--- title: "HVDC power loss is 2/3 of HVAC" subject: "Power Electronics" chapter: 7 key: "semester_7/power_electronics:hvdc-two-thirds-loss" source: https://www.bctengineer.com/q/semester_7/power_electronics/hvdc-two-thirds-loss site: BCT Engineering --- # HVDC power loss is 2/3 of HVAC Power Electronics · Chapter 7: HVDC power transmission - Asked in: 2079 Baishakh, 8 marks; 2073 Chaitra, 8 marks (asked 2 times) - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_7/power_electronics/hvdc-two-thirds-loss - Whole chapter: https://www.bctengineer.com/md/semester_7/power_electronics/chapter-7 ## Question Justify that the total power loss of HVDC transmission line is only 2/3th of total power loss in HVAC transmission line. Make assumption that the power loss per conductor is same for both lines and also the transmission capacity of both lines are same. ## Short answer Assuming identical conductors with equal current and per-conductor loss p, a 3-phase AC line has total loss 3p while a bipolar DC line has 2p. At the typical power factor 0.943, both lines transmit the same power. Thus, total HVDC loss is exactly 2/3 of the HVAC loss. ## Answer The claim compares a three-phase HVAC line (3 conductors) with a bipolar HVDC line (2 conductors) of the same power capacity, assuming each conductor has the same loss. #### Step 1: Show that both lines carry the same power Let both lines use the same conductors (same rms current $I$, resistance $R$ per conductor) and the same insulation (same peak voltage to earth $V_m$). For DC: $V_d = V_m$, $I_d = I$. $$ \begin{aligned} P_{ac} &= 3\cdot\frac{V_m}{\sqrt{2}}\cdot I\cos\phi = 2.121\,V_mI\cos\phi \\ P_{dc} &= 2V_dI_d = 2V_mI \end{aligned} $$ Equating, $P_{dc} = P_{ac}$ when $\cos\phi = \dfrac{2\sqrt{2}}{3} = 0.943$, which is a typical operating power factor. So a 2-conductor DC line has practically the same capacity as a 3-conductor AC line. #### Step 2: Loss per conductor Since both carry the same current $I$ (rms for AC, DC value for DC) through the same resistance $R$: $$ p_{ac} = I^2R = p_{dc} = p $$ (This is the given assumption.) #### Step 3: Total losses $$ \begin{aligned} \text{Loss}_{ac} &= 3I^2R = 3p \\ \text{Loss}_{dc} &= 2I^2R = 2p \end{aligned} $$ $$ \frac{\text{Loss}_{dc}}{\text{Loss}_{ac}} = \frac{2p}{3p} = \frac{2}{3} $$ **Hence the total power loss of the HVDC line is only 2/3 of that of the HVAC line of the same capacity.** ```text HVAC: ===== a (loss p) HVDC: ===== +Vd (loss p) ===== b (loss p) ===== -Vd (loss p) ===== c (loss p) Total: 3p Total: 2p ``` #### Further points - Efficiency of DC is also higher because there is no skin effect (AC resistance > DC resistance) and corona loss is lower. - No reactive (charging) current flows in a DC line, so the full current rating carries real power. - Converter station losses (about 0.5–1% per station) must be added, which is why HVDC pays off only for long distances. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What condition makes the 2-conductor DC line carry the same power as the 3-conductor AC line? A. cos(phi) = 1 B. cos(phi) = 2*sqrt(2)/3 = 0.943 C. cos(phi) = 0.5 D. Vd = 2Vm Answer: B. Setting 2VmI = 3(Vm/sqrt2) I cos(phi) gives cos(phi) = 2sqrt(2)/3 = 0.943. (Key point: Same capacity) 2. Why is the loss per conductor taken as the same p = I^2R for both lines? A. Same current through the same resistance B. Different voltage C. DC has no resistance D. AC has no loss Answer: A. Both use the same conductor (same R) and carry the same current I, so each has loss I^2R. (Key point: Loss per conductor) 3. What are the total losses of the AC and DC lines? A. AC = 2p, DC = 3p B. AC = 3p, DC = 2p C. Both 3p D. AC = 3p, DC = p Answer: B. The AC line has three conductors (3p) and the bipolar DC line has two (2p), so DC/AC = 2/3. (Key point: Total loss) 4. Why is the real DC saving in practice slightly more than the 2/3 figure? A. AC resistance is higher due to skin effect and AC lines have more corona loss B. DC lines are shorter C. Converters have no loss D. DC uses thinner insulation Answer: A. Skin effect raises AC resistance and corona is greater on AC lines, so the DC advantage is somewhat larger. 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