Generator and UPS Sizing: Method

Generator and UPS Sizing

Three sizing calculations of a building's backup power under one select: the engine-generator set from a load schedule, the uninterruptible power supply and its battery from the critical-load schedule, and the unit capacity of a generating plant by the MIL-HDBK-1003/11 procedure. All three are closed-form methods on the entered data. The values a code, a standard or a maker owns (the NEC code-letter kVA per hp, the NFPA 110 class, type and level, the ISO 8528 ratings and performance classes, the IEEE 485 temperature, aging and design-margin factors, the maker's transient reactance, derating curve and fuel curve) are entered inputs with sourced or illustrative defaults, and the page says where the analyst reads them.

Generator: the load schedule

Each row of the schedule is a load with a type (resistive, motor, UPS input, lighting, HVAC or medical), a step in which it is connected, a priority class (uninterruptible, essential or nonessential, the classification of UFC 3-540-01 D-1.1), and its running kW and power factor. A motor row is entered by nameplate horsepower and efficiency, and its input kW is hp × 0.7457 / η (745.7 W per hp, NIST SP 811), the form TM 5-811-14 4-8 uses with kVA ≈ hp as its shortcut. Running kVA is kW / pf and kvar follows; the totals add kW and kvar as phasors, so the group kVA is √(ΣkW² + Σkvar²), a little below the arithmetic sum. The demand factor reduces the connected running load to the coincident demand (UFC 3-540-01 D-1.2: size for the expected demand, not the connected load) and the growth percentage adds the future allowance (TM 5-811-6 4-11b allows about 15 percent on a unit substation; MIL-HDBK-1003/11 5.2.3 sets a plant's firm capacity at 125 percent of the maximum demand).

Generator: step loading and voltage dip

The loads come on in the entered steps (an automatic transfer switch energizes everything at once; larger systems stagger the load with time delays, UFC 3-540-01 D-1.4). The starting block of a step is the sum of its motors' starting kVA, the motors of a step starting together, plus the running kVA of its other loads. A motor started across the line draws the entered locked-rotor multiple of its running kVA (UFC 3-540-01 D-1.5: as much as six times the running current; the code-letter kVA per hp of NEC Table 430.7(B), 6.29 kVA/hp for letter G in TM 5-811-14 eq. G-1, gives the exact value), a soft-started motor the starter's current limit, a drive-started motor the drive's input limit, at the entered starting power factor. The voltage dip is estimated from the alternator's transient reactance X′_d in per unit on its own base: the reactance in series with the starting load, whose impedance on the same base is S_gen/S_st, gives ΔV = X′_d S_st / (S_gen + X′_d S_st) when both are taken as reactances, and the alternator that holds the dip to a fraction d is S_gen ≥ X′_d S_st (1/d − 1). The estimate neglects the pre-load, the regulator's response and the resistive part of the starting current; the maker's dip curves, which are drawn on the transient reactance, replace it when available. The default allowable dip of 15 percent keeps the motor terminal at 85 percent of nominal, the motor-starting criterion of TM 5-811-6 4-16c for a unit substation. The kW block of a step over the set's kW rating is printed because the engine's frequency dip and recovery depend on it; the acceptance limits are the ISO 8528-5 performance classes and the maker's transient-response data, which the page does not compute.

Generator: nonlinear loads, site derating, the set

UPS and drive loads draw non-sinusoidal current. UFC 3-540-01 D-1.3 limits the subtransient reactance to 0.12 per unit when nonlinear loads are 25 percent or more of the load served, and D-2.2 leaves any oversizing of the alternator to the supplier; the entered multiplier on the nonlinear kVA is that supplier rule. The site factor is (1 − r_alt Δalt)(1 − r_T ΔT) with the entered rates above the altitude and ambient up to which the set carries its rating (3,300 ft / 1,000 m and 40 °C are the NEMA MG 1 basis quoted by MIL-HDBK-1003/11 6.2.2); the rates come from the maker's curve for the engine and the defaults are placeholders. The alternator must carry the largest of the running kVA with growth, the nonlinear-adjusted kVA and the kVA for the dip; the engine the running kW with growth and the kW of that kVA at the rated power factor; the nameplate is the site requirement over the site factor, divided among paralleled sets, plus one set when N+1 is chosen. The standby rating (ISO 8528-1 limited-time running power) applies to backup duty, the prime rating when the annual hours or a near-constant full load call for it (UFC 3-540-01 D-2.1). The full-load current is S / (√3 V), the conductors from the generator terminals carry 115 percent of it (NEC 445.13) and the transfer switch is checked against it; the generator breaker is set per the maker (NEC 445.12). A set loaded far below its rating runs wet; UFC 3-540-01 D-2.1 notes that less than 50 percent loading is common.

Generator: fuel and tanks

The fuel rate is the specific consumption at the load fraction, linear between the entered 25, 50, 75 and 100 percent points of the maker's fuel curve, times the engine shaft power (the electrical load over the alternator efficiency), in lb per hp·h with the density in lb/gal (L per kWh of shaft power and kg/L with the SI switch). The default curve ends at 0.367 lb/hp·h, the EPA NONROAD brake-specific fuel consumption of diesel engines above 100 hp (0.408 at 100 hp and below), with the 7.1 lb/gal density that report uses (EPA-420-R-10-018 Table A2); its part-load rise is illustrative. The expected load is entered or taken as the running load with growth over the set rating. The main tank holds the runtime hours at that rate over the usable fraction of the tank; TM 5-811-6 7-6a requires 30 days of storage for continuous and standby plants and 3 days for emergency plants, MIL-HDBK-1003/11 5.4.6 gives 30 and 7 days and sizes the tank from the full-load rate times a 0.75 operating factor, printed beside. The day tank holds the entered hours at full load (2 h prime and 8 h standby in MIL-HDBK-1003/11 5.4.6, 4 h continuous and 10 h standby in TM 5-811-6 7-6a, none for emergency plants). NFPA 110 (cited) designates the system by Class (hours without refueling), Type (seconds to restore power; TM 5-811-1 11-7b counts 10 to 17 s for an engine-generator start) and Level, restated from the entered values.

UPS: load, module and power flow

The critical loads add as phasors with growth. A module rated S kVA at a rated power factor delivers at most S kVA and S × pf kW, so the requirement is the larger of the kVA and the kW over the rated power factor, divided among the N modules that share it; N+1 adds one redundant module (TSEWG TP-19 describes the N+1 and isolated-redundant configurations and lists the motor, transformer, discharge-lighting and leading-power-factor loads a static UPS handles poorly). The dc power from the battery is the output over the inverter efficiency, the input power that over the rectifier efficiency, and the loss is rejected to the room (3,412 Btu/h per kW). The generator sees the input over the input power factor plus the charger: UFC 3-540-01 D-2.3 asks that charging on generator be held to the minimum the UPS allows, that the UPS walk in over 3 to 60 s and that its input filter be energized only after other load is on, so a leading power factor does not run the alternator's voltage up.

UPS: battery runtime

Cells in series are the dc voltage over the nominal cell voltage (2.0 V lead-acid). The discharge is at constant power: with n parallel strings of m cells the current is P / (m V_cell n), and the cell voltage is let fall linearly from the entered start value to the end-of-discharge voltage (usually about 1.75 V per cell for lead-acid, DOE-HDBK-1084-95, dependent on rate and temperature) as the charge is used. Peukert's relation I^k t = I_r^k t_r (Peukert 1897; k = 1 means the capacity does not depend on the rate) is applied to the varying current as a charge fraction, dq = (I/I_r)^k−1 I dt / C, integrated by Simpson's rule in q until q = 1 or the string reaches the inverter's minimum voltage; the test script checks it against scipy's integration of the same equation on ten seeded batteries. The rated capacity is first divided by the aging factor and design margin and multiplied by the temperature factor, the three corrections of IEEE 485 (1.25 for aging so the battery still serves at 80 percent of rated capacity, 10 to 15 percent design margin, the temperature table; all cited and entered). The constant-current form at the mean string voltage, t = t_r (I_r/I)^k, and the rated capacity per string the required time would need at that current, C = I t_r (t/t_r)^1/k times the factors, are printed beside. The number of strings is entered or taken as the smallest that gives the required runtime. DOE-HDBK-1084-95 rates UPS batteries at the 8-hour rate (telecommunications at 10 h) and notes that discharges beyond about 80 percent of capacity shorten life. The recharge current is the ampere-hours removed times the recharge factor over the entered hours (12 h for a station battery after an emergency discharge, TM 5-811-6 4-24c); a constant-voltage charger returns up to 70 percent in the first 30 minutes and tapers, so the mean current is a lower bound on the charger rating.

Plant unit capacity

MIL-HDBK-1003/11 (reprinted in UFC 3-540-04N) sizes the units of a diesel-electric plant from the maximum, average and minimum demands: the firm capacity, the total less spares, is not less than 125 percent of the maximum demand (5.2.3); a unit should run at not less than 50 percent of its rating, so the largest unit is the minimum demand over that fraction and the smallest is the minimum demand itself; for each candidate size the units needed for the firm capacity, their loading at each demand and the units with spares (two for prime duty, one for standby, none for emergency duty in the continental United States, 5.2.2) are tabulated and the size with the fewest units is selected (5.3 and Table 8, whose example of 2,400 / 1,500 / 600 kW the tool's default reproduces: 1,000 kW units, three for the firm capacity and five installed).

Limits

The dip estimate is the usual reactance form without the pre-load and the regulator; the engine's frequency response, the harmonic distortion of the alternator voltage, the regulator's leading-power-factor limit and the generator and UPS protection coordination are the maker's data and a study. The fuel curve, derating rates, reactances, starter limits and battery constants are entered; their defaults are placeholders where no public source prints them, and the page says so. The battery model is a single constant-power period; a multi-period duty cycle with random loads follows the IEEE 485 procedure. Nickel-cadmium and lithium cells, which UFC 3-520-01 restricts, are not treated.