5.3 Touch Voltage, Protective Conductor Sizing, and Main Earthing Terminals

5.3 Touch Voltage, Protective Conductor Sizing, and Main Earthing Terminals

Quick Summary: Verifying electrical safety under SS 638 requires precise calculation of Touch Voltage ($U_t$) and Earth Fault Loop Impedance ($Z_s$). The total loop impedance $Z_s = Z_e + (R_1 + R_2)$ must be corrected for conductor operating temperatures and verified against statutory tables. Circuit Protective Conductors (CPCs) are sized either using simplified selection tables or the Adiabatic Equation ($S = \frac{\sqrt{I^2 t}}{k}$). The Main Earthing Terminal (MET) forms the central grounding node, requiring a removable disconnecting link for earth electrode testing and strict minimum conductor sizing ($6\text{ mm}^2$ minimum copper earthing conductor up to $45\text{ kVA}$).

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1. Mathematical Analysis of Touch Voltage ($U_t$)

During a phase-to-earth insulation fault on a Class I appliance, the exposed metallic enclosure becomes energized. The magnitude of potential appearing on the metal enclosure relative to true earth—or relative to adjacent earthed structural metalwork—is termed the Touch Voltage ($U_t$).

          [ TOUCH VOLTAGE DISTRIBUTION IN A PHASE-TO-EARTH FAULT ]

 Substation Transformer              Consumer Distribution Board       Fault Site
 Phase (230V) -------------[ R1 Line Conductor ]------------------> Exposed Metal
                                                                           |
   Ut = Touch Voltage Across Human Body <----------------------------------+
                                                                           |
 MET Busbar <-------------[ R2 Protective Conductor (CPC) ]---------------+ 
     |
     +---[ Ze Supply Earth Return ]---> Transformer Star Point

Touch Voltage Derivation

Let $U_0$ be the nominal phase-to-earth supply voltage ($230\text{ V AC}$), $Z_e$ be external earth fault loop impedance, $R_1$ be phase conductor resistance, and $R_2$ be Circuit Protective Conductor (CPC) resistance. The prospective earth fault current $I_f$ is:

$$I_f = \frac{U_0}{Z_s} = \frac{U_0}{Z_e + R_1 + R_2}$$

The touch voltage $U_t$ appearing on the faulty appliance casing is the voltage drop across the protective conductor ($R_2$) back to the main equipotential zone:

$$U_t = I_f \times R_2 = U_0 \times \frac{R_2}{Z_e + R_1 + R_2}$$

Where $Z_e$ is small relative to circuit wiring (common in local distribution boards in TN-S systems), the equation simplifies to:

$$U_t = U_0 \times \frac{R_2}{R_1 + R_2}$$

Impact of Conductor Sizing Ratio ($R_1 / R_2$)

• Equal Conductor Sizes ($S_1 = S_2 \implies R_1 = R_2$): $$U_t = 230\text{ V} \times \frac{R_2}{R_2 + R_2} = 230\text{ V} \times 0.5 = 115\text{ V AC}$$ Since $115\text{ V AC}$ greatly exceeds the conventional safe limit ($U_L = 50\text{ V AC}$), Automatic Disconnection of Supply (ADS) MUST isolate the circuit within $0.4\text{ s}$ to prevent fatal injury.
• Oversized Protective Conductor ($S_2 > S_1 \implies R_2 < R_1$): If CPC cross-sectional area is increased such that $R_2 = 0.25 \times R_1$, touch voltage drops to: $$U_t = 230\text{ V} \times \frac{0.25}{1.0 + 0.25} = 230\text{ V} \times 0.20 = 46\text{ V AC}$$ Because $46\text{ V AC} < 50\text{ V AC}$, the touch voltage remains below the dangerous threshold even during the fault duration.

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2. Earth Fault Loop Impedance ($Z_s$) Calculations & Thermal Corrections

To ensure protective devices operate within mandatory disconnection times ($0.4\text{ s}$ for final circuits), the total Earth Fault Loop Impedance ($Z_s$) measured at the furthest point of the circuit must satisfying:

$$Z_s \le Z_{s(\text{max})}$$

Where $Z_{s(\text{max})}$ is the maximum allowable loop impedance published in SS 638 Tables 41.2, 41.3, and 41.4 for the specific rating and trip curve of the circuit breaker or fuse.

                  [ TOTAL EARTH FAULT LOOP PATH (Zs) ]

+-------------------------------------------------------------------------+
| Zs = Ze (External Supply Loop) + R1 (Phase Cable) + R2 (CPC Conductor)  |
+-------------------------------------------------------------------------+
  [Substation Trans.] -> [Intake Service] -> [Phase Wire R1] -> [Fault Point]
          ^                                                          |
          |                                                          v
  [Substation Earth] <- [Cable Sheath Ze] <- [MET Node] <- [CPC Wire R2]

Temperature Correction Factor Adjustment

Standard cable resistance values ($r_1 + r_2$) provided in technical tables are measured at an ambient temperature of $20^\circ\text{C}$. However, during normal operating conditions or fault carrying states, conductor copper temperatures rise to maximum operating limits ($70^\circ\text{C}$ for PVC insulation, $90^\circ\text{C}$ for XLPE insulation).

Because copper resistance increases with temperature ($R_\theta = R_{20}[1 + \alpha_{20}(\theta - 20)]$), SS 638 mandates multiplying ambient measured resistance $(R_1 + R_2)_{20}$ by a thermal correction factor:

• PVC Insulated Cables ($70^\circ\text{C}$ Max Temp): Temperature Correction Factor = $1.20$
• XLPE / Thermosetting Cables ($90^\circ\text{C}$ Max Temp): Temperature Correction Factor = $1.28$

Master Loop Impedance Temperature Formula

$$Z_{s(\text{fault})} = Z_e + 1.20 \times (R_1 + R_2)_{20} \le Z_{s(\text{max})}$$

When performing field testing at ambient $20^\circ\text{C}$, the Licensed Electrical Worker (LEW) must verify that measured ambient loop impedance satisfies the 80% Rule ($Z_{s(\text{measured})} \le 0.80 \times Z_{s(\text{max})}$) to account for thermal rise during actual fault conditions.

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3. Sizing Circuit Protective Conductors (CPCs)

Under SS 638 Regulation 543.1, Circuit Protective Conductors must be sized using one of two approved methods: Method A (Standard Table Selection) or Method B (The Adiabatic Equation).

Method A: Simplified Selection Table (SS 638 Table 54.7)

When the protective conductor is constructed from the same metal (copper) as the line conductor, minimum CPC cross-sectional area ($S_p$) is selected directly from Table 54.7:

Method B: The Adiabatic Equation (SS 638 Regulation 543.1.3)

For precise economic engineering design—or where cable materials differ—the CPC cross-sectional area ($S$) must not be less than the value calculated by the Adiabatic Equation:

$$S = \frac{\sqrt{I^2 t}}{k}$$

Where:

• $S$: Minimum cross-sectional area of protective conductor ($\text{mm}^2$).
• $I$: Prospective earth fault current (rms AC Amperes) for a fault of negligible impedance.
• $t$: Operating disconnection time of the protective device (seconds).
• $k$: Factor taking into account the resistivity, temperature coefficient, and heat capacity of the conductor metal, as well as initial and final conductor temperatures.

Tabulated $k$ Factors under SS 638 (Tables 54.2 to 54.6)

Worked Step-by-Step Engineering Calculation

• Scenario: Calculate minimum copper PVC CPC size for a circuit with prospective fault current $I = 2000\text{ A}$, cleared by an MCB in $t = 0.10\text{ s}$. Copper PVC $k = 115$.
• Step 1: Calculate thermal energy value ($I^2 t$): $$I^2 t = (2000)^2 \times 0.10 = 4,000,000 \times 0.10 = 400,000\text{ A}^2\text{s}$$
• Step 2: Calculate square root of thermal energy: $$\sqrt{I^2 t} = \sqrt{400,000} = 632.455$$
• Step 3: Apply Adiabatic Equation: $$S = \frac{632.455}{115} = 5.50\text{ mm}^2$$
• Step 4: Select commercial cable size: Next standard commercial cable size $\ge 5.50\text{ mm}^2$ is $6.0\text{ mm}^2$.

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4. Main Earthing Terminal (MET) Architecture & Sizing Rules

The Main Earthing Terminal (MET) is the central distribution node where the earthing conductor, main protective bonding conductors, circuit protective conductors, and functional earth conductors are securely interconnected.

                   [ MAIN EARTHING TERMINAL (MET) NODE ]

   SP PowerGrid Cable Sheath / Earth Rod
                  |
                  v
       [ Earthing Conductor ]
                  |
                  v
   +--------------------------------------------------------------+
   |               MAIN EARTHING TERMINAL (MET)                   |
   |  +--------------------------------------------------------+  |
   |  |        REMOVABLE EARTH DISCONNECTING LINK              |  |
   |  +--------------------------------------------------------+  |
   +--------------------------------------------------------------+
        |                         |                        |
        v                         v                        v
 [Main Protective Bonding]   [Circuit Protective]     [Functional Earth]
 (Water/Gas/Steel Pipes)     Conductors (CPCs)       (Clean IT Earth)

Removable Disconnecting Link Requirements

SS 638 mandates that the MET must feature a robust, brass or copper removable disconnecting link. This link can only be unbolted using a tool. It allows the LEW to isolate the earth electrode from the building installation during periodic testing to measure earth electrode resistance ($R_A$) using a 3-pole Earth Resistance Tester without disconnecting active building protective bonding.

Statutory Conductor Sizing Mandates under SS 638

1. Earthing Conductor (Connecting MET to Earth Electrode / Intake Earth):
   • For domestic premises and small commercial intakes up to $45\text{ kVA}$ ($230\text{ V}$ single-phase or $400\text{ V}$ three-phase supplies, $\approx 65\text{ A}$ per phase): Minimum $6\text{ mm}^2$ copper.
   • Buried earthing conductors protected against corrosion but NOT mechanically protected: Minimum $16\text{ mm}^2$ copper.
   • Buried earthing conductors NOT protected against corrosion: Minimum $25\text{ mm}^2$ copper.
2. Main Protective Bonding Conductors (Connecting MET to Extraneous Services):
   • Minimum cross-sectional area: Must not be less than half the required CSA of the earthing conductor of the installation, with a strict minimum of $6\text{ mm}^2$ copper.
   • Maximum capping: Need not exceed $25\text{ mm}^2$ copper regardless of main intake size.