Modeling and Predictive Control Strategies
in Buildings with Mixed-Mode Cooling
Jianjun Hu, Panagiota Karava
School of Civil Engineering (Architectural Engineering Group)
Purdue University
Background - Mixed-Mode Cooling
 Hybrid
approach for space conditioning;
 Combination
of natural ventilation, driven by
wind or thermal buoyancy forces, and mechanical
systems;
 “Intelligent”
 minimize
controls to optimize mode switching
building energy use and maintain occupant
thermal comfort.
2
Background - Mixed-Mode Strategies
When outdoor conditions are appropriate:



Exhaust
Corridor inlet grilles and atria connecting
grilles open;
Atrium mechanical air supply flow rate
reduced to minimum value, corridor air
supply units close;
Atrium exhaust vent open;
Air exchange
with corridor
inlet grilles
Atria
connecting
floor grilles
Institutional building
located in Montreal
3-storey
atria
Mixed-mode
cooling concept
3
(Karava et al., 2012)
- When should we open the windows ?
- For how long?
- Can we use MPC?
Background – MPC for Mixed-Mode Buildings

4
Modeling Complexity

Pump and fan speed, opening position (inverse model identified
from measurement data) - Spindler, 2004

Window opening schedule (rule extraction for real time
application) - May-Ostendorp, 2011

Shading percentage, air change rate (look-up table for a single
zone) – Coffey, 2011

Blind and window opening schedule (bi-linear state space model
for a single zone) – Lehmann et al., 2012
Objectives
 Develop
model-predictive control strategies for
multi-zone buildings with mixed-mode cooling, high
solar gains, and exposed thermal mass.
 Switching modes of operation for space cooling (window
schedule, fan assist, night cooling, HVAC)
 Coordinated shading control
5
MPC: Problem Formulation
Thermal Dynamic Model:
Nonlinear
Discrete Control Variables:
Open/Close (1/0)
Offline MPC
(deterministic);
baseline simulation
study for a mixed-mode
building
Linearized
prediction models
(state-space)
Algorithms for discrete
optimization
On-line MPC
(implementation, identification, uncertainty)
Operable vents
6
MPC: Dynamic Model (Thermal & Airflow Network)

Building section
(9 thermal zones)
G la ss facade
Sectio n 1
7
Sectio n 2
Sectio n 3
Sectio n 4
A trium
MPC: Dynamic Model (Thermal & Airflow Network)

Heat balance for atrium air node
𝑑𝑇𝑎𝑡𝑟
𝐶𝑎𝑡𝑟
=
𝑑𝑡

𝑖
𝑇𝑤𝑎𝑙𝑙
− 𝑇𝑎𝑡𝑟
𝑖
𝑅𝑤𝑎𝑙𝑙_𝑎𝑡𝑟
+ 𝑄𝑎𝑢𝑥 + 𝑚𝑐𝑝 𝑇𝑐𝑜𝑟𝑟 − 𝑇𝑎𝑡𝑟
𝑚 is the air exchange flow rate between zones (obtained
from the airflow network model) :
𝑚 = 𝐶𝐷 𝐴 2𝜌∆𝑃

pressure difference ΔP:
∆𝑃 = 𝑓 𝑃, 𝑇𝑎𝑡𝑟 , 𝑇𝑐𝑜𝑟

8
Solved by FDM method and Newton-Raphson
Thermal model
∆𝑃 = 𝑓 𝑃, 𝑇𝑎𝑡𝑟 , 𝑇𝑐𝑜𝑟
𝑚 = 𝐶𝐷 𝐴 2𝜌∆𝑃
MPC: Dynamic Model (State-Space)

State-space representation:
𝑿 = 𝑨𝑿 + 𝑩𝑼 + 𝑓 𝑿, 𝑼, 𝑚
𝒀 = 𝑪𝑿 + 𝑫𝑼
A, B, C, D: coefficient
matrices
X: state vector
U: input vector
Y: Output vector
Linear time varying (LTV-SS)
𝑿=𝑨 𝒕 𝑿+𝑩 𝒕 𝑼
𝒀 = 𝑪𝑿 + 𝑫𝑼
9
𝑓 𝑿, 𝑼, 𝑚 is a nonlinear term, i.e.: heat
transfer due to the air exchange.
𝑚 = 𝑔 𝑿, 𝑼 obtained from the airflow
network model
MPC: Dynamic Model (State-Space)
States (X): X = [Ti , Tij , Tij,k]T
 i – zone index
 j – wall index
 k – mass node index
Inputs (U): U = [Tout, Sij, Load]T
 Tout – outside air temperature;
 Sij – solar radiation on surfaces ij;
 Load – heating/cooling load;
Outputs (Y): Y= [Ti , Tij , Tij,k]T
 Zone air temperature;
 Wall temperature;
 …………
10
MPC: Dynamic Model (LTV-SS)
𝑿=𝑨 𝒕 𝑿+𝑩 𝒕 𝑼
280×1
𝑇𝑖
𝑇𝑖𝑗
𝑇𝑖𝑗,𝑘
𝐴1,1
⋮
=
𝐴280,1
𝑇𝑖
⋯ 𝐴1,280
⋱
⋮
∙ 𝑇𝑖𝑗
⋯ 𝐴280,280
𝑇𝑖𝑗,𝑘
280×1
𝐵1,1
⋮
+
𝐵280,1
𝑇𝑜𝑢𝑡
⋯ 𝐵1,52
⋱
⋮
∙ 𝑆𝑖𝑗
⋯ 𝐵280,52
𝐿𝑜𝑎𝑑𝑖
52×1
 Find the matrices from the heat balance equations
e.g. atrium zone air node:
𝑑𝑇𝑎𝑡𝑟_𝑏
=
𝑑𝑡
𝑇11𝑤_𝑎𝑡 − 𝑇𝑎𝑡𝑟_𝑏 𝑇11𝑔_𝑎𝑡 − 𝑇𝑎𝑡𝑟_𝑏 𝑇31_𝑎𝑡 − 𝑇𝑎𝑡𝑟_𝑏
+
+
𝑅11𝑤_𝑎𝑖𝑟
𝑅11𝑔_𝑎𝑖𝑟
𝑅31_𝑎𝑖𝑟
𝑇41_𝑎𝑡 − 𝑇𝑎𝑡𝑟_𝑏 𝑇51_𝑎𝑡 − 𝑇𝑎𝑡𝑟_𝑏
+
+
𝑅41_𝑎𝑖𝑟
𝑅51_𝑎𝑖𝑟
+𝑚𝑆𝐸1_𝑎𝑡𝑟 𝑐𝑝 𝑇𝑆𝐸1 − 𝑇𝑎𝑡𝑟_𝑏
+𝑚𝑁𝑊1_𝑎𝑡𝑟 𝑐𝑝 𝑇𝑁𝑊1 − 𝑇𝑎𝑡𝑟_𝑏
+𝑚𝑎𝑡𝑟2_𝑎𝑡𝑟1 𝑐𝑝 𝑇𝑎𝑡𝑟_𝑚 − 𝑇𝑎𝑡𝑟_𝑏
+𝐿𝑜𝑎𝑑𝑎𝑡𝑟_𝑏
𝐶𝑎𝑡𝑟_𝑏
11
𝐴235,1 =
𝐴235,118 =
𝐴235,240 =
𝐴235,241 =
𝐴235,243 =
𝐴235,245 =
𝑚𝑆𝐸1_𝑎𝑡𝑟 𝑐𝑝
𝐶𝑎𝑡𝑟_𝑏
1
𝐶𝑎𝑡𝑟_𝑏 𝑅11𝑤_𝑎𝑖𝑟
𝐴235,118 =
𝑚𝑁𝑊1_𝑎𝑡𝑟 𝑐𝑝
𝐶𝑎𝑡𝑟_𝑏
𝐴235,235 = −1
1
𝐶𝑎𝑡𝑟_𝑏 𝑅11𝑔_𝑎𝑖𝑟
1
𝐶𝑎𝑡𝑟_𝑏 𝑅31_𝑎𝑖𝑟
1
𝐶𝑎𝑡𝑟_𝑏 𝑅41_𝑎𝑖𝑟
1
𝐶𝑎𝑡𝑟_𝑏 𝑅51_𝑎𝑖𝑟
𝐴235,247 =
𝑚𝑎𝑡𝑟2_𝑎𝑡𝑟1 𝑐𝑝
𝐶𝑎𝑡𝑟_𝑏
𝐵235,50 = 1
𝐴
MPC: Control Variable, Cost Function, and Constraints

Control variable: operation schedule

Cost function:
Min: 𝐽 𝐼𝑂𝑡 = 𝐸
where: E is the energy consumption; IOt is vector of binary (open/close)
decisions for the motorized envelope openings
𝐼𝑂𝑡 = 0, 1

Constraints:




12
Operative temperature within comfort range (23-27.6 °C, which corresponds to PPD
of 10%) during occupancy hours;
Use minimal amount of energy: cooling/heating (set point during occupancy hours
8:00-18:00 is 21-23 ˚C, during unoccupied hours is 13-30 °C);
Dew point temperature should be lower than 13.5 °C (ASHRAE 90.1);
Wind speed should be lower than 7.5 m/s.
MPC: Optimization (PSO)


“Offline” deterministic MPC: Assume future predictions are exact
Planning horizon: 20:00 -- 19:00, decide operation status during each hour.
20:00
u
21:00
u
22:00
u
………….
Find optimal operation
schedule
19:00

u
find optimal sequence
from 224 options;
Wetter (2011)
13
MPC: Optimization (Progressive Refinement)

Multi-level optimization
 Decide operation status for each two hours at night (20:00-5:00);
 Use simple rules (based on off-line MPC)
Time frames
Rules
Temperature
Transmitted Solr
Decision
Early morning
(6:00 – 8:00)
Case 1
≥ 21 °C
--
open
Case 2
≤ 21 °C
--
close
Case 1
≤ 23 °C
≤ 400 W/m2
open
Case 2
> 23 °C
≤ 400 W/m2
close
Case 3
≤ 21 °C
> 400 W/m2
open
Case 4
> 21 °C
> 400 W/m2
close
Afternoon
(15:00 – 16:00)
14
Simulation Study
Assumptions:





Local controllers were ideal such that all feedback controllers follow set-points
exactly;
Internal heat gains (occupancy, lighting) were not considered;
An idealized mechanical cooling system with a COP value of 3.5 was modeled.
TMW3 data (Montreal)
Cases:


Air temperature, °C

Baseline: mechanical cooling with night set back
Heuristic: Tamb ∈ [15℃, 25℃], Tdew ≤ 13.5 ℃, Wspeed < 7.5 m/s
T_dry
T_dew
DNI
MPC
30
1000
24
800
18
600
12
400
6
200
15
0
20:00
20:00
20:00
20:00
20:00
Time (20:00 of 8/17 -- 19:00 of 8/23), hour
20:00
0
20:00
Direct normal irradiance,
w/m2

Results: Operation Schedule (Heuristic & MPC)
 Hours during which vents are open are illustrated by cells with grey background
 Heuristic strategy leads to higher risk of over-cooling during early morning (Day 1,
Day 4, and Day 5);
16
30.0
Baseline: FDM
Baseline: LTV-SS
Heuristic: FDM
Heuristic: LTV-SS
26.0
1.0
Operative temperature, °C
Power, kW
3.0
2.0
Heuristic: LTV-SS
MPC: LTVBaseline:
Heuristic: FDM
30.0 FDM
26.0
Baseline:
LTV-SS
Heuristic: LTV-SS
MPC: FDM
MPC: LTV-SS
30.0
0.0
20:00
20:00
20:00
20:00
20:00
20:00
20:00
Time (from 20:00 of 08/17 -- 19:00 of 08/23), hour
22.0
Baseline
300
26.0
Heuristic
Operative temperature, °C
Baseline: LTV-SS
Baseline: FDM
Baseline: LTV-SS
Heuristic: FDM
Heuristic: LTV-SS
MPC: FDM
MPC: LTV-SS
22.0
18.0
20:00 20:00 20:00 20:00 20:00 20:00 20:00
Time (from 20:00 of 08/17 -- 19:00 of 08/23), hour
1.3 C
-3.0 C
MPC
Baseline
Heuristic
MPC
250
200
100
50
0
Operative temperature deviation, C
18.0
22.0
20:00 20:00 20:00 20:00 20:00 20:00
150
Time 18.0
(from 20:00 of 08/17 -- 19:00 of 08/23), ho
20:00 20:00 20:00 20:00 20
Time (from 20:00 of 08/17 -- 19:0
June
July
August
Cooling energy consumption, kWh
Operative temperature, °C
Results: Energy Consumption & Operative Temperature
Heuristic: FDM
MPC: FDM
(FDM &Baseline:
LTV-SS) FDM
0.8
0.7
Comfort Acceptability
reduced from 80% to 60%
0.6
0.5
0.4
0.3
0.2
0.1
0
8/18
8/19
8/20
8/21
Date
17
8/22
8/23
Results: MPC with PSO and Progressive Refinement (ProRe)
LTV-SS: Baseline
LTV-SS: MPC (PSO)
LTV-SS: MPC (ProRe)
Power, kW
3.0
 Similar energy
consumption and
operative temperature;
2.0
1.0
 Much faster calculation
0.0
with ProRe;
20:00
20:00
20:00
20:00
20:00
20:00
20:00
Time (from 20:00 of 8/17 to 19:00 of 8/23), hour
Operative Temperature, °C
LTV-SS: Baseline
LTV-SS: MPC (PSO)
LTV-SS: MPC (ProRe)
30.0
3 Days
26.0
22.0
18.0
20:00 20:00 20:00 20:00 20:00 20:00 20:00
Time (from 20:00 of 8/17 to 19:00 of 8/23), hour
18
3 Hours
Results: MPC with PSO and Progressive Refinement (ProRe)
 Fine-tune rules in Progressive Refinement method for different climate (LA)
19
Conclusions

For the simulation period considered in the present study, mixed-mode
cooling strategies (MPC and heuristic) effectively reduced building energy
consumption.

The heuristic strategy can lead to a mean operative temperature deviation
up to 0.7 °C, which may decrease the comfort acceptability from 80% to
60%. The predictive control strategy maintained the operative temperature
in desired range.

The linear time-variant state-space model can predict the thermal
dynamics of the mixed-mode building with good accuracy.

The progressive refinement optimization method can find similar optimal
decisions with the PSO algorithm but with significantly lower
computational effort.
20
Acknowledgement

This work is funded by the Purdue Research Foundation and
the Energy Efficient Buildings Hub, an energy innovation HUB
sponsored by the Department of Energy under Award Number
DEEE0004261.

In kind support is provided from Kawneer/Alcoa, FFI Inc., and
Automated Logic Corporation
21