Modeling and Predictive Control Strategies in Buildings with Mixed-Mode Cooling

Jianjun Hu, Panagiota KaravaSchool of Civil Engineering (Architectural Engineering Group)

Purdue University

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Background - Mixed-Mode Cooling

Hybrid approach for space conditioning;

Combination of natural ventilation, driven by wind or thermal buoyancy forces, and mechanical systems;

“Intelligent” controls to optimize mode switching minimize building energy use and maintain occupant

thermal comfort.

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Background - Mixed-Mode Strategies

Air exchange with corridor inlet grilles

3-storey atria

Atria connecting floor grilles

ExhaustWhen outdoor conditions are appropriate: 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;

(Karava et al., 2012)

- When should we open the windows ? - For how long?- Can we use MPC?

Institutional building located in Montreal

Mixed-mode cooling concept

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Background – MPC for Mixed-Mode Buildings 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

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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

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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

MPC: Dynamic Model (Thermal & Airflow Network)

Building section (9 thermal zones)

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Glass facade

AtriumSection 1 Section 2 Section 3 Section 4

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Heat balance for atrium air node

is the air exchange flow rate between zones (obtained from the airflow network model) :

pressure difference ΔP:

Solved by FDM method and Newton-Raphson

𝐶𝑎𝑡𝑟𝑑𝑇𝑎𝑡𝑟𝑑𝑡

=∑ 𝑇𝑤𝑎𝑙𝑙𝑖 −𝑇 𝑎𝑡𝑟𝑅𝑤𝑎𝑙𝑙𝑎𝑡𝑟𝑖 +𝑄𝑎𝑢𝑥+�̇�𝑐𝑝 (𝑇𝑐𝑜𝑟𝑟−𝑇 𝑎𝑡𝑟 )

�̇�

�̇�=𝐶𝐷𝐴√2𝜌 ∆𝑃

MPC: Dynamic Model (Thermal & Airflow Network)

∆ 𝑃= 𝑓 (𝑃 ,𝑇 𝑎𝑡𝑟 ,𝑇 𝑐𝑜𝑟 )

Thermal model

�̇�=𝐶𝐷𝐴√2𝜌 ∆𝑃

∆𝑃= 𝑓 (𝑃 ,𝑇 𝑎𝑡𝑟 ,𝑇 𝑐𝑜𝑟 )

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MPC: Dynamic Model (State-Space) State-space representation:

�̇�=𝑨𝑿+𝑩𝑼+ 𝑓 ( 𝑿 ,𝑼 ,�̇� )𝒀=𝑪𝑿 +𝑫𝑼

obtained from the airflow network model�̇�=𝑔 ( 𝑿 ,𝑼 )

Linear time varying (LTV-SS)

A, B, C, D: coefficient matricesX: state vectorU: input vectorY: Output vector

�̇�=𝑨 (𝒕 ) 𝑿+𝑩 (𝒕 )𝑼𝒀=𝑪𝑿 +𝑫𝑼

is a nonlinear term, i.e.: heat transfer due to the air exchange.𝑓 (𝑿 ,𝑼 ,�̇� )

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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; …………

MPC: Dynamic Model (State-Space)

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[ �̇� 𝑖�̇� 𝑖𝑗�̇� 𝑖𝑗 ,𝑘]280× 1

=[ 𝐴1,1 ⋯ 𝐴1,280⋮ ⋱ ⋮𝐴280,1 ⋯ 𝐴280,280] ∙[

𝑇 𝑖𝑇 𝑖𝑗𝑇 𝑖𝑗 ,𝑘]

280×1

+[ 𝐵1,1 ⋯ 𝐵1,52⋮ ⋱ ⋮𝐵280,1 ⋯ 𝐵280,52] ∙[

𝑇 𝑜𝑢𝑡𝑆𝑖𝑗𝐿𝑜𝑎𝑑 𝑖]

52×1

�̇�=𝑨 (𝒕 ) 𝑿+𝑩 (𝒕 )𝑼

Find the matrices from the heat balance equations

e.g. atrium zone air node: 𝐴235,1=�̇�𝑆𝐸 1𝑎𝑡𝑟𝑐𝑝𝐶𝑎𝑡𝑟𝑏

𝐴235,118=�̇�𝑁𝑊 1𝑎𝑡𝑟

𝑐𝑝𝐶𝑎𝑡𝑟 𝑏

𝐴235,118=1

𝐶𝑎𝑡𝑟 𝑏𝑅11𝑤𝑎𝑖𝑟𝐴235,240=

1𝐶𝑎𝑡𝑟𝑏𝑅11𝑔𝑎𝑖𝑟

𝐴235,241=1

𝐶𝑎𝑡𝑟𝑏𝑅31𝑎𝑖𝑟

𝐴235,243=1

𝐶𝑎𝑡𝑟𝑏𝑅41𝑎𝑖𝑟𝐴235,245=

1𝐶𝑎𝑡𝑟𝑏𝑅51𝑎𝑖𝑟

𝐴235,247=�̇�𝑎𝑡𝑟 2𝑎𝑡𝑟 1𝑐𝑝𝐶𝑎𝑡𝑟 𝑏

𝐴235,235=(−1 )∑ 𝐴𝐵235,50=1

MPC: Dynamic Model (LTV-SS)

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MPC: Control Variable, Cost Function, and Constraints Control variable: operation schedule

Cost function:Min: where: E is the energy consumption; IOt is vector of binary (open/close) decisions for the motorized envelope openings

𝐽 ( �⃗�𝑂𝑡 )=𝐸

�⃗�𝑂𝑡= {0 ,1 }

Constraints: 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.

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MPC: Optimization (PSO) “Offline” deterministic MPC: Assume future predictions are exact Planning horizon: 20:00 -- 19:00, decide operation status during each hour.

19:0020:00 21:00 22:00 ………….

Find optimal operation scheduleuuu u

find optimal sequence from 224 options;

Wetter (2011)

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MPC: Optimization (Progressive Refinement)

Time frames Rules Temperature Transmitted Solr Decision

Early morning (6:00 – 8:00)

Case 1 ≥ 21 °C -- open

Case 2 ≤ 21 °C -- close

Afternoon(15:00 – 16:00)

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

Multi-level optimization Decide operation status for each two hours at night (20:00-5:00); Use simple rules (based on off-line MPC)

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Simulation Study

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20:00 20:00 20:00 20:00 20:00 20:00 20:00 Dir

ect

norm

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/m2

Air

tem

pera

ture

, °C

Time (20:00 of 8/17 -- 19:00 of 8/23), hour

T_dry T_dew DNI

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: Baseline: mechanical cooling with night set back Heuristic: Tamb [15 , 25 ], T∈ ℃ ℃ dew ≤ 13.5 , W℃ speed < 7.5 m/s MPC

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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);

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Results: Energy Consumption & Operative Temperature (FDM & LTV-SS)

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8/18 8/19 8/20 8/21 8/22 8/23

Ope

rativ

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mpe

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evia

tion,

�C

Date

Baseline Heuristic MPC

0.0

1.0

2.0

3.0

20:00 20:00 20:00 20:00 20:00 20:00 20:00

Pow

er, k

W

Time (from 20:00 of 08/17 -- 19:00 of 08/23), hour

Baseline: FDM Heuristic: FDM MPC: FDMBaseline: LTV-SS Heuristic: LTV-SS MPC: LTV-SS

0

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June July August

Cool

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onsu

mpti

on, k

Wh

Baseline Heuristic MPC

18.0

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26.0

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20:00 20:00 20:00 20:00 20:00 20:00 20:00Ope

rativ

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mpe

ratu

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C

Time (from 20:00 of 08/17 -- 19:00 of 08/23), hour

Baseline: FDM Heuristic: FDM MPC: FDMBaseline: LTV-SS Heuristic: LTV-SS MPC: LTV-SS

Comfort Acceptability reduced from 80% to 60%

18.0

22.0

26.0

30.0

20:00 20:00 20:00 20:00 20:00 20:00 20:00Operative

tempera

ture,

°C

Time (from 20:00 of 08/17 -- 19:00 of 08/23), hour

Baseline: FDM Heuristic: FDM MPC: FDMBaseline: LTV-SS Heuristic: LTV-SS MPC: LTV-SS

18.0

22.0

26.0

30.0

20:00 20:00 20:00 20:00 20:00 20:00 20:00Operative tem

perature,

°C

Time (from 20:00 of 08/17 -- 19:00 of 08/23), hour

Baseline: FDM Heuristic: FDM MPC: FDMBaseline: LTV-SS Heuristic: LTV-SS MPC: LTV-SS

-3.0 °C1.3 °C

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Results: MPC with PSO and Progressive Refinement (ProRe)

Similar energy consumption and operative temperature;

Much faster calculation with ProRe;

3 Days

3 Hours

0.0

1.0

2.0

3.0

20:00 20:00 20:00 20:00 20:00 20:00 20:00

Pow

er, k

W

Time (from 20:00 of 8/17 to 19:00 of 8/23), hour

LTV-SS: Baseline LTV-SS: MPC (PSO) LTV-SS: MPC (ProRe)

18.0

22.0

26.0

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20:00 20:00 20:00 20:00 20:00 20:00 20:00

Ope

rati

ve T

empe

ratu

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°C

Time (from 20:00 of 8/17 to 19:00 of 8/23), hour

LTV-SS: Baseline LTV-SS: MPC (PSO) LTV-SS: MPC (ProRe)

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Results: MPC with PSO and Progressive Refinement (ProRe)

Fine-tune rules in Progressive Refinement method for different climate (LA)

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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.

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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