3.3 Voltage Drop Limits & Calculation Methods

3.3 Voltage Drop Limits & Calculation Methods

Study focus: Voltage drop compliance is strictly audited by DEWA during building inspection. Candidates must know the exact maximum percentage limits—3% for lighting (6.9 V) and 5% for power (11.5 V single-phase / 20.0 V three-phase)—and apply the $mV/A/m$ formulas for both single-phase and three-phase sub-mains and branch circuits.

Even if an electrical cable satisfies thermal current-carrying capacity criteria ($I_z \ge I_n$), long circuit route lengths can cause excessive voltage drop along the conductor resistance and reactance. Excessive voltage drop impairs equipment performance, causes motor stalling and overheating, creates flickering in luminaires, and wastes electrical energy as line heat losses.

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Principles of Voltage Drop in AC Circuits

When alternating current ($I$) flows through a conductor of length $L$, the internal conductor resistance ($R$) and inductive reactance ($X$) create a complex voltage drop vector:

$$\mathbf{\Delta V} = \mathbf{I} \cdot (R + jX)$$

Operational Consequences of Under-Voltage

1. Electric Motors: Electromagnetic torque decreases with the square of terminal voltage ($T \propto V^2$). A $10\%$ voltage drop reduces motor starting torque by $19\%$, forcing the motor to draw higher current to drive the mechanical load, causing severe winding overheating.
2. Lighting Systems: Incandescent and discharge lighting experience dramatic lumen output drops; LED drivers experience increased input current, reducing electronic component lifespan.
3. Control Relays & Contactors: Excessive line drop causes magnetic contactor chatter, contact welding, or drop-out during motor starting surges.

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DEWA Statutory Voltage Drop Limits

DEWA defines standard nominal low-voltage supply parameters as:

• Three-Phase Supply: $400\text{ V}$ line-to-line ($50\text{ Hz}$).
• Single-Phase Supply: $230\text{ V}$ line-to-neutral ($50\text{ Hz}$).

                      DEWA Permissible Voltage Drop Allocations
  ┌─────────────────────────────────────────────────────────────────────────┐
  │ Total Lighting Limit: 3.0% Max (6.9 V Single-Phase / 12.0 V Three-Phase)│
  ├─────────────────────────────────────────────────────────────────────────┤
  │ Sub-Main Feeder Target: ≤ 1.5% to 2.0%  │ Final Branch Target: ≤ 1.0% to 1.5%│
  ├─────────────────────────────────────────────────────────────────────────┤
  │ Total Power Limit: 5.0% Max (11.5 V Single-Phase / 20.0 V Three-Phase)  │
  ├─────────────────────────────────────────────────────────────────────────┤
  │ Sub-Main Feeder Target: ≤ 2.0% to 2.5%  │ Final Branch Target: ≤ 2.5% to 3.0%│
  └─────────────────────────────────────────────────────────────────────────┘

Statutory Maximum Voltage Drop Table

Note: Voltage drop is cumulative, measured from the primary point of supply (DEWA meter/transformer secondary or Main Distribution Board) to the furthest final utilization point or outlet.

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The Tabulated $mV/A/m$ Calculation Method

BS 7671 and cable manufacturers express voltage drop capability as tabulated millivolts per ampere per meter ($mV/A/m$).

1. Single-Phase Voltage Drop Formula

$$V_{d(1\Phi)} = \frac{(mV/A/m)_{1\Phi} \times I \times L}{1000} \quad \text{[Volts]}$$ $$\%,V_{d(1\Phi)} = \left(\frac{V_{d(1\Phi)}}{230}\right) \times 100\%$$

Where:

• $(mV/A/m)_{1\Phi}$ = Tabulated single-phase voltage drop factor.
• $I$ = Design load current ($I_b$) flowing in the circuit (Amperes).
• $L$ = One-way circuit route length (Meters).

2. Three-Phase Voltage Drop Formula

For balanced three-phase systems, line-to-line voltage drop is calculated as:

$$V_{d(3\Phi)} = \frac{(mV/A/m)_{3\Phi} \times I \times L}{1000} \quad \text{[Volts Line-to-Line]}$$ $$\%,V_{d(3\Phi)} = \left(\frac{V_{d(3\Phi)}}{400}\right) \times 100\%$$

Important Note: Standard BS 7671 tables publish $(mV/A/m)_{3\Phi}$ values that already incorporate the $\sqrt{3}$ multiplier. If you calculate voltage drop using individual conductor single-phase resistance ($r$) and reactance ($x$) values, you must multiply by $\sqrt{3}$:

$$V_{d(3\Phi)} = \frac{\sqrt{3} \times \sqrt{r^2 + x^2} \times I \times L}{1000}$$

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Power Factor ($\cos\phi$) & Inductive Reactance Adjustment

For small conductors ($< 35\text{ mm}^2$), cable impedance is almost purely resistive ($R$). For larger conductors ($\ge 35\text{ mm}^2$), inductive reactance ($X$) becomes significant.

When a load operates at a lagging power factor ($\cos\phi < 1.0$), the combined effective impedance $Z_r$ per unit length is:

$$Z_r = r \cos\phi + x \sin\phi \quad \text{[mV/A/m]}$$

Where:

• $r$ = Conductor resistance per meter at maximum operating temperature ($mV/A/m$).
• $x$ = Conductor inductive reactance per meter ($mV/A/m$).
• $\cos\phi$ = Load power factor (e.g., $0.85$).
• $\sin\phi = \sqrt{1 - \cos^2\phi}$ (e.g., $\sin(\arccos 0.85) = 0.527$).

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Step-by-Step Worked Numerical Example

Problem Statement

A 3-phase, $400\text{ V}$ sub-main feeder cable connects a Main Distribution Board (MDB) to a Sub-Main Distribution Board (SMDB) in a commercial building over a route length of $95\text{ meters}$. The design current is $I_b = 145\text{ A}$ at a power factor of $0.85$ lagging. Protection is a $160\text{ A}$ MCCB ($I_n = 160\text{ A}$). Candidate cable selected based on current capacity: $70\text{ mm}^2$ 4-core Cu/XLPE/SWA/LSZH.

• Tabulated 3-phase voltage drop factor for $70\text{ mm}^2$ XLPE cable (BS 7671 Table 4E4B): $(mV/A/m)_{3\Phi} = 0.60\text{ mV/A/m}$.

Determine whether the candidate cable complies with DEWA voltage drop limits.

Step 1: Calculate Absolute 3-Phase Line Voltage Drop ($V_d$)

$$V_{d(3\Phi)} = \frac{(mV/A/m)_{3\Phi} \times I_b \times L}{1000} = \frac{0.60 \times 145 \times 95}{1000} = \frac{8265}{1000} = 8.265\text{ V}$$

Step 2: Calculate Percentage Voltage Drop on Sub-Main Feeder

$$\%,V_{d(sub-main)} = \left(\frac{8.265\text{ V}}{400\text{ V}}\right) \times 100\% = 2.066\%$$

Step 3: Evaluate Remaining Allowance for Final Branch Circuits

• Maximum allowable cumulative drop for power circuits = $5.0\%$ ($20.0\text{ V}$).
• Remaining voltage drop budget for final power sub-circuits fed downstream from the SMDB:

$$\%,V_{d(final)} = 5.0\% - 2.066\% = 2.934\% \quad (\text{equivalent to } 11.74\text{ V on 400V 3-phase or } 6.75\text{ V on 230V 1-phase})$$

Step 4: Evaluate Lighting Circuit Constraints

• Maximum allowable cumulative drop for lighting = $3.0\%$ ($12.0\text{ V}$ 3-phase / $6.9\text{ V}$ 1-phase).
• If lighting panels are supplied from this SMDB, the remaining voltage drop allowance for final lighting circuits is:

$$\%,V_{d(final\_light)} = 3.0\% - 2.066\% = 0.934\% \quad (\text{only } 2.15\text{ V on 230V 1-phase})$$

Conclusion

The $70\text{ mm}^2$ cable is fully compliant for the sub-main power distribution ($2.07\% \le 2.5\%$ sub-main allocation). However, to ensure final lighting branch circuits do not exceed the $3.0\%$ cumulative limit, lighting circuits should either use larger final conductor sizes ($4\text{ mm}^2$) or be supplied from a dedicated lighting sub-main closer to the MDB.