Predictive Building Energy Optimization: Modeling Thermodynamic Drift and PV Generation with Edge IoT Telemetry

Most commercial smart home thermostats operate on naive rule engines: if ambient temperature falls below setpoint $tau – delta$, trigger relay. In dynamic energy pricing environments where microgeneration meets severe thermal inertia, this bang-bang control loop wastes significant kilowatt-hours. Replacing reactive thresholds with model predictive control (MPC) requires treating residential units as distributed thermodynamic state-spaces observed through noisy edge telemetry.

Thermodynamic State-Space Framing and Sensor Drift

To forecast indoor temperature decay, we model a single zone via lumped-capacitance equivalents (RC networks). The primary differential equation governing indoor temperature $T_{in}$ relative to exterior ambient conditions $T_{out}$ is defined as:

$$C_h frac{dT_{in}}{dt} = frac{1}{R_{th}}(T_{out} – T_{in}) + Q_{HVAC} + Q_{solar} + Q_{internal}$$

Where $C_h$ represents lumped thermal mass, $R_{th}$ is the bulk thermal resistance of the envelope, and $Q$ denotes internal and external thermal flux vectors. Estimating $R_{th}$ empirically exposes immediate real-world failure modes: material degradation and gaps in thermal envelopes invalidate manufacturer ratings. In structural telemetry tests, empirical envelope resistance diverges sharply based on the physical properties of the building’s insulation and moisture ingress over multi-year deployments.

Our raw data pipeline ingested 1-minute telemetry packets via MQTT over TLS from ESP32 nodes coupled with Bosch BME280 environmental sensors and non-invasive split-core current transformers (SCT-013). Honestly, the annoying part of running sensor telemetry at the edge isn’t feature extraction—it’s managing silent packet loss over residential Wi-Fi and ADC voltage noise on cheap current clamps around copper mains. We reject raw imputation via forward-fill because thermal decay isn’t step-wise. Instead, missing intervals under five minutes undergo cubic Hermite spline interpolation, while gaps exceeding five minutes trigger sequence truncation.

Photovoltaic Microgeneration and Load Forecasting

Balancing grid draw against distributed generation requires forecasting local array yield. The premise that investing in solar panels helps you save more by lowering your energy bills holds mathematically only when self-consumption is optimized ahead of dynamic tariff spikes. Passive installations export generation during mid-day price troughs and pull from the grid during evening demand peaks.

To eliminate this mismatch, we constructed a two-stage predictive engine. First, localized irradiance is predicted over an 18-hour rolling horizon using an ensemble of Extreme Gradient Boosting (XGBoost) regressors and a temporal convolutional network (TCN). Features incorporate:

• Solar zenith and azimuth angles derived from physical ephemeris calculations
• Direct Normal Irradiance (DNI) and Diffuse Horizontal Irradiance (DHI) from Open-Meteo satellite-derived numerical weather prediction (NWP) feeds
• Historical 15-minute rolling averages of actual inverter output power
• Dynamic cloud optical thickness index

Unlike recurrent neural architectures that suffer from gradient dissipation across multi-day sequences, causal 1D dilated convolutions let the TCN capture diurnal seasonality without explosive parameter counts. Rigorous benchmarks on building microgrid telemetry published in the IEEE Power & Energy Society literature confirm that combining local pyranometer sensors with NWP data reduces Mean Absolute Percentage Error (MAPE) on day-ahead irradiance forecasts from 18.4% down to 7.2%.

Algorithmic Control: Moving Horizon Optimization

We rejected deep reinforcement learning (DRL) for runtime HVAC actuation. In production, unconstrained policy gradient methods frequently hallucinate edge states, oscillating heating loops at 30-second cycles that trip compressor safety cutouts and destroy contactor relays. Instead, we implemented rolling-horizon Mixed-Integer Linear Programming (MILP) solved every fifteen minutes via the HiGHS solver library wrapped in Python.

The objective function minimizes total grid expenditure across horizon $K$ while penalizing deviation from occupant comfort bounds $[ au_{min}, tau_{max}]$:

$$min_{u} sum_{k=0}^{K} left( c_k P_{grid, k} Delta t + lambda max(0, T_{in, k} – tau_{max}, tau_{min} – T_{in, k}) right)$$

Where $c_k$ represents the time-of-use tariff rate at step $k$, $P_{grid, k}$ is net purchased active power, $u_k in {0, 1}$ is the binary heat-pump compressor state, and $lambda$ is the slack penalty parameter. The optimization is subject to operational constraints: minimum compressor runtime ($t_{on} ge 10text{ min}$), maximum battery state-of-charge limits ($0.20 le text{SoC}_k le 0.90$), and inverter rated apparent power limits.

Empirical Evaluation and Production Tradeoffs

We evaluated the system over a continuous 90-day winter heating regime across three residential structures instrumented with home-assistant-integrated submeters. Ground-truth thermal parameters were fit using extended Kalman filters (EKF) tracking real-time building envelope response to weather shocks.

• Baseline Reactive Thermostat: Static setpoint at 21.0°C; total consumed active power: 1,842 kWh; mean comfort boundary violation: 0.12°C.
• Standard Predictive MPC (Deterministic): Used point estimates for solar and outdoor ambient temperature; total power: 1,514 kWh (17.8% reduction); comfort violation: 0.84°C during unexpected cloud covers.
• Stochastic MPC with Covariance Inflation: Tracked thermal drift under uncertainty; total power: 1,563 kWh (15.1% reduction vs baseline); comfort violation bounded to 0.18°C.

The operational tradeoff is stark: squeezing the theoretical maximum thermal efficiency from predictive algorithms requires accepting either tighter comfort tolerances or wider state-of-charge margins on local battery assets. When unexpected cold fronts coincide with sensor latency, deterministic optimization aggressively pre-heats the structure too early, wasting thermal energy through the building envelope before occupancy triggers. Modeling uncertainty directly into the optimization constraints costs roughly 2.7% in theoretical peak savings, but it prevents the controller from draining the reserve storage during erratic tariff fluctuations.