Baseline Estimation of Commercial Building HVAC Fan Power Using Tensor Completion Shunbo Lei 1 , David Hong 2 , Johanna L. Mathieu 1 , and Ian A. Hiskens 1 1: Michigan Power & Energy Lab., University of Michigan-Ann Arbor 2: Wharton Statistics Dept., University of Pennsylvania This material is based upon work supported in part by the U.S. Department of Energy Building Technologies Office under contract number DE-AC02-76SF00515. Hong was supported in part by the U.S. NSF BIGDATA grant IIS 1837992 and the Dean’s Fund for Postdoctoral Research of the Wharton School.
Outline • Background and motivation • Proposed tensor completion based baseline method • Metrics and data • Numerical results • Conclusion and future work
Existing Baseline Methods • Averaging methods (Y-day simple average, HighXofY, MidXofY, LowXofY, NearestXofY; additive and multiplicative adjustments) Easy to implement, but typically have large errors • Regression methods (Load ↔ explanatory variables, esp.: outdoor temp.) Weather-sensitive loads V.S. weather-insensitive loads • Control group methods (Look for similar customers/buildings) Require large data sets: a large number of buildings and/or over a long time • Machine learning methods (neural network models, etc.) Hard to interpret, and require large data sets Developed based on whole-building power profiles
Short-term load shifting of HVAC system supply and return fans • Why return and supply fans of HVAC systems in commercial buildings? Commercial buildings: ~20% of energy consumed in U.S. HVAC systems: large thermal inertia of buildings Supply and return fans: primary response (secondary from chillers) • Examples of modulating HVAC fans: Fans tracking a regulation signal [1] Our experiments in UM buildings • Baselining HVAC fan power: For more accurate/granular analysis [1] H. Hao, Y. Lin, A. S. Kowli, P. Barooah, and S. Meyn , “Ancillary service to the grid through control of fans in commercial building HVAC systems,” IEEE Trans. Smart Grid, 2014.
HVAC Fan Power Baseline Methods • Signal bandwidth separation [1] Much lower bandwidth of baseline fan power compared with demand response signal Applicable when the signal is high-frequency • Simple linear interpolation [2] [3] Least squares fitting: 5 min before/after DR Inconsistent performance [1] H. Hao, Y. Lin, A. S. Kowli, P. Barooah, and S. Meyn , “Ancillary service to the grid through control of fans in commercial building HVAC systems ,” IEEE Trans. Smart Grid, 2014. [2] I. Beil, I. A. Hiskens , and S. Backhaus, “Round -trip efficiency of fast demand response in a large commercial air conditioner,” Energy Build., 2015. [3] A. Keskar, D. Anderson, J. X. Johnson, I. A. Hiskens , and J. L. Mathieu, “Experimental investigation of the additional energy consumed by building HVAC systems providing grid ancillary services,” in Proc. 20th ACEEE Summer Study Energy Effic. in Build., 2018.
Tensor Decomposition • 3-way tensor based on HVAC fan power data: 𝒬 Per-fan power data • Rank-r tensor decomposition by minimizing Tensor analogue to PCA More interpretable results Exploit correlation along different modes/dimensions (time, fan, and day here)
Tensor Decomposition • Works well in capturing dominant fan power patterns [4] [4] D. Hong, S. Lei, J. L. Mathieu, and L. Balzano , “Exploration of tensor decomposition applied to commercial building baseline estimation,” in Proc. 7th IEEE Global Conf. Signal & Inf. Process. (GlobalSIP), 2019.
Tensor Completion • Tensor decomposition with missing/unknown entries Minimize Missing entries can be estimated, assuming they follow patterns of known entries • In our application scenario: Assume missing data within demand response windows on demand response days Estimate their values, assuming they follow fan power patterns represented by the known data • Optimization algorithm Limited-memory BFGS with bound constraints Multiple runs/trials (non-convex)
Performance Metrics • Coefficient of variation (CV): ASHRAE standard metric Standard deviation of estimation errors / mean of the true values Measure accuracy • Normalized mean bias error (NMBE): ASHRAE standard metric Mean bias errors / mean of the true values Measure bias • Additional energy consumption (AEC) [3]: Similar to NMBE, without normalization Indicating baseline errors in terms of energy consumption [3] A. Keskar, D. Anderson, J. X. Johnson, I. A. Hiskens , and J. L. Mathieu, “Experimental investigation of the additional energy consumed by building HVAC systems providing grid ancillary services,” in Proc. 20th ACEEE Summer Study Energy Effic. in Build., 2018.
Data • For each building-year: Original data: 1-minute resolution Assume a morning (9-11am) and an afternoon (1-3pm) demand response event windows Tested on baseline days: no DR events, measured power = true baseline Leave-one-out cross-validation: assume one demand response day in each test of the tensor completion
Results: Impact of Temporal Frequency of the Data • Generally acceptable performance ASHRAE suggested tolerances when using hourly data: 30% for CV, and +/- 10% for NMBE • 15-min data: best performance Harder to achieve a lower CV than to achieve a lower NMBE • 1-min data: worst performance Hard to capture high frequency variation seen in the 1-min interval fan power data
Results: Per-Fan Power Data V.S. Total Fan Power Data (15-min interval) • Tensor completion with per-fan power data: better performance Support the use of 3-mode per-fan power data Capture dominant per-fan power patterns that are consistent among different fans and over different days Mean values of CV and NMBE of the tensor completion method with per-fan and total fan power data. (The error bars represent standard deviations.)
Results: Compared with other baseline methods (15-min, per-fan) • Benchmarks: Linear interpolation 5-day average Nearest3of6 • Tensor completion & linear interpolation: Better than the other two Tensor completion is generally the best Boxplots of CV and AEC for different building-years. (BL1: Tensor; BL2: Linear interpolation; BL3: 5-day average; BL4: Nearest3of6.)
Results: Compared with other baseline methods (15-min, per-fan) • AEC bias: especially important for financial settlement, etc. • Tensor completion V.S. linear interpolation: Tensor: better for morning DR window, comparable for afternoon DR window Linear: better for afternoon DR window, much larger bias in BBB-2018 (morning) and WH-2017 (both morning and afternoon)
Conclusion and Future Work • Conclusion: Tensor completion baseline: looks promising (generally the best in our evaluation) Resolution (temporal and spatial) of data: impact the baseline method performance • Future work: Tensor rank selection: tradeoff between data overfit and approximation errors Adaptive baseline method selection: different baseline methods work well in different situations/conditions
Thank you! Q&A
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