Sources and References

Primary texts — Kreider, Curtiss, and Rabl, Heating and Cooling of Buildings: Principles and Practice of Energy Efficient Design, 3rd ed. (CRC Press). ASHRAE, ASHRAE Handbook — Fundamentals, current edition.

Supplementary texts — Clarke, Energy Simulation in Building Design, 2nd ed. (Butterworth-Heinemann). Hensen and Lamberts (eds.), Building Performance Simulation for Design and Operation, 2nd ed. (Routledge). McQuiston, Parker, and Spitler, Heating, Ventilating, and Air Conditioning: Analysis and Design, 6th ed. (Wiley).

Online resources — MIT OpenCourseWare 4.401/4.464 Environmental Technologies in Buildings. ASHRAE Standard 90.1 (Energy Standard for Buildings Except Low-Rise Residential). ASHRAE Standard 55 (Thermal Environmental Conditions). ISO 52016-1 (Energy needs for heating and cooling). U.S. DOE EnergyPlus Engineering Reference (open documentation). NREL Commercial Reference Building technical reports.

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Chapter 1: Foundations of Building Energy Analysis

Whole-building energy analysis treats a building as a dynamic thermodynamic system exchanging energy with its occupants, its mechanical systems, and its outdoor environment. Unlike component-level analysis, the focus is on the interaction among envelope, systems, loads, and controls, so that design decisions can be evaluated in terms of annual energy use, peak demand, comfort, carbon emissions, and life-cycle cost.

1.1 Energy Flows and the Building Energy Balance

Consider a single thermal zone at uniform air temperature \( T_i \). The first-law energy balance on the zone air is

\[ C_{\text{air}} \frac{dT_i}{dt} = \dot{Q}_{\text{env}} + \dot{Q}_{\text{sol}} + \dot{Q}_{\text{int}} + \dot{Q}_{\text{inf}} + \dot{Q}_{\text{sys}} . \]

Here \( \dot{Q}_{\text{env}} \) is conduction through the envelope, \( \dot{Q}_{\text{sol}} \) is transmitted solar gain, \( \dot{Q}_{\text{int}} \) lumps internal gains from lighting, equipment, and people, \( \dot{Q}_{\text{inf}} \) accounts for infiltration and ventilation, and \( \dot{Q}_{\text{sys}} \) is the net delivery from the HVAC system. Every downstream topic in this course revisits one term of this equation at increasing resolution.

1.2 Degree-Days and Steady-State Screening

For quick screening, assume \( dT_i/dt \approx 0 \) and that heat loss is linear in \( T_i - T_o \). Annual heating energy scales with heating degree-days \( \mathrm{HDD}_b \) relative to a base temperature \( T_b \):

\[ Q_H = \frac{UA_{\text{tot}}}{\eta_H}\, \mathrm{HDD}_b \cdot 24 , \]

where \( UA_{\text{tot}} \) is the effective envelope conductance and \( \eta_H \) the seasonal heating efficiency. The balance temperature \( T_b = T_i - \dot{Q}_{\text{gain}}/UA_{\text{tot}} \) captures the offset from free heat. Degree-day methods are transparent but hide dynamics, solar decoupling, and control nonlinearity.

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Chapter 2: Heat Transfer Through the Envelope

2.1 Conduction and Thermal Resistance

Steady one-dimensional conduction across a wall of thickness \( L \) and conductivity \( k \) gives a unit resistance \( R = L/k \). Series assemblies sum resistances; parallel paths (studs, insulation cavities) combine conductances. The whole-wall \( U \)-factor also accounts for surface films \( h_i, h_o \):

\[ U = \left( \frac{1}{h_i} + \sum_j \frac{L_j}{k_j} + \frac{1}{h_o} \right)^{-1} . \]

Two-dimensional thermal bridging at framing, balconies, and corners is handled through the linear transmittance \( \psi \) and point transmittance \( \chi \) per ISO 10211, producing an effective assembly \( U \).

2.2 Transient Response

Buildings rarely operate at steady state. The thermal mass of concrete floors and masonry walls introduces time lag and amplitude decrement in the response to outdoor swings. For a periodic outdoor temperature at angular frequency \( \omega \), the admittance method represents each surface by a complex admittance \( Y \) and transmittance \( U(\omega) \), giving a phase-shifted heat flux. The Conduction Transfer Function (CTF) method used in EnergyPlus and ESP-r expresses inside surface heat flux as

\[ q_{\text{in}}(t) = \sum_{k=0}^{n} X_k T_o(t-k\Delta) - \sum_{k=0}^{n} Y_k T_i(t-k\Delta) + \sum_{k=1}^{m} \phi_k q_{\text{in}}(t-k\Delta) , \]

with coefficients \( X_k, Y_k, \phi_k \) precomputed from the layer properties.

2.3 Fenestration and Solar Gains

Glazing performance is summarized by \( U \)-value, solar heat gain coefficient (SHGC), and visible transmittance. Transmitted solar is split into direct and diffuse components and distributed on interior surfaces. Net gain through an opaque wall uses the sol-air temperature

\[ T_{\text{sa}} = T_o + \frac{\alpha G_t - \varepsilon \Delta R}{h_o} , \]

so the envelope balance absorbs solar and long-wave radiation exchange with the sky into a single driving temperature.

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Chapter 3: Psychrometrics and Zone Loads

3.1 Moist-Air Fundamentals

Air-conditioning processes are plotted on the psychrometric chart with axes of dry-bulb temperature \( T \) and humidity ratio \( W \). Useful identities include

\[ W = 0.622 \frac{p_w}{p - p_w}, \qquad h = c_{pa} T + W\,(h_{fg0} + c_{pv} T) , \]

where \( p_w \) is the partial pressure of water vapour. Saturation pressure is given by ASHRAE’s formulation of the Clausius–Clapeyron relation. Processes — sensible heating, cooling and dehumidification, adiabatic humidification, mixing — appear as straight lines whose slopes encode the sensible heat ratio.

3.2 Sensible and Latent Load Calculation

The cooling coil load decomposes into

\[ \dot{Q}_{\text{sens}} = \dot{m}_a c_p (T_{\text{in}} - T_{\text{out}}), \qquad \dot{Q}_{\text{lat}} = \dot{m}_a h_{fg}(W_{\text{in}} - W_{\text{out}}) . \]

Peak block loads for equipment sizing use the Radiant Time Series (RTS) method: hourly heat gains are split into radiant and convective fractions, the radiant part is distributed over time through radiant time factors, and convective components act instantly on the air node.

3.3 Ventilation, Infiltration, and Indoor Air Quality

ASHRAE 62.1 sets minimum outdoor-air rates as \( V_{bz} = R_p P_z + R_a A_z \), with people- and area-based components. Infiltration is driven by stack, wind, and mechanical pressurization. The AIM-2 model expresses the infiltration flow as

\[ Q_{\text{inf}} = \sqrt{(C_s \Delta T)^{n} + (C_w U^{2})^{n}} , \]

where \( C_s, C_w \) are stack and wind coefficients calibrated to blower-door leakage.

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Chapter 4: Auditing, Benchmarking, and Measurement

4.1 Audit Levels

ASHRAE defines three audit levels: walk-through, energy survey and analysis, and detailed analysis of capital-intensive modifications. A Level II audit produces an energy end-use breakdown, identifies low-cost operational measures, and scopes retrofits with simple payback under three years.

4.2 Benchmarking

End-use intensity \( \mathrm{EUI} = E_{\text{annual}}/A_{\text{floor}} \) in kWh/m²·yr enables comparison with peer buildings through CBECS, NRCan’s SPB, or ENERGY STAR Portfolio Manager. Statistical benchmarking regresses EUI on climate, operating hours, and plug-load density to isolate avoidable consumption from unavoidable drivers.

4.3 Measurement and Verification

IPMVP Options A–D specify how savings from retrofits are measured:

Option	Approach	Typical use
A	Retrofit isolation, key parameter measured	Lighting upgrades
B	Retrofit isolation, all parameters measured	Motor/VFD
C	Whole-facility regression	Deep retrofits
D	Calibrated simulation	New construction, no pre-data

The pre/post regression model \( E = a + b\,\mathrm{HDD} + c\,\mathrm{CDD} + \varepsilon \) is evaluated by CV(RMSE) and NMBE thresholds (14% and ±5% monthly per ASHRAE Guideline 14).

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Chapter 5: Whole-Building Simulation

5.1 Simulation Architecture

Modern tools (EnergyPlus, ESP-r, IDA ICE, TRNSYS) couple a heat-balance zone solver to system and plant models. At each timestep the engine iterates: surface heat balance → zone air balance → HVAC system response → plant dispatch. Convergence is enforced by Gauss–Seidel relaxation or a Newton step on the coupled residuals.

5.2 Weather Data

Typical Meteorological Year (TMY3) files assemble the most representative months over a multi-decade record. Each hour supplies dry-bulb, dew-point, wind, global and diffuse horizontal radiation, and sky cover. Design-day files drive peak sizing; full-year files drive consumption and demand.

5.3 Calibration and Uncertainty

Calibration adjusts uncertain inputs (infiltration, schedules, plug density, equipment efficiency) until simulated and measured monthly energy agree within ASHRAE 14 tolerances. Sensitivity analysis via Morris screening or Sobol indices identifies the few inputs that matter. Probabilistic simulation propagates input distributions to produce credible intervals on predicted savings.

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Chapter 6: Economic and Environmental Impact

6.1 Life-Cycle Cost

Present worth of an energy project is

\[ \mathrm{PW} = -C_0 + \sum_{n=1}^{N} \frac{S_n - M_n}{(1+r)^n} + \frac{R_N}{(1+r)^N} , \]

with capital \( C_0 \), yearly savings \( S_n \), maintenance \( M_n \), residual \( R_N \), and discount rate \( r \). Energy escalation and carbon pricing enter as time-varying \( S_n \). Levelized cost of conserved energy (LCCE) normalizes annualized cost by annual savings.

6.2 Emissions and Grid Interaction

Operational carbon uses time-resolved grid intensity \( \gamma(t) \) in kgCO₂/kWh:

\[ \mathrm{CO_2} = \int_0^T \gamma(t)\, P_e(t)\, dt . \]

Buildings with flexible loads can shift consumption to low-intensity hours; peak-shaving reduces coincident demand on generation and transmission. Net-zero energy requires matching annual on-site generation to annual consumption, while net-zero carbon aligns emissions, not energy.

6.3 Occupant Behaviour

Occupants drive thermostat setpoints, window openings, blinds, and plug loads. Stochastic behaviour models (Markov chains for occupancy, logistic regression for window operation) are increasingly integrated into simulation, acknowledging that realistic behaviour can shift predicted energy by 20–50% relative to fixed-schedule assumptions. Designing for robustness — building forms that perform acceptably across behavioural scenarios — is a central competence of the building energy engineer.