3.2 Temperature, Grouping & Installation Derating Factors for Dubai

3.2 Temperature, Grouping & Installation Derating Factors for Dubai

Study focus: Dubai's harsh summer climate imposes severe thermal stress on electrical installations. DEWA enforces base ambient temperatures of $45^\circ\text{C}$ in air and $35^\circ\text{C}$ in ground. Candidates must know how to combine multiple correction factors ($C_a, C_g, C_i, C_f, C_s, C_d$) to calculate the overall derating multiplier and select compliant cable sizes.

Tabulated current-carrying capacities published in standard reference tables (such as BS 7671 Table 4E4A or IEC 60364) are based on standardized reference environmental conditions—typically $30^\circ\text{C}$ ambient air temperature in the UK/Europe and $20^\circ\text{C}$ ground temperature. Operating electrical cables in Dubai's extreme desert climate without proper derating will result in severe thermal overload, accelerated insulation breakdown, and catastrophic fire hazard.

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The Dubai Climatic Context & DEWA Ambient Bases

During Dubai summer months (May through September):

• Ambient shade air temperatures regularly exceed $45^\circ\text{C}$ to $48^\circ\text{C}$.
• External metal containment (conduits, cable trays, trunking exposed to direct solar radiation) can reach internal air temperatures exceeding $55^\circ\text{C}$ to $60^\circ\text{C}$.
• Unconditioned ceiling voids, roof plant rooms, and transformer enclosures frequently operate at $50^\circ\text{C}$.
• Ground temperatures at standard cable burial depths ($0.8\text{ m}$ to $1.0\text{ m}$) reach $35^\circ\text{C}$ to $40^\circ\text{C}$.

Because conductor current capacity is governed by the rate at which $I^2 R$ electrical heat can dissipate into the surrounding environment, a higher ambient temperature reduces the thermal gradient ($\Delta T = T_{\text{max}} - T_{\text{ambient}}$), drastically lowering permissible continuous current.

                      Thermal Dissipation Headroom (XLPE 90°C)
  ┌─────────────────────────────────────────────────────────────────────────┐
  │ Base 30°C Ambient Air:  ΔT = 90°C - 30°C = 60°C Headroom (Ca = 1.00)    │
  ├─────────────────────────────────────────────────────────────────────────┤
  │ Dubai 45°C Ambient Air: ΔT = 90°C - 45°C = 45°C Headroom (Ca = 0.87-0.90)│
  ├─────────────────────────────────────────────────────────────────────────┤
  │ Dubai 50°C Plant Room:  ΔT = 90°C - 50°C = 40°C Headroom (Ca = 0.82)   │
  └─────────────────────────────────────────────────────────────────────────┘

DEWA Standard Base Ambient Temperatures

• Cables Installed in Air / Trunking / Conduit: $45^\circ\text{C}$ base ambient air temperature.
• Cables Buried Underground / in Ducts: $35^\circ\text{C}$ base ground temperature.

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Ambient Temperature Correction Factor ($C_a$)

When using standard BS 7671 base tables (which assume a $30^\circ\text{C}$ air reference base), an ambient temperature correction factor $C_a$ must be applied.

The theoretical thermal rating factor follows the mathematical square-root relation:

$$C_a = \sqrt{\frac{T_{\text{max}} - T_{\text{ambient}}}{T_{\text{max}} - T_{\text{reference}}}}$$

Where $T_{\text{max}}$ is $90^\circ\text{C}$ for XLPE and $70^\circ\text{C}$ for PVC.

Notice that PVC suffers much steeper capacity loss than XLPE at elevated temperatures due to its lower maximum continuous thermal ceiling ($70^\circ\text{C}$ vs $90^\circ\text{C}$).

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Grouping Correction Factor ($C_g$)

When multiple power circuits or multi-core cables are installed in close physical proximity (bunched together in trunking, conduit, or stacked on cable trays), mutual thermal radiation prevents heat from escaping. The grouping correction factor $C_g$ penalizes closely packed cables.

Key Grouping Factors (BS 7671 Table 4C1)

1. Enclosed in Trunking or Conduit (Touching):

   • $2$ circuits: $C_g = 0.80$
   • $3$ circuits: $C_g = 0.70$
   • $4$ circuits: $C_g = 0.65$
   • $6$ circuits: $C_g = 0.57$
   • $9$ circuits: $C_g = 0.50$ (Cable current capacity is cut in half!)

2. Single Layer Touching on Perforated Cable Tray / Ladder:

   • $2$ cables touching: $C_g = 0.88$
   • $3$ cables touching: $C_g = 0.82$
   • $4$ cables touching: $C_g = 0.77$
   • $6$ cables touching: $C_g = 0.73$

3. Spaced Cable Installation ($1 D$ Clearance):

   • Maintaining a physical gap equal to one cable diameter ($1 D$) between adjacent cables allows free air convective cooling, keeping $C_g \approx 0.95 - 1.00$ regardless of the number of cables.

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Thermal Insulation Correction Factor ($C_i$)

When cables pass through or are embedded in building thermal insulation (e.g., glass wool, mineral fiber, or foam insulation in modern green building envelopes in Dubai):

• Cable totally surrounded by thermal insulation over a length $\ge 500\text{ mm}$: $C_i = 0.50$ (Capacity reduced by $50\%$).
• Cable in thermal insulation over $100\text{ mm}$ length: $C_i = 0.88$.
• Cable in thermal insulation over $200\text{ mm}$ length: $C_i = 0.78$.
• Cable in thermal insulation over $400\text{ mm}$ length: $C_i = 0.55$.

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Ground & Underground Installation Factors ($C_s, C_d, C_f$)

For direct burial underground feeders or cables routed in subterranean ducts:

1. Soil Thermal Resistivity ($C_s$): Standard ratings assume soil thermal resistivity of $1.2\text{ K}\cdot\text{m/W}$. Dry sand or uncompacted backfill in Dubai has high resistivity (up to $2.0\text{ K}\cdot\text{m/W}$), yielding $C_s \approx 0.85$. Using thermally stabilized sand backfill maintains $C_s = 1.0$.
2. Depth of Burial ($C_d$): Standard DEWA burial depth is $0.8\text{ m}$ under footpaths and $1.0\text{ m}$ under roadway crossings. Depths exceeding $1.5\text{ m}$ reduce heat loss, requiring $C_d \approx 0.95$.
3. Semi-Enclosed Ducting ($C_f$): Cables routed in underground non-metallic ducts experience restricted air circulation compared to direct soil burial ($C_f \approx 0.85 - 0.90$).

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Combined Derating Equation

The effective current-carrying capacity ($I_z$) under combined site conditions is:

$$I_z = I_t \times (C_a \cdot C_g \cdot C_i \cdot C_f \cdot C_s \cdot C_d)$$

To size the required tabulated cable rating ($I_t$):

$$I_t \ge \frac{I_n}{C_a \cdot C_g \cdot C_i \cdot C_f \cdot C_s \cdot C_d}$$

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Step-by-Step Worked Numerical Example

Problem Statement

A main sub-distribution feeder in a Dubai commercial high-rise connects a Main Distribution Board (MDB) to a secondary distribution panel located in an unconditioned rooftop HVAC plant room.

• System Voltage: 3-phase, $400\text{ V}$, $50\text{ Hz}$.
• Design Load Current ($I_b$): $210\text{ A}$.
• Protective Device: $250\text{ A}$ 3-Pole MCCB ($I_n = 250\text{ A}$).
• Cable Type: 4-core Copper XLPE/SWA/LSZH cable.
• Installation Condition: Installed on an open ladder rack in the rooftop plant room where peak summer ambient air temperature reaches $50^\circ\text{C}$. The cable is touching $3$ other fully loaded 3-phase cables in a single layer (total of $4$ grouped cables touching on ladder rack).
• Thermal Insulation: None ($C_i = 1.0$).

Calculate the required cable cross-sectional area.

Step 1: Identify Individual Derating Factors

1. Ambient Temperature Factor ($C_a$): For XLPE insulation at $50^\circ\text{C}$ air ambient (relative to $30^\circ\text{C}$ base), $C_a = 0.82$.
2. Grouping Factor ($C_g$): For 4 single-layer cables touching on a cable ladder, $C_g = 0.77$.
3. Other Factors: $C_i = 1.0$, $C_f = 1.0$.

Step 2: Compute Combined Derating Factor ($C_{\text{total}}$)

$$C_{\text{total}} = C_a \times C_g = 0.82 \times 0.77 = 0.6314$$

Step 3: Determine Minimum Required Tabulated Capacity ($I_t$)

$$I_t \ge \frac{I_n}{C_{\text{total}}} = \frac{250\text{ A}}{0.6314} = 395.95\text{ A}$$

Step 4: Select Cable Cross-Section from BS 7671 Table 4E4A

Consult BS 7671 Table 4E4A (4-Core XLPE Armored Copper Cable, Method E in Air):

• $120\text{ mm}^2$ Cu XLPE cable: $I_t = 358\text{ A}$ (Insufficient: $358 < 395.95\text{ A}$)
• $150\text{ mm}^2$ Cu XLPE cable: $I_t = 407\text{ A}$ (Sufficient: $407 \ge 395.95\text{ A}$)
• $185\text{ mm}^2$ Cu XLPE cable: $I_t = 461\text{ A}$

Step 5: Verify Effective Derated Capacity ($I_z$)

$$I_z = I_t \times C_{\text{total}} = 407\text{ A} \times 0.6314 = 256.98\text{ A}$$

Since $I_b (210\text{ A}) \le I_n (250\text{ A}) \le I_z (256.98\text{ A})$, the $150\text{ mm}^2$ 4-core Cu/XLPE/SWA/LSZH cable is fully compliant.