6.2 Maximum Demand Calculation and Diversity Factors for ≤45 kVA

6.2 Maximum Demand Calculation and Diversity Factors for ≤45 kVA

Quick Summary: Maximum Demand (MD) is the maximum load current or power drawn by an electrical installation from the supply grid during any specified operational interval. Because not all electrical appliances, lights, or socket outlets operate simultaneously at full rated capacity, calculating maximum demand using Diversity Factors under SS 638 Appendix 4 allows engineers to determine the realistic peak load. Proper maximum demand calculation prevents costly over-design while ensuring incoming supply cables, main cut-out fuses, and circuit breakers do not trip under normal peak operating conditions.

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1. Connected Load vs. Maximum Demand

Before sizing intake cables and protective switchgear, a clear distinction must be made between Connected Load and Maximum Demand:

• Total Connected Load ($P_{conn}$ or $S_{conn}$): The mathematical sum of the full-load power ratings of all installed electrical equipment, luminaires, socket outlets, motors, and appliances connected to the installation.
• Maximum Demand ($I_{md}$ or $S_{md}$): The maximum current or apparent power actually drawn by the installation at any one time under normal operating conditions. It is calculated by applying standardized diversity factors to individual sub-circuits.
• Diversity Factor: The ratio of the sum of individual maximum demands of sub-circuits to the maximum demand of the complete installation. In practical design, diversity factors are expressed as derating percentages or fixed allowances applied to connected loads.

$$\text{Maximum Demand} = \sum \left( \text{Connected Sub-Circuit Load} \times \text{Diversity Factor} \right)$$

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2. Supply Capacity Boundaries in Singapore (≤45 kVA Regime)

In Singapore, SP PowerGrid classifies low-voltage electricity supplies based on load capacity boundaries:

Single-Phase 230V Supply Limits

• 30A Single-Phase: Equivalent to $30\text{ A} \times 230\text{ V} = 6.9\text{ kVA}$. Standard intake for small domestic apartments.
• 60A Single-Phase: Equivalent to $60\text{ A} \times 230\text{ V} = 13.8\text{ kVA} \approx 14\text{ kVA}$. Maximum permissible single-phase supply allocation for residential or commercial units.
• Threshold Rule: If the calculated maximum demand exceeds $60\text{ A}$ (or $14\text{ kVA}$), SP PowerGrid mandates an upgrade to a Three-Phase 400V supply to prevent severe phase imbalance on the distribution network.

Three-Phase 400V Supply up to 45 kVA

• 45 kVA 3-Phase Rating: The maximum capacity boundary for standard small-commercial, food shop, office, or residential house installations operating on direct CT-less or standard 63A meter cut-outs.
• Current per Phase Calculation: For a balanced $45\text{ kVA}$ 3-phase supply at $400\text{ V}$ line voltage:

$$S = \sqrt{3} \times V_L \times I_L$$ $$45,000\text{ VA} = \sqrt{3} \times 400\text{ V} \times I_L = 692.82 \times I_L$$ $$I_L = \frac{45,000}{692.82} = 64.95\text{ A} \approx 63\text{ A per phase}$$

Thus, a $45\text{ kVA}$ 3-phase supply corresponds to a standard $63\text{ A}$ 3-pole main isolator / MCCB per phase.

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3. SS 638 Appendix 4 Diversity Factor Rules

Singapore Standard SS 638 Appendix 4 provides prescriptive rules for estimating maximum demand across domestic, commercial, and small industrial premises. The table below summarizes the mandatory diversity allowances:

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4. Single-Phase and Three-Phase Power Formulas

To compute phase currents accurately from connected active power ($P$ in kW) or apparent power ($S$ in kVA), use the standard electrical power equations:

Single-Phase Calculations (230V AC)

$$\text{Active Power: } P = V \times I \times \cos\phi$$ $$\text{Design Current: } I_b = \frac{P}{V \times \cos\phi} = \frac{P}{230 \times \cos\phi}$$ $$\text{Apparent Power: } S = V \times I = 230 \times I_b$$

Three-Phase Calculations (400V Line-to-Line / 230V Line-to-Neutral)

$$\text{Active Power: } P = \sqrt{3} \times V_L \times I_L \times \cos\phi$$ $$\text{Line Current: } I_L = \frac{P}{\sqrt{3} \times V_L \times \cos\phi} = \frac{P}{692.82 \times \cos\phi}$$ $$\text{Apparent Power: } S = \sqrt{3} \times V_L \times I_L = 0.6928 \times I_L \text{ (kVA)}$$

Phase Balancing and Neutral Current

In a 3-phase 4-wire installation, single-phase loads must be distributed evenly across Phase L1, Phase L2, and Phase L3. If the phase currents $I_1, I_2, I_3$ are balanced ($I_1 = I_2 = I_3$), the neutral current $I_N = 0\text{ A}$. For unbalanced loads, the resultant vector neutral current is calculated using:

$$I_N = \sqrt{I_1^2 + I_2^2 + I_3^2 - (I_1 I_2 + I_2 I_3 + I_3 I_1)}$$

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5. Comprehensive Step-by-Step Worked Maximum Demand Calculation

Example Scenario:

A small commercial office unit with a 3-phase 400V supply has the following connected loads:

1. Lighting: $40 \times 2 \times 18\text{W}$ LED panel fittings ($0.95$ power factor, total $1.52\text{ kW}$). Distributed equally: $0.507\text{ kW}$ per phase.
2. Socket Outlets: 6 separate $13\text{A}$ twin ring final circuits ($32\text{A}$ protection each). 2 ring circuits connected to L1, 2 to L2, 2 to L3.
3. Water Heating: $2 \times 3.5\text{ kW}$ single-phase instantaneous water heaters ($15.2\text{ A}$ each at $230\text{V}$). Heater 1 on L1, Heater 2 on L2.
4. Air-Conditioning: $3 \times 3\text{HP}$ 3-phase cassette air-conditioners ($3\text{ kW}$ each, $\cos\phi = 0.85$, total $9\text{ kW}$). Line current per AC unit $= \frac{3000}{\sqrt{3} \times 400 \times 0.85} = 5.1\text{ A}$.

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Step-by-Step Calculation Solution:

Step 1: Calculate Diversity for Lighting (Commercial: 90% allowance)

• Total Connected Lighting Power $= 1,520\text{ W}$
• Maximum Demand Power $= 1,520\text{ W} \times 0.90 = 1,368\text{ W}$
• Total 3-Phase Current $= \frac{1368}{\sqrt{3} \times 400 \times 0.95} = 2.08\text{ A per phase}$

Step 2: Calculate Diversity for 13A Socket Outlets (Commercial: 100% largest + 50% remaining)

• Each phase has 2 ring circuits rated at $32\text{A}$ capacity.
• Per Phase Socket Maximum Demand $= 100\% \text{ of Circuit 1 } (32\text{A}) + 50\% \text{ of Circuit 2 } (32\text{A} \times 0.50 = 16\text{A})$
• Per Phase Socket Maximum Demand $= 32\text{A} + 16\text{A} = 48\text{A per phase}$

Step 3: Calculate Diversity for Instantaneous Water Heaters (Commercial: 100% 1st + 100% 2nd)

• Heater 1 on L1 $= 15.2\text{ A}$
• Heater 2 on L2 $= 15.2\text{ A}$
• L3 Water Heater Load $= 0\text{ A}$

Step 4: Calculate Diversity for Air-Conditioning Units (3-Phase Motors: 100% 1st + 80% 2nd + 60% 3rd)

• Unit 1 (Largest) $= 100\% \times 5.1\text{ A} = 5.1\text{ A}$
• Unit 2 $= 80\% \times 5.1\text{ A} = 4.08\text{ A}$
• Unit 3 $= 60\% \times 5.1\text{ A} = 3.06\text{ A}$
• Total AC Maximum Demand per Phase $= 5.1 + 4.08 + 3.06 = 12.24\text{ A per phase}$

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Step 5: Tabulate Maximum Demand per Phase (L1, L2, L3)

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Step 6: Determine Overall Maximum Demand in kVA and Verify Supply Class

• Peak Phase Line Current occurs on L1 / L2 at $77.52\text{ A}$.
• Overall 3-Phase Apparent Power Demand:

$$S_{md} = \sqrt{3} \times V_L \times I_{max} = \sqrt{3} \times 400\text{ V} \times 77.52\text{ A} = 53,707\text{ VA} = 53.71\text{ kVA}$$

Technical Conclusion & Design Verification:

Since the calculated Maximum Demand is $53.71\text{ kVA}$ ($77.52\text{ A per phase}$), this exceeds the standard $45\text{ kVA}$ / $63\text{ A}$ supply limit. To bring this installation within the $45\text{ kVA}$ limit, the LEW must either:

1. Apply load management or re-group socket circuits (reducing socket demand to $32\text{A}$ per phase base), or
2. Upgrade the intake submission to SP PowerGrid for a $100\text{ A}$ 3-phase supply ($69.3\text{ kVA}$).