Experimental Verification of Distributed Parameters on Indian Residential Networks for Power Line Communication

To characterize and model an indoor power line channel, it is of utmost importance to estimate the distributed parameters accurately. These distributed parameters are influenced by several factors that may vary from each location. In this paper, the distributed parameters are estimated on Indian residential networks considering the different aspects of electrical wiring. The results obtained through simulation are compared with other commercially available simulators and are also verified experimentally using a Vector Network Analyser. The attenuation for different wiring configurations is also obtained in the paper. Keyword Attenuation, Channel transfer function, Distributed parameters, Impedance.


II. DISTRIBUTED PARAMETERS FOR RESIDENTIAL ELECTRICAL WIRING
The residential electrical network in India typically contains 3 wires viz. the Live or Phase wire (L), Neutral wire (N) and earth wire (E) as shown in Fig. 1. The phase and neutral wires enter the distribution box connected through the service mains and the earth wire is terminated in the house premises. These wires are very loosely twisted together and connected from the PVC switch boxes to different appliances in the room. These wires are drawn through the PVC conduit pipes along the concrete walls of a room. The conductors used in the residential wiring are usually with a cross-section of either 1.5 sq.mm or 2.5 sq. mm based on electrical appliances used [11].

A. Resistance
The Resistance of the single core cable for a two-wire transmission line is given as ( 1 ) The skin depth (δ) of the cable is given by ( 2 ) Where r is the radius of the conductor, D is the distance between the conductors, σ is the conductivity and µ is the permeability of the cable. However, if the cable is stranded in nature, the correction factor is given as Where r w is the radius of each strand in the conductor. The resistance obtained in (1) is for unit length of a single conductor. If a two-wire transmission model is considered, the resistance has to be doubled. For a 3-wire residential network, the presence of earth wire has an influence on the overall resistance due to proximity effect.

B. Inductance
The inductance of two-wire power line cable includes the self-inductance of each conductor and mutual inductance between them. It is given as Where, µ r is the relative permeability of the conductor. For a stranded conductor a correction factor should also to be multiplied to the total inductance, but many authors neglect this value [16].
Where n w is the number of strands in the conductor As per [14], the effective resistance of the wire may increase due to skin effect but the inductance of the wire decreases. The correction factor for the skin effect on the inductance is given as The presence of earth wire in the conduit and the geometry of the cables placed in the conduit will affect the overall inductance leading to an additional factor of uncertainty.

C. Capacitance
Since the cables in residential electrical networks are placed in conduit pipes, the capacitive coupling effects of the conduit, the geometry of the cable and the cable twist also affect the capacitance of the wiring. As per [15], for a twisted power line, the correction factor for equivalent dielectric constant (ε q ) is given as Where, T is the number of twists per meter length of wiring. Though the wires in the residential building are loosely twisted, the impact on the capacitance cannot be neglected due to the smaller cross-section of the conduit. Another aspect that is needed to be taken in to account is the geometry of the cable. The three wires are placed neither equilaterally nor right angled throughout the conduit, but certainly have an impact on the capacitance.
The capacitance between any two conductors is given as Where ε q is the equivalent dielectric constant obtained by As per [12], the total capacitance of a cable when placed in a conduit is given as Where C cndt is the capacitance between the cable and the conduit which is given as ( 1 1 ) Here, ε c is the dielectric permittivity between the cable and conduit and b is the radius of the conduit.

D. Conductance
The conductance of the cable is given by the equation ( 1 2 ) The presence of the conduit influences the conductance of the cable and it can be obtained directly from the capacitance in (10).
( 1 3 ) The four intrinsic parameters obtained from (1) to (13) can be used to determine the characteristic impedance (Zo) and the propagation constant (γ).The Characteristic impedance is given as:

Z
( 1 4 ) and the propagation constant is given by

III. COMPARISON OF PROPOSED PARAMETERS WITH OTHER SIMULATORS
In the last decade, researchers have developed numerous models to characterize and model a power line channel. In each model certain assumptions are made in estimating the distributed parameters. In the subsequent paragraphs of this section, few such model and their assumptions are discussed, The FTW PLC simulator [6] realized in MATLAB makes use of the technical data published by the cable manufacturer. In the simulation method, the Inductance and Capacitance are frequency independent and the effective Resistance and conductance are given by The channel parameters as proposed by Mlynek in [8] are frequency dependant unlike the FTW PLC simulator. But the distributed parameters are insensitive to the factors mentioned in the previous section except skin effect on the resistance.
Meng has assumed in [12] that the transmission line parameters are based on several factors that influence the R, L, G, C parameters. The effect of strands on resistance, the influence of earth wire and the effect of conduit on the capacitance are considered in estimating these distributed parameters.
In all the above three approaches, the authors have not considered the proximity effect on resistance, the geometry of the cable, twist pitch and the effect of skin depth on the inductance.
In this article, a comparative analysis is carried out on all the above mentioned models. The cable used for the study is the commonly used 2.5 sq.mm cable of size 36/0.3mm. The conductor is an unsheathed class 2 conductor. For the sake of FTW simulator, the capacitance and inductance values of the cable are deliberated as 15 pF/m and 1.08 µH/m. These results are compared with the distributed parameter values obtained from the proposed model. The distributed parameters R, L, G and C obtained from the various simulation methods are compared with the proposed method and are shown in Fig. 2, Fig. 3, Fig. 4 and Fig. 5 respectively. It can be depicted from the figures that the distributed parameters are dependent upon the nature of material used; spacing between the live and neutral wire, frequency of operation and physical properties of the wiring. The increase in the resistance can be attributed to the correction factor due to stranded conductor and due to the proximity effect of the earth wire. Similarly, the significant difference in inductance is observed when compared to other methods due to the multiplying factor considered for the geometry of the cable laid in the conduit. This is in addition to the skin effect.
Similarly, the variation in the capacitance and conductance by the proposed parameters is due to the multiplication factor from the geometry of the cable and the number of twists of the wiring placed in the conduit pipe. The capacitance between the wires and the conduit pipe also has a significant influence on the capacitance. In the proposed method, these values are found to be different for as the cross-section of wiring is changed, but in FTW PLC simulator L and C are the same irrespective of cross-section of the wire. From the distributed parameters obtained, the intrinsic parameters viz. impedance and propagation constant can be estimated using (18) and (19). As shown in Fig. 6, the impedance obtained from the proposed method is almost two times higher than the models proposed by Mlynek and Meng but significantly less than the one proposed in FTW PLC simulator.

IV. EXPERIMENTAL VERIFICATION OF PARAMETERS
A typical Indian residential wiring of 3x2.5 sq.mm unsheathed flexible PVC cable placed in a conduit is considered for experimental verification of the parameters. The measurements are carried out using the R&S ZVL Network Analyser.
Using the Network Analyzer, the input impedance of open circuit and short circuit ended cables is obtained and from the transmission line theory, the impedance of the power line can be obtained as ( 1 8 ) Where, Z oc Z sc is the input impedances of open circuited and short circuited cables respectively. The impedance obtained experimentally is compared with the simulated value from the proposed method and the same is shown in Fig. 8. It can be observed that the impedance obtained from the proposed distributed parameters is almost similar to the impedance achieved through measurements. The wiring in the residences need not be of uniform cross-section throughout. It differs with the appliances connected to it, so as to carry the load current without exceeding the thermal limits of the insulation. For example, 1.5 sq.mm wiring can be used for a simple lighting circuit but for a higher rating device like oven or refrigerator, a 2.5 sq.mm wiring is used. Fig. 9 represents the transfer function measured in terms of attenuation for different cable dimensions commonly used in Indian residences. It can be observed from the figure that, there is a little change in the attenuation among different cable dimensions. Typically, the residential electrical wiring in India contains of three wires viz., live, earth and neutral, but in such locations of the residence where class II electronics devices (which operate on low current) are to be connected, earth wire may not be used. In that case Fig. 10 shows the attenuation of two wiring and three wiring systems placed in a conduit pipe and placed without a conduit pipe. It can be perceived from the figure that the wiring placed in the conduit pipe has more attenuation then the one without the conduit pipe.

V. CHANNEL FREQUENCY RESPONSE
A sample single branch network as shown in Fig. 11 is examined in the article to verify the channel transfer function obtained from the proposed distributed parameters. The transfer function in terms of attenuation is measured from the S 21 parameters of Network Analyser. In this exercise, the frequency response up to 30 MHz is only measured for the sake of simplicity. The channel frequency response of a single branch network is simulated using the transmission line theory approach as in [17]. The obtained Amplitude response with the proposed distributed parameters is compared with the measured transfer function S 21 of the analyser. The same is represented in Fig. 12. The position of peaks and notches of the derived amplitude response almost match with the measured values, by which it can be deduced that an extensive analysis need to be carried out in understanding the various factors influencing the parameters. For further study of the channel transfer function, the impedance of few typically used electrical appliances is measured and is shown in Fig. 13. The loads considered in this article are 40 watts incandescent bulb, a laptop, 1200 watts Vacuum Cleaner and LED TV Monitor. It can be noticed that, at a particular frequency there is sharp change in the impedances for appliances.
The impedance of these loads is obtained in two stages. First, the impedance of the line (Z Line ) is measured without any load connected to the network and then the impedance of line is measured with different loads (Z Tot ) connected to the network. Since the line and the load are in parallel to each other, the total impedance of the line will be parallel sum of line impedance and the load impedance. Thus the load impedance (Z Load ) can be obtained by | | ( 1 9 ) VI. CONCLUSION The distributed parameters are evaluated on Indian residential networks by considering several factors that influence the power line. The obtained results from the proposed model are compared in detail with the available simulators. These values are also verified experimentally. In addition to the analysis made on the distributed parameters, the input impedance may also have an impact on the results obtained. Apart from the physical characteristics and material used for the wiring, the environment and the ambient conditions will also impact the distributed parameters. The channel transfer function is simulated for a sample network on the proposed parameters and verified experimentally. For further study, the behaviour of typical domestic appliances is also evaluated.