How to determine Economical Transmission Voltage for any transmission line?

Economical Transmission Voltage

Have you ever wondered why transmission lines operates on certain values, and how they are determined? What are the factors that affect the operating voltage of a transmission line? In this article, you will learn how to calculate the most economical transmission voltage for any particular transmission line project.

There are different types of transmission lines used in power systems operating on high voltages from 11kv up to 765kv and more. But there are certain parameters that are used to calculate the most economical transmission voltage value of that line.

We all know that increasing the value of transmission voltage will reduce the line current as both are inversely proportional. And due to reduced current, the transmission losses (I²R) will be reduced. But there is a limit in increasing the voltage as well. Because due to increased voltage, the cost of switchgears, transformers and other system apparatus will be increased. Hence, we can only increase the voltage to some extent and after that, the cost reduction will saturate. That saturating point will give the most economical transmission voltage value.

Basic Method

One basic method to calculate the economical transmission voltage value is by using following formula:

\( \mathrm{\mathit{V}\mathrm{\, =\, }5.5\times \sqrt{0.62\mathit{L}\mathrm{\, +\, }\frac{3\mathit{P}}{150}}} \)

Or,

\( \mathrm{\mathit{V}\mathrm{\, =\, }5.5\times \sqrt{0.62\mathit{L}\mathrm{\, +\, }\frac{Q}{150}}} \)

Where,

• P = Per phase maximum power to be transferred in kW
• L = Length of the transmission line in km
• Q = Max. total power in kVA
• V = Economical Transmission Voltage of transmission line

By using above formula, you can calculate the economical transmission voltage for any transmission line by using its given length and power to be transmitted.

For example, for a transmission line of 50 km length and of 600 kVA, the economical transmission voltage from the above formula will be around 32.53 kV, which is nearly 33kV. So the economical transmission voltage for that line will be 33kV.

Kelvin’s Law for Economical Size of Conductor

Kelvin’s law states that when the cost of annual depreciation and interest on the capital cost of conductor material, is equal to the cost of energy losses, will be the most economical size of conductor.

The capital cost of conductor material is directly proportional to the line length and cross section area of the conductor. While the cost of energy losses will be inversely proportional to the cross section area of conductor, because the value of resistance increases as the area decreases.

So the most economical design will be when both of these costs are equal. Using this method, we can calculate the cross section area of the conductor, because the line length will be fixed. And by using the cross section area, we can easily calculate the value of operating voltage.

Let us assume, C1 is the interest and depreciation on capital cost of conductor. It will be directly proportional to the value of cross section area of conductor.

S1 ∝ a

Hence, S1 = K1×a

Assume S2 as total cost of energy losses annually, which will be inversely proportional to the cross section area of conductor.

S2 ∝ 1/a

Hence, S2 = K2/a

Here K1 and K2 are constants.

Total Annual cost S will be S1 + S2.

S = S1 + S2

S = K1*a + K2/a

So for most economical size, the differentiation of S with respect to a must be zero. Thus,

dS/da = d(K1*a + K2/a) / da = 0

K1 – K2/a² = 0

K1 = K2/a²

Hence the most economical cross section area,
\( \mathrm{\mathit{a}\mathrm{\, =\, \sqrt\frac{K2}{K1}}} \)

Importance of Economical Transmission Voltage

Why do we need to figure-out the most economical transmission voltage for each transmission line? Isn’t the voltage and current and losses and costs are co-related? If we increase the voltage, then the cross section area of the conductor will decrease. But at the same time, due to reduced area, the resistance will increase ultimately increasing the losses (I²R). Also if we do not increase the voltage, then the current will be higher which will also result in increased losses. Hence it is important to determine the perfect point where both capital costs and cost of transmission losses will be minimum.

Factors Affecting the Cost of Transmission Line:

Here are some major points that affects the capital cost of any particular transmission line:

• Length of the transmission line
• Maximum Power to be transmitted
• Conductor material
• Cost of Switchgears, transformers, etc. (More expensive auxiliaries for higher voltages)
• Geography and weather of the area where the line is to be installed

Conclusion

Determining the most economical transmission voltage level for power transmission is necessary, but it is usually predetermined by most companies in the sector. They just have to make some changes in the general design according to the needs of particular projects like specific terrain and weather conditions, regulatory compliances, etc. Most of the transmission lines of same span and power capacity are similar in design with some minor changes.