Why is transmission line 11KV or 33KV, 66KV not in 10KV, 20KV, or 30KV?

Why is Transmission line 11KV or 33KV, 66KV Not in 10KV, 20KV, or 30KV?

                                        

Many people cite Form Factor as a reason for so. Form Factor is defined as RMS Value to Average value of a given AC voltage and it is different for different waveforms.

Now the commonly used AC waveform we know is Sine Wave. A sine wave AC waveform has a form factor of 1.11 (Approx.). So, the reason given is that the transmitted voltage of 10kV, 20kV, 60kV, etc. is multiplied to this form factor to obtain such results which you described in the question like

For 10kV → 10 x 1.11 = 11.1 kV (Okay! It is approximately correct)

For 20kV → 20 x 1.11 = 22.2 kV (Okay! approximately 22kV)

For 60kV → 60 x 1.11 = 66.6 kV (Error! it is 66kV)

Like that

120 x 1.11 = 133.2kV (A big error of about +1.2kV because it is 132kV as used)

So, at each subsequent step, an amount of deviation has been seen which differs the actual and calculated result. Moreover, the deviation is not constant and increasing (see the last result, about +1kV deviation). Such results are intolerable and bring to the conclusion that this is the worst way of a calculation you can ever have. Because Form Factor has nothing to do here. Though it sounds convincing at a glance, yet it is utter nonsense to cite that as a reason.

The generation companies tends to generate round figure voltages like 10kV, 20kV, 60kV, 120kV, etc. But this huge voltage needs to be transmitted over a huge distance. The overhead line through which the power will be transmitted has its own impedance which will cause a considerable amount of voltage drop. This drop as being calculated is near about 10% based on all Physical factors. That’s why generation companies add 10% more in their actual target which neutralizes the line losses and the receiving end gets the targeted result. So,

Net Voltage = Target Voltage + 10% of Target Voltage

→ 132kV = 120kV + 12kV (10% of 120kV)

→ 66kV = 60kV + 6kV

→ 11kV = 10kV + 1kV

Hope that helps. Regards

EDIT: Modern EHV and UHV lines operate at much higher voltage like 400–800kV. The higher voltage at same kVA reduces the flow of current and thus reduces I²R loss. With the decreased value of I²R losses, we don't need to care much about line drop as that will automatically decrease. Increase in current causes increase in current density (current/unit cross-section area of the cable) and thus causes an increase in Electric field Intensity in the surrounding (as J=σE where J is the current density and E is Electric Field Intensity). This E causes corona discharge and thus corona loss. These aren't the problems when it comes to high voltage transmission and thus voltages like 765kV or similar mid-range voltages are possible to transmit. The only main concern with HV transmission is distance, insulation of the line and height of the tower. Voltage drop becomes insignificant. The lower value of current reduces corona as well but there is a separate set of things we use to reduce corona and HV interference with telecommunication lines.