Electrical demand calculation: demand factor, diversity and reserve

What an electrical demand study is

A demand study answers a deceptively simple question: how much power will this installation actually draw at its worst moment? The naive answer — add up every motor, lamp and socket on the equipment list — gives the connected (installed) load, a number no real plant ever reaches, because loads do not all run at full rating at the same instant. The useful answer is the maximum demand: the connected load filtered through a chain of factors that model how the installation truly behaves.

That demand is the single most consequential number in the project. It sizes the upstream transformer and the standby generator, sets the ampacity of every feeder and the frame of every main breaker, and decides whether a board has room for the loads still on the drawing. Get it too low and the source trips or burns; get it too high and you have paid for copper and iron that will never carry current — and a transformer running far below its nameplate sits at a poor power factor.

From nameplate to installed power

The study works bottom-up, one load at a time. A motor nameplate gives mechanical shaft power (in kW or cv); the grid must supply more than that, because the motor itself has losses and draws reactive power. Two conversions bring the nameplate to the electrical installed value:

S_inst = (P_shaft / η) / cosφ

Dividing by the efficiency η turns shaft power into electrical active power (the motor’s losses are real load on the cable); dividing by the power factor cosφ turns active power [kW] into apparent power [kVA], which is what conductors and transformers are rated for. A load already specified in kVA (a lighting board, an electronic panel) skips the efficiency step — it is already an electrical figure.

From installed power to demand

No load runs at its full installed power continuously. The demand factor FD captures the fraction it actually draws at peak. The demanded power of a single load is simply:

S_dem = S_inst · FD

The service factor FS does not enter here. FS (typically 1.15 for continuous motors) is the motor’s permissible thermal overload, not a load of regime — it is consumed downstream by the protection (it caps the overload-relay / motor-breaker setting, 125 % FLC when FS ≥ 1.15), while the running margin at the branch and the global expansion margin cover the rest. Folding FS into the demand inflates every level of the tree by ~15 %.

A load declared as standby (reserve) duty contributes zero — by definition it is not running while its duty partner is. This is the single most common source of oversizing: counting both halves of a redundant pair.

Rolling demand up the tree

Loads feed panels; panels feed other panels and transformers; transformers feed the grid or a generator. The study walks this tree from the leaves up, accumulating kW, kVAr and kVA. At a panel, two project factors are applied to the sum of its children:

S_panel = (Σ S_dem,i) · g · (1 + r)

The diversity (simultaneity) factor g is below 1 because the individual peaks of many circuits do not coincide — the more, smaller circuits a board aggregates, the lower g can safely be. The reserve fraction r then adds spare capacity (often 20 %) so the board and its source can absorb future loads. A transformer node is pass-through: it simply sums its children, with no extra diversity or reserve, because those were already applied at the panels below it.

A critical discipline here: diversity is applied once, at the panel that genuinely aggregates independent circuits — not compounded at every level. Multiplying a factor below 1 at each tier of a deep tree silently drives the source dangerously undersized.

Current, source and emergency demand

Once a panel’s demand in kVA is known, the line current that sets its main breaker and incoming feeder follows directly:

I = S · 1000 / (√3 · V) for a three-phase board (use S·1000/V single-phase).

To pick the transformer or generator, a 15 % expansion margin is added over the rolled-up demand and the result is rounded up to the next standard commercial rating. The same roll-up, restricted to the loads flagged essential, yields the emergency demand — the kVA a standby generator must carry — which ISO 8528 then refines for motor inrush and step loading.

Reading the result

A healthy demand study shows each level loaded comfortably below its nameplate capacity:

• Per panel, the occupancy (demand ÷ capacity) should leave the declared reserve free — green well under 80 %, amber as it approaches the limit, red above 100 %.
• Per transformer, the rolled-up demand plus the 15 % expansion margin should land on a standard size with the spare capacity you intended, not scrape the next size up.
• Per generator, the essential-load sum must include the largest motor’s starting step, not just the steady demand.
• Installed vs demanded, the gap between the two (here ~87 kVA installed against ~70 kVA demanded before diversity) is the tangible value of the study — it is the capacity you did not have to buy.

Practical cautions

• Group by load nature. Lighting, motors, sockets and process loads each have their own demand-factor range; a single plant-wide FD hides the real picture.
• Keep the service factor out of the demand. FS sizes the motor’s overload protection (relay / breaker setting), not the demanded power; the demand uses FD only.
• Exclude standby duty. Reserve units are covered by their duty partners; counting them inflates source and generator alike.
• Apply diversity once. At the aggregating panel — never compounded level by level.
• Align factors with the standard. NBR 5410 (and IEC 60364) frame demand and utilization factors for low voltage; IEEE 141 gives industrial guidance; ISO 8528 governs the generator rating.

Followed in this order — nameplate to installed, installed to demanded, roll-up with diversity and reserve, then current and source — the demand study produces the load schedule that every downstream decision (cable, protection, transformer, generator) depends on, and keeps the installation both safe and economical.