Power system conductor volume calculation Dr Audih alfaoury T&D power systems 2017-1018 Electrical Energy Engineering Department Dr Audih alfaoury 1
The transmission of electric power is carried at high voltages due to the following reasons : 1- Reduces volume of conductor material. Consider the transmission of electric power by a threephase line, Let: P = power transmitted in watts V = line voltage in volts cos Φ = power factor of the load l = length of the line in meters R = resistance per conductor in ohms ρ = resistivity of conductor material a = area of X-section of conductor Dr Audih alfaoury 2
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It is clear that for given values of P, l, ρ and, the volume of conductor material required is inversely proportional to the square of transmission voltage and power factor. ( In other words, the greater the transmission voltage, the lesser is the conductor material required) and the best system for transmission of power is that for which the volume of conductor material required is minimum. 2- Increases transmission efficiency Input power = Power output+ Total losses Assuming J to be the current density of the conductor, J=I/a then, a =I/J Dr Audih alfaoury 4
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As J, ρ and l are constants, therefore, transmission efficiency increases when the line voltage is increased. 3- Decreases percentage line drop As J, ρ and l are constants, therefore, percentage line drop decreases when the transmission voltage increases. Dr Audih alfaoury 6
From the last discussion, it might appear advisable to use the highest possible voltage for transmission of power to save conductor material, however, it must be realized that high transmission voltage results in: (i)- the increased cost of insulating the conductors. (ii)- the increased cost of transformers, switchgear and other terminal apparatus. There is a limit to the higher transmission voltage.this limit is reached when the saving in cost of conductor material due to higher voltage is offset by the increased cost of insulation, transformer, switchgear etc.. Dr Audih alfaoury 7
Comperation between ac single and three phase systems 1- Single phase 2-wire a.c. system with one conductor earthed. Figure shows a single phase 2-wire a.c. system with one conductor earthed. The maximum voltage between conductors is Vm so that r.m.s. value of voltage between them is Vm / 2. Assuming the load power factor to be cos φ, Dr Audih alfaoury 8
Volume of conductor material required Dr Audih alfaoury 9
It is a usual practice to make this system (K) as the basis for comparison with other systems. Where k is for this system is : Dr Audih alfaoury 10
2. 3-Phase, 3-wire system. This system is almost universally adopted for transmission of electric power. The 3-phase, 3-wire system may be star connected or delta connected. Fig. shows 3-phase, 3-wire star connected system. The neutral point N is earthed. R.M.S. voltage per phase =Vm/ 2, and power transmitted per phase = P/3. Dr Audih alfaoury 11
Let a be the area of X-section of each conductor. Dr Audih alfaoury 12
Volume of conductor material required The equation above show us that is the relation between volume of conductor and phase voltage is Inversely proportional. Dr Audih alfaoury 13
Example : 50 km long transmission line supplies a load of 5 MVA at 0 8 p.f. lagging at 33kV. The efficiency of transmission is 90%. Calculate the volume of aluminum conductor required for the line when: a) single phase,2-wire system is used b) 3-phase, 3-wire system is used. The specific resistance of aluminum (resistivity) is 2 85 10 8 Ω m. Solution: Dr Audih alfaoury 14
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Note: that volume of conductor (and hence weight) required is less in case of 3-phase, 3-wire system. Dr Audih alfaoury 16
From the above analysis, the following conclusions can be drawn: 1. For a particular value of P, there is one value of conductor cross-section and one value of voltage which give the minimum total cost per unit length per unit power. 2. With the increase in power the economic values of conductor cross-section and voltage increase in proportion to P. The above simplified analysis also confirms that a very limited number of voltage levels with an appropriate value of conductor cross-section may be used in a system without deviating too far from the optimum value. The voltage level practically can be taking from table in the next slide.. Dr Audih alfaoury 17
In practice it is possible to determine the economic optimum voltage for lines more than 30km long using the following empirical formula : kv 5.5 km 1.6 load in KVA 150 That s all. Dr Audih alfaoury 18