Underground cables

In short

An underground cable carries power through a conductor surrounded by solid insulation, a metallic earthed sheath and mechanical protection, buried in the ground instead of strung in air. It is the standard choice for urban distribution, industrial plants, substation interconnections, river and runway crossings, and increasingly for EHV links in Indian metros. Because the insulation is thin and the field is radial and intense, the examinable theory is almost entirely about electric stress, grading, capacitance, dielectric loss, heating and fault location. It is a scoring GATE/university topic and a routine interview area for roles in state DISCOMs, Power Grid, Tata Power, Adani, L&T, Sterlite, Polycab, KEI, Havells, RR Kabel and EPC contractors working under RDSS urban underground-cabling packages.

Explained

Construction and materials

• Conductor: stranded aluminium (most Indian power cables) or copper; compacted circular for small sizes, shaped (sector) cores in multi-core cables, Milliken (segmental) conductors above about 1000 mm² to cut skin effect.
• Conductor screen: semi-conducting layer that smooths the stranded surface so field lines are radial and no void sees high stress.
• Insulation: impregnated paper (older), PVC (LT only), XLPE (cross-linked polyethylene — the present standard), EPR, vulcanised rubber for flexibles.
• Insulation screen + metallic screen/sheath: semi-con layer plus copper tape/wires or lead/aluminium sheath — holds the outer surface at earth potential, carries charging and fault current, keeps moisture out.
• Bedding, armour, serving: bedding protects the sheath; armour (galvanised steel strip for multi-core, aluminium wire for single-core to avoid eddy losses) takes mechanical and crushing load; PVC/HDPE outer sheath (FRLS or FR-LSH grades indoors) resists corrosion.
• Single-core cables must never use magnetic steel armour individually — circulating eddy currents overheat it.

Classification

• By voltage: LT up to 1.1 kV; HT 3.3–11 kV; super-tension 22–33 kV; extra-high-tension 33–66 kV; extra-super-voltage beyond 132 kV.
• By number of cores: 1, 2, 3, 3½ (reduced neutral), 4 core.
• Belted cable (up to ~11 kV): three cores laid up, filler, then a common "belt" of insulation and one sheath. Field is partly tangential to the paper laminations, which have poor tangential strength — so belted construction is not used above about 11 kV.
• Screened cables (22–66 kV): H-type (Höchstädter) — each core wrapped in perforated metallised paper, all screens in contact, making the field purely radial in each core; S.L. (separate lead) type — each core has its own lead sheath, then a common armour. Both remove tangential stress; the H-type also improves heat dissipation, as its screens touch the sheath.
• Pressure cables (above ~66 kV, legacy): voids form in paper insulation on load cycling and ionise. Oil-filled cables keep low-viscosity oil under pressure through a hollow conductor or oil ducts, fed by reservoir tanks; gas-pressure cables use nitrogen at 12–15 bar (external-pressure type). They allow much higher working stress but need pressure plant and leak monitoring.
• XLPE has displaced paper and pressure cables in India for new work up to 400 kV: no oil, 90 °C continuous / 250 °C short-circuit rating, lower dielectric loss, lighter, easier joints.

Electric stress and grading

• In a single-core cable the field is radial; stress at radius x is g = V / (x·ln(R/r)) — maximum at the conductor surface (x = r), minimum at the sheath (x = R). Most of the insulation is therefore under-worked.
• Raising R indefinitely does not help: for a given V and permissible gmax, the most economical design has R/r = e = 2.718, giving r = V/gmax and insulation thickness r(e − 1).
• Capacitance (dielectric) grading: use layers of decreasing permittivity outward so that ε₁r = ε₂r₁ = ε₃r₂, flattening the stress profile. Limitation: the dielectric nearest the conductor must have both the highest permittivity *and* the highest strength — few real materials do, and spare material cannot be sourced freely.
• Intersheath grading: insert thin metallic intersheaths at chosen radii held at fixed potentials by a transformer tap, splitting one large stress cone into several smaller ones. Limitation: intersheaths carry charging current, are hard to maintain at correct potential, and a damaged intersheath is dangerous.
• Modern practice uses neither: XLPE with clean, void-free, screened extrusion has high enough uniform strength that grading is unnecessary.

Capacitance, charging current and dielectric loss

• A cable's capacitance per km is roughly 20–40 times that of an overhead line of the same voltage (small spacing, εr ≈ 2.3–4), so charging current and reactive generation are large.
• Charging current rises with length and voltage; at EHV it consumes conductor ampacity and sets a critical length beyond which the cable can carry no useful load without shunt reactor compensation — a key reason long EHV AC cable routes are rare and HVDC cable is used for sea crossings.
• Cable surge impedance is low (~30–50 Ω against ~400 Ω for a line), so travelling waves reflect strongly at cable–line junctions; cables also act as surge absorbers for connected equipment.
• Dielectric loss Wd = V²ωC·tanδ appears as heat in the insulation and is a rating limit at EHV. tanδ (loss tangent) is about 0.002–0.004 for XLPE and 0.003–0.01 for impregnated paper; a rising tanδ is a classic ageing indicator.
• 3-core belted cable: two capacitances exist — core-to-sheath Cs and core-to-core Cc. The effective capacitance per phase is CN = Cs + 3Cc, found from two simple bridge measurements (see worked example).

Heating, current rating and losses

• Rating is thermal, not mechanical: the conductor hot-spot must stay within 70 °C (PVC) or 90 °C (XLPE) continuous.
• Heat sources: I²R conductor loss (use ac resistance — skin and proximity effects), dielectric loss, and sheath/armour losses (circulating + eddy currents).
• Heat path: insulation → bedding → serving → soil, each a thermal resistance (thermal ohms, °C/W). Soil thermal resistivity (typically 100–250 °C·cm/W, worse in dry sandy ground) usually dominates; special thermal backfill is used for EHV routes.
• Derating factors multiply the base rating: ambient/ground temperature, depth of laying, grouping of circuits, soil resistivity, and duty cycle. IS 3961 (parts by cable type) and IS 7098 tables give base ratings and derating factors; manufacturers' tables are used in practice.
• Sheath bonding: *solid bonding* (both ends earthed) is simple but allows circulating current and loss — fine for short/LT runs; *single-point bonding* with a parallel earth continuity conductor eliminates circulating current but creates standing sheath voltage at the far end, limited by sheath voltage limiters (SVLs); *cross-bonding* transposes sheaths in three sections so induced voltages cancel — standard for long EHV circuits.

Laying, accessories, testing and fault location

• Direct laying: cable in a sand-bedded trench with protective bricks/tiles and route markers — cheapest, best heat dissipation, poorest for later alterations.
• Draw-in system: cables pulled into PVC/HDPE/DWC ducts between manholes — easy replacement and extension, lower current rating, used under roads; HDD (horizontal directional drilling) for trenchless road, rail and river crossings.
• Solid system: cables in bitumen-filled troughing/ducts — costly, now rare.
• Typical minimum cover (IS 1255): about 0.75 m for LT, 0.9 m for 3.3–11 kV, 1.05 m for 22–33 kV, more at road crossings; verify against the current edition and the utility's own standard, which may be stricter.
• Accessories: straight-through joints, heat-shrink/cold-shrink/pre-moulded terminations, stress cones (to control the stress concentration where the screen is cut back), separable connectors (elbows) for RMUs. Most cable failures are in joints and terminations, not the cable.
• Tests: IS 10810 and IS 7098 cover type, routine and acceptance tests — insulation resistance (Megger), high-voltage withstand, partial discharge, tanδ, bending, heat-shock, hot-set for XLPE. On site, high dc testing damages XLPE (space charge), so VLF (0.1 Hz) withstand and partial-discharge/tanδ diagnostics are the modern practice.
• Fault location: sectionalising + Megger/continuity to classify the fault (earth, short, open, intermittent); Murray loop and Varley loop bridge methods for low-resistance earth faults; Blavier test for an earth fault when no healthy core is available; TDR (echo) for open circuits and joints; surge generator ("thumper") with arc-reflection or impulse-current methods plus an acoustic/magnetic pinpointing coil for high-resistance faults; sheath faults by the step-voltage (A-frame) method.

Underground versus overhead, standards and Indian practice

• Underground wins on safety, aesthetics, immunity to storms, lightning, tree-faults and theft/tapping; loses on cost (several times the overhead cost per km), fault-location time, repair time and limited overload capability.
• Key Indian standards: IS 7098 XLPE cables — Part 1 (up to 1100 V), Part 2 (3.3–33 kV), Part 3 (66 kV up to 220 kV); IS 1554 PVC-insulated cables; IS 694 PVC wiring cables up to 1100 V; IS 1255 code of practice for laying and maintenance of power cables up to 33 kV; IS 3961 current ratings; IS 10810 test methods; IS 732 and SP 30 (National Electrical Code) for installations; internationally IEC 60502, 60840 and 62067.
• Statutory frame: Electricity Act 2003 and the CEA (Measures relating to Safety and Electric Supply) Regulations — the 2010 regulations were superseded by a 2023 edition; check the current notified text before quoting clearances and earthing clauses.
• Indian context: metro distribution in Mumbai, Delhi, Kolkata, Bengaluru and Hyderabad is largely 11/33 kV XLPE with RMUs; RDSS funds urban underground cabling and feeder segregation; 220 kV and 400 kV XLPE cable links are in service in Mumbai, Delhi and Bengaluru.

Key points

• Belted cable – common belt of insulation over three cores; tangential stress limits it to about 11 kV.
• H-type / S.L. type – screened constructions that make the field radial in every core, used 22–66 kV.
• Pressure cable – oil- or gas-filled to suppress void ionisation at EHV; largely replaced by XLPE.
• XLPE – 90 °C continuous, 250 °C short-circuit, low tanδ, no oil; today's default in India.
• Insulation resistance – R = (ρ/2πl)·ln(R/r); it *decreases* as cable length increases (resistances in parallel).
• Capacitance – increases with length; C = 2πε₀εr/ln(R/r) per metre.
• Stress is non-uniform – maximum at the conductor surface, minimum at the sheath, ratio R/r.
• Most economical conductor size – R/r = e, so r = V/gmax; it gives the smallest overall diameter for that V and gmax, equivalently the lowest gmax for a given overall size.
• Capacitance grading – ε₁r = ε₂r₁ = ε₃r₂ makes peak stress equal in every layer.
• Intersheath grading – metallic intersheaths at fixed potentials split the stress cone.
• Dielectric loss – Wd = V²ωC·tanδ; rising tanδ means ageing or moisture ingress.
• CN = Cs + 3Cc – effective per-phase capacitance of a 3-core belted cable.
• Charging current – large in cables; sets a critical length at EHV, needing shunt reactors.
• Rating is thermal – limited by soil thermal resistivity, grouping, depth and ambient; always derate.
• Sheath bonding – solid, single-point (with ECC and SVLs) or cross-bonding for long EHV runs.
• Water treeing – moisture plus field degrades XLPE; prevented by metallic moisture barriers and TR-XLPE.
• Murray/Varley loop – bridge methods locating a low-resistance earth fault as a fraction of loop length.
• Weak link – joints and terminations cause most failures, not the cable body.

Formulas and examples

Example 1 — Insulation resistance. Single-core cable, conductor diameter 2 cm, inner sheath diameter 5 cm, insulation resistivity 4.5 × 10¹⁴ Ω·cm, length 1 km.

• ρ = 4.5 × 10¹⁴ Ω·cm = 4.5 × 10¹² Ω·m; R/r = 2.5; ln 2.5 = 0.9163.
• R_ins = (4.5 × 10¹² × 0.9163) / (2π × 1000) = 4.1234 × 10¹² / 6283.2 = 6.56 × 10⁸ Ω ≈ 656 MΩ.
• For a 5 km length the same cable gives 656/5 = 131 MΩ — longer cable, lower insulation resistance.

Example 2 — Capacitance, charging current and dielectric loss. Same geometry (r = 1 cm, R = 2.5 cm), εr = 3.5, 33 kV 3-phase 50 Hz, 5 km, tanδ = 0.004.

• log₁₀ 2.5 = 0.39794 → C = 0.02416 × 3.5 / 0.39794 = 0.2125 μF/km → 1.0625 μF per phase for 5 km.
• Vph = 33000/√3 = 19 052.6 V; ωC = 314.16 × 1.0625 × 10⁻⁶ = 3.338 × 10⁻⁴ S.
• Ic = 3.338 × 10⁻⁴ × 19 052.6 = 6.36 A per phase; charging kVAr = 19 052.6 × 6.36 ≈ 121 kVAr per phase (363 kVAr total).
• Wd = 121 165 × 0.004 = 485 W per phase, about 1.45 kW for the three phases (≈97 W/km/phase).

Example 3 — Stress distribution and economical size. Single-core cable, conductor diameter 3 cm, insulation thickness 1.5 cm, 66 kV between conductor and sheath.

• r = 1.5 cm, R = 3.0 cm, ln(R/r) = ln 2 = 0.6931.
• gmax = 66 / (1.5 × 0.6931) = 63.5 kV/cm at the conductor; gmin = 66 / (3 × 0.6931) = 31.7 kV/cm at the sheath (ratio 2, as R/r = 2).
• Redesign for a permissible gmax of 60 kV/cm: r = 66/60 = 1.1 cm (conductor diameter 2.2 cm), R = 2.718 × 1.1 = 2.99 cm, insulation thickness = 1.89 cm. Note the smaller conductor needs *more* insulation but gives the lowest possible peak stress.

Example 4 — Capacitance of a 3-core belted cable. Bridge tests on an 11 kV, 3-core belted cable: (a) three cores bunched against sheath → 0.9 μF; (b) two cores and sheath bunched against the third core → 0.7 μF. Find CN and the charging current at 50 Hz.

• Test (a): 3Cs = 0.9 → Cs = 0.3 μF.
• Test (b): Cs + 2Cc = 0.7 → Cc = (0.7 − 0.3)/2 = 0.2 μF.
• CN = Cs + 3Cc = 0.3 + 0.6 = 0.9 μF per phase.
• Vph = 11000/√3 = 6350.9 V; Ic = 314.16 × 0.9 × 10⁻⁶ × 6350.9 = 1.80 A per phase.

Example 5 — Murray loop fault location. A 2 km cable has an earth fault on one core; the faulty core is looped to a healthy identical core at the far end and the bridge balances with ratio arms P = 70 Ω and Q = 30 Ω (Q adjacent to the faulty core).

• Loop length = 2L = 4 km. x = 4 × 30 / (70 + 30) = 1.2 km from the test end.
• Check: remaining loop = 4 − 1.2 = 2.8 km; 2.8/1.2 = 2.333 = 70/30 ✓.

Where it is used

• Urban distribution: 11 kV and 33 kV XLPE feeders with ring main units in BEST/Adani Mumbai, Tata Power-DDL and BSES Delhi, CESC Kolkata, BESCOM Bengaluru — ring and open-ring networks laid under RDSS and smart-city programmes.
• EHV city links: 220 kV and 400 kV XLPE cable circuits feeding load centres where overhead right-of-way is unavailable, with cross-bonded sheaths and distributed temperature sensing (DTS) fibre.
• Industrial and generating plants: LT and HT cabling for motors, MCCs and transformers in refineries, steel plants and cement works, designed to IS 1554/IS 7098 with cable schedules, trays, trenches and short-circuit withstand checks.
• Renewables: 33 kV inter-array and pooling cables in solar parks and wind farms; submarine cable for offshore and island links.
• Metro rail, airports and ports: cables in ducts and trenches with FRLS/zero-halogen sheaths for life-safety compliance.
• Job roles: distribution and electrical design engineers (cable sizing, derating, voltage drop, short-circuit withstand), cable jointers and testing engineers (VLF, PD, tanδ, fault location), O&M engineers in DISCOMs, and QA/production roles with Polycab, KEI, Finolex, Havells and Apar.

Interview questions

• Q: Why is a belted cable not used above about 11 kV? A: The field in the belt region has a tangential component across the paper laminations, where dielectric strength is low, so breakdown and void ionisation occur; screened (H or S.L.) types make the field radial.
• Q: Where is the electric stress maximum in a single-core cable, and why? A: At the conductor surface, because g = V/(x·ln(R/r)) and x is smallest there; it falls hyperbolically to a minimum at the sheath.
• Q: What is the most economical conductor size for a cable? A: The one with R/r = e = 2.718, which minimises gmax for a given voltage and overall insulation radius; then r = V/gmax.
• Q: Why does the insulation resistance of a cable fall as its length increases, while conductor resistance rises? A: Leakage paths through the insulation act in parallel along the length, so resistance ∝ 1/l, whereas the conductor path is a series resistance ∝ l.
• Q: Why is capacitance so much larger in a cable than in an overhead line? A: The conductor–earthed sheath spacing is a few centimetres instead of metres, and the solid dielectric has εr of 2.3–4 instead of 1.
• Q: What limits the length of an EHV AC cable circuit? A: Charging current, which flows along the whole length and consumes conductor ampacity; beyond the critical length no load current can be carried without shunt reactor compensation.
• Q: Compare capacitance grading and intersheath grading. A: Capacitance grading uses layers of falling permittivity to equalise stress but needs materials with high permittivity *and* high strength together; intersheath grading uses metallic sheaths at fixed potentials, which is effective but hard to maintain and hazardous if one fails.
• Q: What is tanδ and why is it measured? A: The loss tangent of the insulation; it fixes dielectric loss Wd = V²ωC·tanδ, and an increasing or voltage-dependent tanδ indicates moisture, voids or ageing.
• Q: Why is high-voltage DC testing avoided on XLPE cables in the field? A: DC injects space charge into the polymer and can cause failure later in service; VLF withstand with partial-discharge/tanδ measurement is used instead.
• Q: What is cross-bonding and when is it needed? A: Transposing the metallic sheaths of a three-phase single-core circuit over three equal sections so induced sheath voltages cancel, eliminating circulating current loss on long EHV routes while keeping sheath voltages safe.
• Q: Why is steel wire armour avoided on single-core AC cables? A: The alternating flux of a single core induces eddy and hysteresis losses in the magnetic armour, causing heating; non-magnetic aluminium wire armour is used instead.
• Q: How would you locate an earth fault on an 11 kV feeder? A: Isolate and Megger each core to classify the fault, use a Murray/Varley loop or TDR to get the approximate distance, then a surge generator with an acoustic/magnetic pinpointer to find the exact spot before excavation.

Common mistakes

• Treating insulation resistance like conductor resistance — forgetting that it varies inversely with length.
• Mixing radius and diameter in ln(R/r), or mixing cm and m in the stress and insulation-resistance formulas.
• Comparing an rms voltage with a dielectric strength quoted as a peak value when checking gmax.
• Writing CN = 3Cs + Cc instead of Cs + 3Cc for a 3-core belted cable, or forgetting that charging current uses phase voltage, not line voltage.
• Sizing a cable on ampacity alone — ignoring derating for grouping, depth, soil resistivity and ambient, and skipping voltage-drop and short-circuit withstand checks.
• Assuming capacitance/intersheath grading is modern practice; it is historical, replaced by void-free extruded XLPE with semi-conducting screens.
• Forgetting that joints and terminations, not the cable run, cause most failures — and that a cable fault is almost always permanent, unlike an overhead line fault.

Related topics

Transmission lines and cables · High-voltage engineering and insulation · Distribution systems and substations · Power system protection: relays and circuit breakers · Power quality and harmonics · HVDC transmission