--- title: "When HVDC is economical; equal transmission capacity" subject: "Power Electronics" chapter: 7 key: "semester_7/power_electronics:hvdc-economical-bulk-power" source: https://www.bctengineer.com/q/semester_7/power_electronics/hvdc-economical-bulk-power site: BCT Engineering --- # When HVDC is economical; equal transmission capacity Power Electronics · Chapter 7: HVDC power transmission - Asked in: 2072 Chaitra, 8 marks - Video: [hvdc transmission system | hvdc transmission line | hvdc transmission system in hindi | what is hvdc](https://www.youtube.com/watch?v=H-fAaLeulYo) — Mind of Engineer - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_7/power_electronics/hvdc-economical-bulk-power - Whole chapter: https://www.bctengineer.com/md/semester_7/power_electronics/chapter-7 ## Question Justify the statement "HVDC power transmission is only economical than HVAC transmission if bulk amount of power has to be transmitted over a long distance". And also justify that the power transmission capacity of HVDC and HVAC lines are equal. ## Short answer HVDC has high fixed terminal cost but lower line cost per km due to 2 conductors, no stability limits, and lower losses. Total cost becomes cheaper only beyond the break-even distance, requiring bulk power to offset terminals. For equal capacity: with same conductor and insulation, V_d = V_m, I_d = I, AC power factor 0.943 yields P_dc = 2V_mI = 2.121 V_mI * 0.943 = P_ac, so capacities match. ## Answer HVDC needs costly converter stations (thyristor valves, converter transformers, filters, reactive compensation) at both ends, but its line is cheaper per km and has lower losses. So HVDC becomes economical only when the line saving is large enough to pay for the terminals, i.e. for **bulk power over a long distance**. #### Justification of the statement - **Terminal cost:** HVDC terminal cost is much higher than AC substations. This is a fixed cost, independent of distance. - **Line cost:** DC line needs 2 conductors instead of 3, lighter towers, less insulation and narrower right of way, so cost per km is lower. Its losses are about 2/3 of AC. - **Total cost** = terminal cost + (cost per km × distance). The AC curve starts low but rises steeply; the DC curve starts high but rises slowly. They cross at the **break-even distance** (about 500–800 km for overhead lines, 40–80 km for cables). ```text Cost | / AC | / | / _____ DC | _____X----- | _____- / : | DC - / : | / : | AC / : | / : | / : +-----------------:------> km break-even distance ``` - **Power level:** converter cost per MW falls as rating rises, and the 2-conductor saving grows with power; for small power the fixed terminal cost cannot be recovered. - Also, long AC lines need series and shunt compensation and are stability-limited ($P = \frac{V_1V_2}{X}\sin\delta$), adding cost; DC has no such limit. So HVDC is cheaper than HVAC **only** when large power is sent beyond the break-even distance (or for long cables / asynchronous links). #### Power transmission capacity of HVDC and HVAC lines are equal **Assumptions:** same conductor size and current $I$, same insulation (peak voltage to earth $V_m$), DC voltage $V_d = V_m$, $I_d = I$. $$ \begin{aligned} P_{ac} &= 3\cdot\frac{V_m}{\sqrt{2}}\cdot I\cos\phi = 2.121\,V_mI\cos\phi \\ P_{dc} &= 2V_dI_d = 2V_mI \\ \frac{P_{dc}}{P_{ac}} &= \frac{0.943}{\cos\phi} \end{aligned} $$ For a normal power factor of $\cos\phi = 0.943$, $P_{dc} = P_{ac}$. Thus a bipolar DC line with **2 conductors** has the same capacity as a three-phase AC line with **3 conductors**, while its losses are $2I^2R$ against $3I^2R$ (2/3) and it saves one conductor and its insulators. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Why does HVDC become economical only beyond a certain distance? A. Its converter terminals are cheap but the line is costly B. Its terminals have high fixed cost, but its line cost per km is lower, so the saving eventually pays for the terminals C. Its losses are higher so it needs shorter lines D. AC lines need no terminals so they are always cheaper Answer: B. HVDC has a high fixed terminal cost independent of distance but a lower cost per km, so total cost curves cross at the break-even distance. (Key point: Terminal versus line cost) 2. According to the answer, the break-even distance for overhead lines is about: A. 40-80 km B. 5-10 km C. 500-800 km D. 5000 km Answer: C. About 500-800 km for overhead lines, while for cables it is about 40-80 km. (Key point: Break-even distance) 3. Which is NOT a reason the HVDC line costs less per km than HVAC? A. Only two conductors are needed B. Lighter towers and narrower right of way C. It needs no converter transformers D. Less insulation is required Answer: C. Converter transformers are part of the costly HVDC terminals; the line saving comes from fewer conductors, lighter towers, less insulation and narrower right of way. (Key point: Reasons for lower DC line cost) 4. Why must the power be bulk for HVDC to be economical? A. Converter cost per MW falls with rating and the two-conductor saving grows with power, recovering the fixed terminal cost B. Small power cannot be converted to DC at all C. AC lines cannot carry bulk power D. DC losses fall to zero at high power Answer: A. For small power the fixed terminal cost cannot be recovered, whereas at bulk power the savings outweigh it. (Key point: Power level effect) 5. With the same conductor current I and same peak voltage Vm to earth, the bipolar DC power is: A. 3 Vm I B. 2 Vm I C. 2.121 Vm I D. Vm I / 2 Answer: B. Pdc = 2 Vd Id = 2 Vm I, whereas the AC power is 3(Vm/sqrt2) I cos(phi) = 2.121 Vm I cos(phi). (Key point: Equal capacity derivation) 6. Pdc/Pac = 0.943/cos(phi). The two capacities are equal when cos(phi) is: A. 1.0 B. 0.5 C. 0.8 D. 0.943 Answer: D. Setting 0.943/cos(phi) = 1 gives cos(phi) = 0.943, a normal power factor, so a 2-conductor DC line matches a 3-conductor AC line. (Key point: Power ratio and equality) ## Related in Power Electronics - [Why HVDC over HVAC: mathematical comparison](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_electronics%3Ahvdc-vs-hvac-comparison) — Power Electronics, chapter 7, asked 4× - [HVDC power loss is 2/3 of HVAC](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_electronics%3Ahvdc-two-thirds-loss) — Power Electronics, chapter 7, asked 2× - [Compare HVAC and HVDC; 2/3 power loss](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_electronics%3Acompare-ac-dc-two-thirds-loss) — Power Electronics, chapter 7 - [HVDC advantages and power transfer capacity](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_electronics%3Ahvdc-power-transfer-capacity) — Power Electronics, chapter 7, asked 2× - [HVDC two conductors vs HVAC three conductors](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_electronics%3Ahvdc-two-vs-three-conductors) — Power Electronics, chapter 7, asked 2× - [HVDC vs HVAC line conductor saving](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_electronics%3Ahvdc-conductor-saving) — Power Electronics, chapter 7, asked 2× ## Related in other subjects - [HVDC for long distance and B2B significance](https://www.bctengineer.com/question.md?key=semester_8%2Fhigh_voltage_engineering%3Ahvdc-long-distance-b2b) — High Voltage Engineering, chapter 1 - [T/F: HVDC better for longer lines](https://www.bctengineer.com/question.md?key=semester_8%2Ftransmission_and_distribution_system_design%3Atf-hvdc-longer-length) — Transmission and Distribution System Design, chapter 1 - [Justify higher voltage/more circuits for more power](https://www.bctengineer.com/question.md?key=semester_8%2Ftransmission_and_distribution_system_design%3Ajustify-higher-voltage-more-circuits) — Transmission and Distribution System Design, chapter 2 - [HVDC vs HVAC and HVDC scope in Nepal](https://www.bctengineer.com/question.md?key=semester_8%2Fhigh_voltage_engineering%3Ahvdc-hvac-compare-nepal) — High Voltage Engineering, chapter 1