# Economic choice of transmission voltage

While designing any transmission line, economy is one of the most important factors the engineer must consider. An electrical power transmission line must be designed in such a way that the maximum economy is achieved. Economics of electric power transmission is influenced by various factors such as the right of way, supporting structures, conductor size, transmission voltage etc. Transmission voltage closely influences the economics of power transmission. Generally, electric power is transmitted using 3-phase AC system at high voltages. Before studying how to choose economic transmission voltages, one should know the advantages and limitations of high voltage transmission.

### Advantages of high voltage transmission

• Efficient transmission of larger amounts of power:
In a 3 phase AC system, power is calculated as P=√3*VIcosɸ. It is clear that, for a large amount of power to be transmitted at a lower voltage, the amount of current will be very large. Let's take an example, 200 MW of power is to be transmitted at 11kV and consider cosɸ = 0.8 lagging. In this case, the amount of current that will flow through the line would be 200,000,000 / (√3 * 11,000 * 0.8) ≈ 13,122 A. For safely carrying this much large current, a conductor with very large diameter or much more number of conductors in bundled form may be required. And if the same power is transmitted at 220kV, the current would be 200,000,000 / (√3 * 220,000 * 0.8 ) ≈ 656 A. As the power lost in a conductor is given as I2R, you can see large saving in losses can be achieved by transmitting electricity at higher voltages. From this example, it is clearly not feasible and practical to transmit larger power at lower voltages. Also, transmission of electricity at higher voltages is more efficient.
• Saving in conductor material: As shown above, for the same amount of power transmitted at a higher voltage the current will be relatively lower. Current carrying capacity of a conductor depends on the diameter of the conductor (conductor size) along with few other factors. That means, for larger currents to be transmitted, the conductor size must be larger. Hence, transmitting power at higher voltages will reduce the amount of current to be carried and consequently the required conductor size would also be lesser.
• Improved voltage regulation:
Decreased current will also result in decreased voltage drop across the line. Voltage regulation is defined as (VS  - VR)/VS. As voltage drop is decreased, the difference between sending end voltage and receiving end voltage is also decreased. Thus, voltage regulation is improved.

### Limitations of high transmission voltage

With increase in the transmission voltage
• cost of insulators increases
• cost of transformers increases
• cost of switchgear increases
• cost of lightning arrestor increases
• cost of support towers increases (as taller towers with longer cross arms are required)

## Economic choice of transmission voltage

From the above advantages and limitations of high voltage transmission, we can say that with increase in transmission voltage the cost of conductor material can be reduced and the efficiency can be increased. But the cost of transformers, insulators, switchgear etc. is increased at the same time. Thus, for overall economy, there is an optimum transmission voltage. The limit to use of higher transmission voltage is reached when the saving in cost of conductor material is offset by the increased cost of transformers, switchgear, insulators etc. The economical transmission voltage is one for which the sum of cost of conductor material, transformers, switchgear, insulators and other equipment is minimum.
If the power to be transmitted and the length of transmission are known, calculations are made for various transmission voltages. Initially, some standard transmission voltage is selected and the relative total cost of equipment is determined. A graph is drawn for the total cost of transmission with respect to various transmission voltages as shown in the figure at right. The lowest point on the curve gives the optimum transmission voltage. As here in the graph, point P is the lowest and the corresponding voltage OA is the optimum transmission voltage.
The above method of finding economical transmission voltage very rarely used as it is hard to pre-determine the costs of various equipment. Instead, an empirical formula, according to the American practice, is used. According to this formula, an economical transmission voltage for a 3 phase AC system is given as,
Where, V = line voltage in kV
P = maximum power per phase (in kW) to be delivered over single circuit
L = distance of transmission in km
Economical transmission voltage depends on the power to be transmitted and the length of transmission. If the power to be transmitted is large, cost per kW of terminal equipment reduces. This results in increased economic transmission voltage. If the distance of transmission is increased, saving in the cost of conductor material can be significantly increased by increasing the transmission voltage.