🏢 Real estate — office building operations Live model

Basis — the model behind the numbers

Every relation the simulator uses, with its source. Constants marked as assumptions are illustrative calibrations.

The building as a small heat network: room air and inner surfaces have no storage, the concrete structure does. Heat flows through each link in proportion to the temperature difference.

air: H_ve(θo − θa) + H_is(θs − θa) + Φ_ia + Φ_HC = 0; surface: H_is(θa − θs) + H_w(θo − θs) + H_ms(θm − θs) + Φ_st = 0; mass: C_m·dθm/dt = H_ms(θs − θm) + H_em(θo − θm) + Φ_m[1][2]

Standard values for a heavy building: the structure stores 260 kJ per kelvin for every m² of floor and is tightly coupled to the room surfaces. Half of the internal heat goes straight into the air, the rest and the sunshine land on surfaces and mass.

C_m = 260 000·A_f J/K, A_m = 3.0·A_f, A_tot = 4.5·A_f, H_is = 3.45·A_tot, H_ms = 9.1·A_m (W/K); Φ_ia = 0.5·Φ_int, Φ_m = (A_m/A_tot)(0.5·Φ_int + Φ_sol)[1][2]

Every cubic metre per second of outdoor air carries 1.2 kW per kelvin of difference between inside and outside.

H_ve = ρc·(Q_oa + Q_inf), ρc = 1200 J/(m³K)[1]

Fanger's comfort model balances the heat a person produces against what they lose by convection, radiation, sweat and breath. PMV 0 is neutral; ±0.5 is the usual comfort band, where about 10 % are still dissatisfied.

PMV = (0.303·e^(−0.036M) + 0.028)·[(M − W) − heat losses(θa, θ_r, v, p_a, I_cl)], θ_r ≈ θs; PPD = 100 − 95·exp(−0.03353·PMV⁴ − 0.2179·PMV²)[3][4]

Ventilation rate procedure for offices: one part per person, one part per floor area. Demand control follows the people actually present.

V_bz = R_p·N + R_a·A = 2.5 L/s·N + 0.3 L/s·m²·A; fixed = V_bz(design 250 people) = 2,125 L/s; DCV = V_bz(N present); purge = 100 % outdoor air (6 m³/s, the AHU limit)[5]

CO₂ in a well-mixed building: occupants add it, outdoor air dilutes it. The level heads for C_out + N·G/Q with a time constant V/Q — about an hour and a half at design flow.

V·dC/dt = Q(C_out − C) + N·G, G = 0.0048 L/s; C_ss = C_out + N·G/Q, τ = V/Q[6][5][7]

Internal heat: people, lights and office equipment; sunshine through the windows peaks in the early afternoon.

Φ_int = 75 W·N + lights 7 W/m² + plugs 10 W/m²·(0.25 + 0.75·N/250); Φ_sol = 100 kW·sin(π(h − 6)/13)·cloud[8]Assumption: the building size, envelope, plant capacities, heat-gain densities, the Carnot fraction, fan power, schedules and weather are illustrative values for a generic office; the heat-balance, comfort, ventilation and CO₂ relations are the published ones.

A chiller works harder the hotter it is outside, a heat pump the colder it is — both modelled as a fixed fraction of the ideal (Carnot) efficiency.

COP_cool = 0.45·T_e/(T_c − T_e), T_e = 5 °C, T_c = θo + 12 K; COP_heat = 0.45·T_c/(T_c − T_e), T_c = 45 °C, T_e = θo − 8 K[9]Assumption: the building size, envelope, plant capacities, heat-gain densities, the Carnot fraction, fan power, schedules and weather are illustrative values for a generic office; the heat-balance, comfort, ventilation and CO₂ relations are the published ones.

The meter records the average power of every 15 minutes; a demand charge bills the highest one, so a single bad quarter-hour sets the charge.

P = Q_cool/COP_cool + Q_heat/COP_heat + fans (6 kW + 1.5 kW per m³/s outdoor air) + lights + plugs; billing demand = max over 15-min intervals of P[11]Assumption: the building size, envelope, plant capacities, heat-gain densities, the Carnot fraction, fan power, schedules and weather are illustrative values for a generic office; the heat-balance, comfort, ventilation and CO₂ relations are the published ones.

Pre-cooling stores 'cold' in the concrete overnight, when the chiller is efficient and demand is low; in the afternoon the cool structure soaks up heat the plant would otherwise remove.

cool the mass before the peak (θm ↓), then raise the setpoint: H_ms(θs − θm) absorbs part of the afternoon gain instead of the plant[10]

Optimal start: the colder the structure and the weather, the longer the recovery from setback, so the plant must start that much earlier.

recovery time after setback grows with (θ_set − θm) and with colder weather; plant start = occupancy − recovery time[12][1]

Other operating constants used by the model.

5,000 m² office, 3 m storeys · windows 800 m² at U 1.8 (H_w 1,440 W/K), opaque envelope 1,000 W/K, infiltration 0.1 ACH · cooling capacity 350 kW, heat pump 300 kW (thermal) · unoccupied limits 15/30 °C · occupancy 07:30–18:30, attendance ~ N(85 %, 5 %) · outdoor temperature cosine + N(0, 0.8 K) hourly · RH 50 %, 0.1 m/s, 1.2 metAssumption: the building size, envelope, plant capacities, heat-gain densities, the Carnot fraction, fan power, schedules and weather are illustrative values for a generic office; the heat-balance, comfort, ventilation and CO₂ relations are the published ones.

Randomness: a seeded mulberry32 generator; distributions used — uniform, exponential (inverse CDF), normal (Box–Muller), Poisson (Knuth). The seed is shown and shareable.

Sources

1. ISO 13790:2008 — Energy performance of buildings — Calculation of energy use for space heating and cooling (simple hourly method, 5R1C network, Annex C; Table 12 mass classes) — International Organization for Standardization, 2008
2. Modelica Buildings Library — Buildings.ThermalZones.ISO13790 (Zone5R1C: h_is = 3.45, h_ms = 9.1 W/m²K, gain split; mass classes, e.g. Data.Heavy: 260 000 J/(K·m²), mass area factor 3.0) — Lawrence Berkeley National Laboratory
3. ISO 7730:2005 — Ergonomics of the thermal environment — Analytical determination and interpretation of thermal comfort using calculation of the PMV and PPD indices (Annex D program, Table D.1 check values) — International Organization for Standardization, 2005
4. ANSI/ASHRAE Standard 55 — Thermal Environmental Conditions for Human Occupancy (PMV −0.5…+0.5 comfort zone, PPD < 10 %) — ASHRAE, 2020
5. ANSI/ASHRAE Standard 62.1 — Ventilation and Acceptable Indoor Air Quality (Table 6-1, office space: R_p = 5 cfm (2.5 L/s) per person, R_a = 0.06 cfm/ft² (0.3 L/s·m²), 5 people / 1000 ft²; demand-controlled ventilation) — ASHRAE, 2022
6. A. Persily, L. de Jonge — Carbon dioxide generation rates for building occupants (office occupants ≈ 0.0048 L/s per person; steady-state ΔC = G/Q) — Indoor Air 27(5):868–879, 2017
7. 실내공기질 관리법 시행규칙 별표 2 — 실내공기질 유지기준 (이산화탄소 1,000 ppm 이하) — 대한민국 환경부 (국가법령정보센터)
8. ASHRAE Handbook — Fundamentals, Chapter 18 Nonresidential Cooling and Heating Load Calculations (Table 1: moderately active office work, sensible ≈ 75 W per person) — ASHRAE, 2021
9. Y. A. Çengel, M. A. Boles — Thermodynamics: An Engineering Approach (reversed Carnot cycle: COP_R = T_L/(T_H − T_L), COP_HP = T_H/(T_H − T_L)) — McGraw-Hill, 9th ed., 2019
10. J. E. Braun — Load Control Using Building Thermal Mass (pre-cooling and setpoint adjustment to shift and reduce peak cooling demand) — ASME Journal of Solar Energy Engineering 125(3):292–301, 2003
11. J. McLaren, S. Mullendore — Identifying Potential Markets for Behind-the-Meter Battery Energy Storage: A Survey of U.S. Demand Charges (demand charge on the highest metered interval demand, kW) — NREL / Clean Energy Group, NREL/BR-6A20-68963, 2017
12. J. E. Seem, P. R. Armstrong, C. E. Hancock — Algorithms for predicting recovery time from night setback (optimal start) — ASHRAE Transactions 95(2), 1989