Experimental Demonstration of Frequency Regulation by Commercial Buildings - Part I: Modeling and Hierarchical Control Design

• BAS means Building Automation System, and CWS means Central Working Station.Source: Acronyms · p. 2
• HVAC means Heating, Ventilation and Air-Conditioning; MPC means Model Predictive Control; PI means Proportional-Integral; and PID means Proportional-Integral-Derivative.Source: Acronyms · p. 2
• PJM means Pennsylvania, Jersey, and Maryland Power Market; RES means Renewable Energy Source; RMSE means Root Mean Squared Error; SAT means Supply Air Temperature; TSO means Transmission System Operator; VAV means Variable Air Volume; and VFD means Variable Frequency Drive.Source: Acronyms · p. 2

1.1 Motivation and Related Work

• Fluctuating renewable sources increase demand for frequency reserves, while prior commercial-building regulation demonstrations and field tests remain few.Source: §1.1 · pp. 2, 4
• Commercial HVAC is presented as suitable for frequency control because it represents around 20% of US electricity demand, has thermal inertia, and often has BAS infrastructure.Source: §1.1 · p. 3
• Prior work explored building frequency regulation through heat-pump, duct-pressure, fan-power, and chiller approaches, alongside methods for estimating reserve capacity and baseline power.Source: §1.1 · pp. 3–4

1.2 Contribution and Organization of this Paper

• The paper presents a first experimental demonstration addressing reserve bidding, operating power, comfort, and accurate fan-speed tracking together.Source: §1.2 · p. 4
• The design uses robust day-ahead reserve optimization, robust MPC, different building models for scheduling and control, and a Kalman filter for state estimates.Source: §1.2 · p. 4
• For VAV systems, the authors develop tractable reformulations for nonlinear fan dynamics and a switched feedforward-feedback controller described as high-performing and stable.Source: §1.2 · p. 5

2.1 FLEXLAB: our Test Facility

• Thermally isolated, identical FLEXLAB cells let one cell provide frequency regulation while the other serves as a real-time benchmark under the same external conditions.The experimental bay has a south orientation and 120 m2 total floor area.Source: §2.1 · p. 5

2.2 Control Approach

• The external hierarchical controller replaces zone-temperature PI control with MPC-based airflow setpoints while chilled-water and supply-air-temperature loops remain active.Source: §2.2 · p. 6

2.2.1 Level 1: Reserve Scheduler

• The reserve scheduler uses a multi-period robust optimization problem to determine capacity for the next day.Source: §2.2.1 · pp. 6–7

2.2.2 Level 2: Room Climate Controller

• The room climate controller uses robust MPC and a Kalman filter every 15 minutes to set airflow while minimizing energy and maintaining comfort under reserve provision.Source: §2.2.2 · p. 7

2.2.3 Level 3: Frequency Regulation Controller

• The frequency-regulation controller tracks the signal every 4 seconds by changing fan power through a VFD, using feedforward and feedback PI control.Source: §2.2.3 · p. 7

3.1 Building Thermal Model

• The two-state thermal model includes room and lumped-mass temperatures, with air flow as its input and ambient conditions, solar irradiance, and internal gains as disturbances.The unmeasured thermal-mass state makes the parameter-identification regression nonlinear; stability constraints are used to avoid overfitting when data are limited or control inputs lack excitation.Source: §3.1 · pp. 7–9
• The two-state, one-day-ahead model achieves the lowest RMSE among the compared variants and is used in the frequency-regulation experiments.The comparisons cover one- and two-state models with one-step- and one-day-ahead prediction; RMSE decreases as the number of states or prediction horizon increases.Source: Table 1 · p. 9, Figure 5 · p. 9, §3.1 · p. 10
• The proposed one-day-ahead identification formulation substitutes the predicted room temperature for the measured room temperature in the regression.The authors expect this more flexible formulation to improve predictions up to one day ahead; a one-state model is also possible if the lumped thermal mass is neglected.Source: §3.1 · p. 10

3.2 Fan Model

• A steady-state fan model maps air flow and fan speed to power for use in the MPC and frequency-regulation controller.The fan setpoint was varied from 10% to 90% of rated fan power in 5% steps; fitting RMSE was 5 W for the speed-to-power model and 21 W for the flow-to-power model.Source: §3.2 · pp. 10–11, Figure 6 · p. 11

4.1 Robust Reserve Scheduling Formulation

• The scheduler chooses electric reserve capacities by balancing energy cost and reserve profit while enforcing robust airflow and temperature constraints under uncertain regulation requests.The signal is bounded by [-1, 1] for worst-case power activation and by [-wlim, wlim] to represent its 15-minute energy limit.Source: §4.1 · pp. 11–13

4.2 Reformulation and Approximation

• The robust counterpart enforces constraints at uncertainty boundaries and is equivalent to the original formulation when the building operates in cooling mode.Its trajectories represent worst-case higher and lower states.Source: §4.2 · pp. 13–14
• The fan-curve linearization yields a simpler formulation equivalent to the robust counterpart only when wlim = 1, not for 0 < wlim ≤ 1.For the broader energy-limit range, the approximation overestimates both maximum and minimum room temperatures, increasing robustness above the upper comfort limit while reducing it below the lower limit.Source: §4.2 · pp. 14–15

4.3 Energy Limit of Regulation Signal

• Historical RegD data from December 2012 to January 2013 set wlim = 0.25 at the 97.5th percentile, so 15-minute requested energy is below 25% of reserve capacity with 97.5% probability.The observed worst case, wlim = 0.88, was rejected as too conservative; the scheduler also takes each time step’s worst case independently, adding robustness to model and forecast uncertainty.Source: §4.3 · p. 15

4.4 Modeling Reserve Product Constraints

• Reserve-product constraints can require capacities to remain constant over minimum-duration blocks or require symmetric up- and down-reserves.The paper uses four 15-minute steps for one-hour blocks and imposes thermal symmetry to limit room-temperature impact; nonlinear fan behavior can still make electric reserves asymmetric.Source: §4.4 · p. 16

5.1 MPC Formulation

• The robust MPC selects airflow and thermal reserve levels to provide the scheduler’s fixed electric reserves while minimizing energy cost.It uses updated weather forecasts and soft comfort constraints with high penalties to reduce infeasibility from plant-model mismatch or forecast errors.Source: §5.1 · p. 17

5.2 Kalman Filter

• An extended Kalman filter estimates the building state for the MPC and reserve scheduler because mass temperature is unmeasured and room-temperature measurements are noisy.The filter uses system-dynamics and output Jacobians with assumed process and measurement noise covariances.Source: §5.2 · pp. 17–18

6 Level 3: Frequency Regulation Controller

• A model-based feedforward loop (Ctrl1) tracks power using the static fan model, while a model-free PI feedback loop (Ctrl2) reduces steady-state error.The feedforward loop is inherently stable because it has no feedback; PI stability is not guaranteed and requires gain tuning.Source: §6 · p. 18
• The controller activates Ctrl2 when |enew| ≤ ε and Ctrl1 when |enew| > ε, with ε representing the fan model’s accuracy.It computes desired power from baseline consumption, reserve, and the regulation signal, then compares it with measured fan power.Source: §6 · pp. 18–19
• After a large setpoint change, Ctrl1 stays active until the tracking error is within ε; switching to Ctrl2 resets integral error, and PI output is bounded to 10%–90% fan speed.The reset prevents large overshoots from accumulated errors.Source: §6 · p. 18
• Five operating regions use gain-scheduled PI gains initialized with Ziegler–Nichols and finalized by trial and error.Final Kp gains are lower and Ki gains higher than Ziegler–Nichols recommendations because Ctrl2 corrects steady-state error rather than recovering from large setpoint changes; tuned gains are listed in Table 5.Source: §6 · p. 19, Table 5 · p. 19
• The switched controller improves stability and performance over the open-loop controller of and closed-loop controller of.Ctrl1 tracks sudden power-setpoint changes without requiring high Ctrl2 gains that would compromise stability.Source: §6 · p. 19

7 Conclusion and Outlook

• Part I presents FLEXLAB, compares building models for day-ahead reserve scheduling and climate-control MPC, and proposes tractable reformulations for nonlinear fan dynamics and a switched frequency-regulation controller.The controller is described as accurate and inherently stable; Part II reports extensive experimental results using the developed models and controllers.Source: §7 · p. 20

A Proof of Lemma 2

• The proof begins from the definition of ∆uk in (13) and (12).The passage does not specify the resulting expression.Source: A Proof of Lemma 2 · p. 20
• The proof obtains a result by substituting the minimizer −wlim in (30).It identifies Equation (19) as a special case of (17).Source: A Proof of Lemma 2 · p. 20
• The maximization cases for (18) and (20) are proved analogously, with details omitted for brevity.The derivation also uses (8).Source: A Proof of Lemma 2 · p. 20

B Proof of Proposition 1

• The proof establishes that input constraints (16d) are equivalent to (14c), and state constraints (16b), (16c), and (16e) to (14b) and (14d).The input equivalence follows from (19) and (20).Source: B Proof of Proposition 1 · p. 20
• Constraint (14d) applies only to the first state Tr,k = Cxk, where C = [1 0] is the output matrix.Under assumption 1, the minimum state trajectory supports the lower-bound implication for (14d).Source: B Proof of Proposition 1 · pp. 20–21
• An analogous argument shows that (35) yields (16b) and xk ≤ xmax,k, equivalent to the upper side of (14d).The proof omits those details for brevity.Source: B Proof of Proposition 1 · p. 21

• The proof invokes convexity and monotonicity of f, then identifies Fig. 7 as a graphical interpretation of (37).Source: C Proof of Proposition 2 · p. 21
• The proof derives k by combining (37), (16b), and (22b), using the argument from Proposition 1 about b(Ts −Tr,k) ≤0.Source: C Proof of Proposition 2 · p. 21
• It also establishes uk + wlimru,k ≤ f−1(Pk + wlimRd,k).Source: C Proof of Proposition 2 · p. 21