Losses in Electrical Transmission Lines - Term Paper Example

Title: Report on Transmission of Electrical Energy Name: Unit: Date: Table of Contents Introduction 3 Theoretical Maximum Power 3 Therefore P is Maximum when R=r 4 Aim 4 Equipment 4 Results 5 Table 1: Resistive Line: 5 Table 2: Inductive Line: 5 Table 3: Compensated Inductive Line: 5 Analysis 6 Graphs 6 Discussion 8 Conclusion 8 Works Cited 8 Introduction Study of losses found in electrical transmission lines is of great importance since the distance covered by these lines expounds on the problem. This is because transmission of power is basically the bulk movement of electrical energy Power transmission over the years has been improved to bring efficiency as it is the major pillar of all economies. A unique problem faced by the power industry is the inability to store electrical energy. There exists therefore a need for almost matching generation and consumption of power. More consumption than generation may lead to system failures whereas more generation than consumption is uneconomical. Losses due to wastage are great taking into consideration the large capital outlay of the power generation systems. This therefore negates the need of a sophisticated control system to safeguard consumer and producers gadgets. The interchange of alternating current is a function of differences in phases between any two nodes. A difference of zero degrees between any two phases is an indication that no power has been transmitted between the two nodes since as earlier stated, power transmission is a function of phase difference.[Oke12] A phase difference of between 1 and 90 degrees results into a stable transmission and any power transmission whose phase angle is greater than 90 degrees is referred to as unstable.[Oke12] A load resistance will dissipate maximum power transfer when it is equal to the Norton resistance of the same network that supplies the power. The Norton resistance of the system is taken as a datum whereby if the load resistance has a value that is higher or lower than the datum, then the power dissipated will not be maximum. [Abd10] Theoretical Maximum Power Consider the diagram below Voltage = E (volts); Resistance = r (ohms); Load Resistance = R; Electric Current = i Power delivered to load R; Substituting equation 1 into 2 Differentiating P with respect to R P maximum is found when and solve for R Therefore P is Maximum when R=r Therefore replacing R with r in equation 3 Aim To determine the maximum power that can be delivered by a transmission line with fixed impedance to a resistive load. Equipment Digital Multimeter (DMM) Digital Storage Oscilloscope (DSO) Synthesized Function Generator (SFG) Resistors: 150Ω, 1KΩ Potentiometer. Capacitor: 3.3nF (non-polarised) Inductor: 47uH Results Table 1: Resistive Line: RL VL (V) P (mW) 0 0 0 100 1.65 2.31 150 1.35 2.93 200 1.19 2.75 250 1.09 2.48 300 1 2.22 350 0.977 1.99 400 0.935 1.81 450 0.917 1.66 500 0.885 1.518 Table 2: Inductive Line: RL VL (V) P (mW) 0 0 0 50 2.23 8.24 100 1.23 12.58 150 0.957 13.55 200 0.858 12.95 250 0.790 11.86 300 0.767 10.73 350 0.743 9.70 400 0.729 8.80 450 0.720 8.025 500 0.711 7.36 Table 3: Compensated Inductive Line: RL VL (V) P (mW) 0 0 0 50 2.16 9.3 100 1.14 12.9 150 0.800 4.2 200 0.647 2.1 250 0.564 1.3 300 0.514 0.88 350 0.482 0.66 400 0.463 0.53 450 0.449 0.45 500 0.435 0.38 Analysis Graphs Figure 1: Resistance Line Figure 2: Compensated Inductive Line (14mW) Figure 3: Compensated Induction Line (13mW) Discussion Sample calculation for compensated inductive line From the graphs, it was seen that the line impendence affected the power output sharply from the start and the evened out on further increase of load resistance. This indicates an optimum value where the lines will be most efficient below and above which power output will be below par. This therefore creates a challenge in power transmission requiring the need to determine optimum voltages for transmission depending on type of cables used and distance. Distance becomes an issue since it magnifies the resistance that the system will be subjected to. Conclusion The compensated inductive line gave the maximum power output hence can be considered as the most appropriate Works Cited Oke12: , (Oke, 2012), Abd10: , (Abdullah, 2010), Read More