--- title: "Compare HVAC and HVDC; 2/3 power loss" subject: "Power Electronics" chapter: 7 key: "semester_7/power_electronics:compare-ac-dc-two-thirds-loss" source: https://www.bctengineer.com/q/semester_7/power_electronics/compare-ac-dc-two-thirds-loss site: BCT Engineering --- # Compare HVAC and HVDC; 2/3 power loss Power Electronics · Chapter 7: HVDC power transmission - Asked in: 2078 Bhadra, 8 marks - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_7/power_electronics/compare-ac-dc-two-thirds-loss - Whole chapter: https://www.bctengineer.com/md/semester_7/power_electronics/chapter-7 ## Question Compare AC transmission over HVDC transmission. Justify that total power loss in HVDC is only 2/3th of total power loss in HVAC transmission lines. ## Short answer HVAC uses 3-phase, has stability limits, skin effect, and requires reactive compensation; HVDC uses 2 conductors, has no stability limit, and no reactive power in line. For same power, conductor, and insulation, AC power factor 0.943 gives equal capacity. DC line loss is 2I²R vs AC 3I²R, so HVDC loss is 2/3 of HVAC loss. ## Answer HVAC transmission sends power as three-phase AC through transformers; HVDC converts AC to DC at the sending end (rectifier), transmits DC, and converts back to AC (inverter). Each is best in a different range. #### Comparison of AC and DC transmission | Point | HVAC | HVDC | |---|---|---| | Conductors | 3 (3-phase) | 2 (bipolar), 1 (monopolar) | | Stability limit | Yes, $P \propto \sin\delta / X$ | None | | Reactive power | Charging current, needs compensation | None in line | | Skin effect / corona | Present / more | Absent / less | | Terminal cost | Low (transformers) | High (converters, filters) | | Line cost per km | High | Low | | Interconnection | Synchronous only | Asynchronous possible | | Fault current | High | Limited by converter control | | Voltage change | Easy (transformer) | Needs converter | | Harmonics | Little | Converter harmonics, filters needed | AC is cheaper for short and medium distances because terminals are simple; DC is cheaper for long distances (beyond the break-even distance) and for long cables. #### Justification of the 2/3 loss **Assumptions:** same power capacity, same conductor size and current $I$, same loss per conductor $p = I^2R$, same insulation (peak voltage to earth $V_m$, with $V_d = V_m$). **Same capacity:** $$ \begin{aligned} P_{ac} &= 3\cdot\frac{V_m}{\sqrt{2}}\cdot I\cos\phi = 2.121\,V_mI\cos\phi \\ P_{dc} &= 2V_mI \end{aligned} $$ These are equal for $\cos\phi = 0.943$, so a 2-conductor bipolar DC line has the same capacity as a 3-conductor AC line. **Total losses:** $$ \frac{\text{Loss}_{dc}}{\text{Loss}_{ac}} = \frac{2I^2R}{3I^2R} = \frac{2p}{3p} = \frac{2}{3} $$ **Hence the HVDC line loss is only 2/3 of the HVAC line loss** for the same power. In practice the saving is a little more, because the AC resistance is higher due to skin effect and AC lines have more corona loss. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Which statement about AC and DC economics is correct? A. AC is cheaper for short and medium distances; DC is cheaper beyond the break-even distance B. DC is always cheaper C. AC is cheaper for long cables D. They cost the same Answer: A. AC terminals are cheap, but DC line cost per km is lower, so DC wins beyond the break-even distance. (Key point: Cost by distance) 2. Which is a disadvantage of HVDC compared with HVAC? A. High terminal cost and converter harmonics needing filters B. Skin effect C. Stability limit D. Charging current Answer: A. Converter stations are expensive and produce harmonics that need filters; voltage cannot be changed by a simple transformer. (Key point: Terminal differences) 3. What does equal capacity P_ac = P_dc require? A. cos(phi) = 0.943 B. cos(phi) = 0.5 C. Different currents D. V_d = 2Vm Answer: A. 2VmI = 2.121 Vm I cos(phi) gives cos(phi) = 0.943. (Key point: Same capacity condition) 4. What is Loss_dc/Loss_ac under the stated assumptions? A. 3/2 B. 1/2 C. 2/3 D. 1 Answer: C. 2I^2R / 3I^2R = 2/3. 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