ARX models for Building Energy Performance Assessment Based on In-situ Measurements

ARX models for Building Energy Performance Assessment Based on In-situ Measurements

• 1.
  DTU Compute, TechnicalUniversity of Denmark 07 August 2015 ARX MODELS FOR BUILDING ENERGY PERFORMANCE ASSESSMENT BASED ON IN-SITU MEASUREMENTS IEA EBC Annex 71 Common Exercise 1, Subtask 3 Physical Parameter Identification Christoffer Rasmussen ([email protected]), Peder Bacher, Henrik Madsen
• 2.
  DTU Compute, TechnicalUniversity of Denmark 07 August 2015 MODEL ARX model as used in Annex 58, Subtask 3, Part 2 • Output: Indoor temperature • Input: Heating power Outdoor temperature Solar radiation Annex 71, CE1 ST3 – October 23-25, 20172 𝜙 𝐵 𝑇$ % = 𝜔( 𝐵 Φ$ ( + 𝜔+ 𝐵 𝑇$ + + 𝜔,-. 𝐵 𝑄$ ,-. + 𝜖$
• 3.
  DTU Compute, TechnicalUniversity of Denmark 07 August 2015 DATA REQUIREMENTS FOR THE GOOD FIT High signal-to-noise ratio – Daily mean outdoor temperature below 5 ºC Minimal disturbances in data from occupants – Out-of-the-house vacation: • No disturbances • Limited periods throughout the year. – Out-of-the-house weekdays: • No disturbances • Only applicable if occupants actually leave the house regularly for several hours – Night-time: • Few disturbances • New data accessible every night (normally) Annex 71, CE1 ST3 – October 23-25, 20173
• 4.
  DTU Compute, TechnicalUniversity of Denmark 07 August 2015 MODEL ARX model as used in Annex 58, Subtask 3, Part 2 ARX model as used in Annex 71, Common Exercise 1, Subtask 3 • Output: Indoor temperature • Input: Heating power Outdoor temperature • Data: Only night-time • Time resolution: 10 minutes Annex 71, CE1 ST3 – October 23-25, 20174 𝜙 𝐵 𝑇$ % = 𝜔( 𝐵 Φ$ ( + 𝜔+ 𝐵 𝑇$ + + 𝜔,-. 𝐵 𝑄$ ,-. + 𝜖$ 𝜙 𝐵 𝑇$ % = 𝜔( 𝐵 Φ$ ( + 𝜔+ 𝐵 𝑇$ + + 𝜖$
• 5.
  DTU Compute, TechnicalUniversity of Denmark 07 August 2015 DOWN-WEIGHTING DAY-TIME DATA Annex 71, CE1 ST3 – October 23-25, 20175 051015 Heat consumption, day and night Energy[kW] 18:00 00:00 06:00 12:00 18:00 00:00 06:00 Day (weight = 0) Night (weight = 1)
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  DTU Compute, TechnicalUniversity of Denmark 07 August 2015 ACF AND CCF ISSUES N Time Residual ⋮ ⋮ ⋮ 35 2014/01/01 06:50 +0.05 36 2014/01/01 07:00 –0.02 37 2014/01/01 19:30 –0.01 38 2014/01/01 19:40 +0.04 ⋮ ⋮ ⋮ Annex 71, CE1 ST3 – October 23-25, 20176 𝛾33 𝜏 = Cov 𝑋 𝑡 , 𝑋 𝑡 + 𝜏 𝜌33 𝜏 = 𝛾33 𝜏 𝜎3 =
• 7.
  DTU Compute, TechnicalUniversity of Denmark 07 August 2015 SEPARATING SPACE HEATING & DHW 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 Summer data Water consumption [m3 ] Heat[kW] Hot water and space heating Hot water Space heating 0510152025 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 All data Water consumption [m3 ] 0510152025 Annex 71, CE1 ST3 – October 23-25, 20177
• 8.
  DTU Compute, TechnicalUniversity of Denmark 07 August 2015 SEPARATING SPACE HEATING & DHW Annex 71, CE1 ST3 – October 23-25, 20178 0515 Energy[kW] 00:00 03:00 06:00 09:00 12:00 15:00 18:00 21:00 24:00 Hot water production Space heating 0.000.020.04 Waterconsump.[m3 ] 00:00 03:00 06:00 09:00 12:00 15:00 18:00 21:00 24:00 20.021.5 Indoortemp.[°C] 00:00 03:00 06:00 09:00 12:00 15:00 18:00 21:00 24:00
• 9.
  DTU Compute, TechnicalUniversity of Denmark 07 August 2015 CASE DIFFERENT OCCUPATION PERIODS Annex 71, CE1 ST3 – October 23-25, 201712 Different occupation periods Sample period [nights] HLC[W/K] 335075100125150 1 3 5 7 9 11 13 15 17 Estimate (occupation period 2) 95 % CI Assumed 83.4 (±16.3) W/K
• 10.
  DTU Compute, TechnicalUniversity of Denmark 07 August 2015 CASE DIFFERENT OCCUPATION PERIODS Annex 71, CE1 ST3 – October 23-25, 201713 Different occupation periods Sample period [nights] HLC[W/K] 335075100125150 1 3 5 7 9 11 13 15 17 Estimate (occupation period 1) Estimate (occupation period 2) 95 % CI Assumed 83.4 (±16.3) W/K 63.2 (±5.1) W/K
• 11.
  DTU Compute, TechnicalUniversity of Denmark 07 August 2015 RESIDUAL ANALYSIS Annex 71, CE1 ST3 – October 23-25, 201714 0 10 20 30 40 −0.050.05 ACF (Residuals) ACF 0 10 20 30 40 −0.060.04 CCF (Residuals & Outdoor temperature) CCF 0 10 20 30 40 −0.060.04 CCF (Residuals & Heating power) Lags CCF
• 12.
  DTU Compute, TechnicalUniversity of Denmark 07 August 2015 RESIDUAL ANALYSIS Annex 71, CE1 ST3 – October 23-25, 201715 20.521.522.523.5 One−step predictions Indoortemp.(°C) Measured Predicted −0.050.000.05 Residuals ε Night 1 Night 2 Night 3 Night 4 Night 5 Night 6 Night 7 Night 8 Night 9 Night 10 Night 11 Night 12 Night 13 Night 14 Night 15 Night 16
• 13.
  DTU Compute, TechnicalUniversity of Denmark 07 August 2015 RESIDUAL ANALYSIS Annex 71, CE1 ST3 – October 23-25, 201716 0.0 0.1 0.2 0.3 0.4 0.5 0.00.20.40.60.81.0 Frequency Cumulative periodogram −3 −2 −1 0 1 2 3 −0.050.000.05 Q−Q plot Theoretical quantiles Samplequantiles Histogram Sample quantiles Density −0.10 −0.05 0.00 0.05 0.10 051015
• 14.
  DTU Compute, TechnicalUniversity of Denmark 07 August 2015 CONCLUSIONS Data – Obtain good time series where input and output is well-exercised. – Prober filtering of domestic hot water consumption. – Get representative indoor temperatures. – Model internal heat gains from occupants. E.g. through CO₂ measurements. Assumed and estimated HLC – Air leakages. – Thermal bridges. – All heat is assumed to be transferred to the air. – Heat capacity of building not taken into account Annex 71, CE1 ST3 – October 23-25, 201717
• 15.
  DTU Compute, TechnicalUniversity of Denmark 07 August 2015 PERSPECTIVE Evaluation of building performance and occupants effect on energy consumption 1. Apply occupant models to estimate if apartment is empty or not. 2. Use periods where apartment is un-occupied and of occupants are sleeping, instead of night-time only, to include solar radiation in model. 3. Use fitted model on all data and estimate the effect of the occupants on the energy consumption. Annex 71, CE1 ST3 – October 23-25, 201718
• 16.
  DTU Compute, TechnicalUniversity of Denmark 07 August 2015 MODEL MATRIX Annex 71, CE1 ST3 – October 23-25, 201719 HLC estimate and standard deviation obtained from best model: 63.2 (±5.1) W/K 10 min data of: Indoor temperature Outdoor temperature Heating power
• 17.
  DTU Compute, TechnicalUniversity of Denmark 07 August 2015 MODEL MATRIX Annex 71, CE1 ST3 – October 23-25, 201720 HLC estimate and standard deviation obtained from best model: 63.2 (±5.1) W/K 10 min data of: Indoor temperature Outdoor temperature Heating power