#### Transcript Modeling and Predictive Control Strategies in Buildings with Mixed

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