1. Overview of Model Predictive Control in Buildings
Tony Kelman
MPC Lab, Berkeley Mechanical Engineering
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2. Outline Model predictive control Modeling and MPC in buildings
Basic idea and elements
Advantages, disadvantages
Modeling and MPC in buildings
What works, what doesn’t
Generating models using historical data
Advanced control behavior
Experimental projects
Success stories
Increased scope and capabilities over time
Introduce MPC context

3. Model Predictive Control
System model – state evolution vs inputs and disturbances
Constraints on inputs or states – requirements, actuator limits
Cost function – reference tracking, energy, comfort
Forecast trajectories of future disturbance inputs – weather, occupancy, utility rates
Optimization algorithm – fast enough to solve in real time
Use predictive knowledge for control
Basic components
System model
Constraints on inputs or states
Cost function
Forecast trajectories of future disturbance inputs
Optimization algorithm
Advantages: multivariable, model based, nonlinear, constraint satisfaction, incorporates predictions
Disadvantages: computational complexity, design effort of accurate modeling
Additional info in grey for readability

4. Model Predictive Control
Initialize with current measurements at time t
Predict response over horizon of p steps
Solve for best input sequence, apply first element u*(t)
Repeat at time t+1 with new measurements (feedback)

5. Optimization Formulation
Predicted states xk, inputs uk, disturbances wk
At each time step, solve:
Constrained finite time optimal control problem
Optimization much faster if explicit structure of J, f, g (and derivatives) can be provided

6. Outline Model predictive control Modeling and MPC in buildings
Basic idea and elements
Advantages, disadvantages
Modeling and MPC in buildings
What works, what doesn’t
Generating models using historical data
Advanced control behavior
Experimental projects
Success stories
Increased scope and capabilities over time

7. Modeling for Building Energy Systems
Common practice is black-box simulation
DOE2, EnergyPlus, TRNSYS, etc
Useful for design, very difficult to use for control
Derivative-free optimization not very efficient or scalable
Need model structure for optimization and control
Simpler approach: reduced order modeling
Physics based model structure
Data driven parameter identification
Can adjust accuracy vs complexity tradeoff
Large scale real time optimization tractable

8. HVAC Example System
HVAC good target for energy savings by better control
Common configuration for commercial buildings: VAV with reheat
Control inputs: supply fan, cooling coil, heating coils, zone dampers, air handling unit dampers
States: zone temperatures

9. Thermal Zone Model

10. Simplest Useful Model Abstraction
Network of bilinear systems A
(simple extension to multiple states per zone, RC network analog)
Thermal zone model
Static nonlinearities
Equipment performance maps (chillers, cooling towers, pumps, fans, coils)
Equality and inequality constraints
Comfort range
Dynamic coupling: thermal zones, supply air & return air
Uncertain load predictions
Human: occupancy, thermal comfort, …
Environment: ambient temperature, solar radiation, …

11. How to Generate Reduced Models
Several options to create model data
Direct physics based lumped parameters
Model reduction from high fidelity design tools
Use historical data for model identification
Identification results vs measured data, Bancroft library

12. Using Data to Quantify Uncertainty
SMPC
Prediction model
Historical load
realization
Load
Ambient temperature

13. Advanced Control Behavior
A. Kelman, Y. Ma, A. Daly, F. Borrelli, Predictive Control for Energy Efficient Buildings with Thermal Storage: Modeling, Stimulation, and Experiments, IEEE Control System Magazine, 32(1), page 44-64, February 2012.
Time-varying price
Penalize peak power
MPC is able to incorporate time-varying energy price and reduce peak power consumption

14. Outline Model predictive control Modeling and MPC in buildings
Basic idea and elements
Advantages, disadvantages
Modeling and MPC in buildings
What works, what doesn’t
Generating models using historical data
Advanced control behavior
Experimental projects
Success stories
Increased scope and capabilities over time

15. Experimental Projects
UC Merced –, Merced, CA
4% Improvement
LBNL+UTRC- Storage, Chiller Optimization
Horizon 24hrs, Sampling 30min
Problem Size: ~300 variables , ~1440 constraints
CERL Engineering Research Laboratory, Champaign, IL
15% improvement.
UTRC- HVAC distribution – 5 zones
Horizon 4hrs, Sampling 20 min,
Problem Size: ~1600 variables , ~1400 constraints
Naval Station Great Lakes, North Chicago, Illinois
UTRC- Conversion + Storage – 250 zones
Problem Size: ~~20k variables , ~?? constraints
CITRIS Building (UC Berkeley) – Major issues
Siemens - Generation + HVAC distribution -135 Zones
Problem Size: ~~10k variables , ~?? constraints
Brower Center (Slab Radiant), Berkeley, CA
Architecture Department
Models based on step tests experiments
White Oak, Silver Spring, MD
Honeywell
Microgrid Optimization
Simplified models and BLOM tool critical for real-time implementation of large MPC experiments

16. Distributed Implementation

17. Distributed Implementation
Coordinator
Dual variables
Supply Fan
Cooling coil
damper
Heating coil
VAV damper
Zone temperature