. The most prominent factor in causing the additional attenuation is the strain that contributes 80.56% in the attenuation loss. The other 3.41% of the attenuation is caused by the fluctuation of the source light input along with the negligible effect of the electric field generated in the cable. The contribution from temperature and strain in the attenuation in the optical fiber at the normal operating condition is shown in Fig. 14.
Previously the work has been reported in structural optimization of OPLC cable to decrease the additional attenuation by reducing the temperature escalation at the fiber unit. This research shows that the attenuation caused by increase of temperature only caused 16.03% of attenuation that leaves strain being most influential factor in causing the additional attenuation occur in optical fiber. The study conducted in this paper shows that the decrease of stress should be taken as the objective function while conducting the structural optimization on OPLC cable. As the temperature increase the filling material expands and as a result it exerts more external pressure on the optical fiber so the material should be added as a filling material that expands less and apply less external pressure on the optical fiber. For this purpose a new microtube structure will be introduced in the OPLC cable that will have air as the filling material. This new microtube structure will be able to decrease the factor of stress to its minimum value and in this way it will be possible to eliminate the attenuation caused by stress in optical fiber.
7. Conclusion
In this paper, the OPLC cable is simulated for analyzing the temperature and stress distribution in its normal operating condition. The OPLC cable is meant to perform the function of transmitting electrical power as well as carrying out communication while the temperature and strain cause the attenuation. The amount of temperature and strain are analyzed that can play an active role in attenuation. Further, the contribution of these two factors is analyzed in additional attenuation. The optical fiber is immersed in the filling jelly in the optical unit that eliminates the additional pressure exerted by the expansion of outer insulation layers but at the same time as the temperature increase the jelly expands and due to finite space inside the optical unit the expansion of filling paste exerts external pressure on the optical fiber from all directions that cause the strain at the optical fiber. This strain is the major contributor to the additional attenuation with increasing current in the OPLC cable. The study conducted in this paper shows that strain being the most influential factor for causing the attenuation in the optical fiber must be reduced so a new structure of micro-tube is under consideration that can reduce the strain to the minimum value as in micro-tube structure air is used as a filling medium that exerts less external pressure at the fiber that can decrease the additional attenuation to the minimum value.
Funding
Ministry of Science and Technology of the People's Republic of China (2016YFB0901200).
Acknowledgments
The authors thank the National Key Research and Development Program of China and Shanghai Electric Cable Research Institute, Shanghai, China for their support.
Disclosures
The authors declare no conflicts of interest.
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