Statistical Modeling for Anomaly Detection, Forecasting and Root Cause Analysis of Energy Consumption for a Portfolio of Buildings

This paper describes the statistical analytics technology being developed to help K-12 public schools in New York City reduce the energy consumption. A multi-step statistical analysis procedure is proposed, to assess energy consumption and to identify energy saving opportunities for large portfolios of buildings such as the NYC K-12 public school buildings. The method borrows strength from and makes integrated use of the Variable Base Degree Day (VBDD) regression model, multivariate regression model and the Auto Regressive Integrated Moving Average (ARIMA) model. In the first step, we build a regression model which correlates the energy consumption with building characteristics for the whole portfolio of buildings. The energy related building characteristics are then identified through the stepwise variable selection technique. The results are valuable in providing building energy performance scores for the whole portfolio and benchmarking. Additionally, it offers insights for the energy consumption level of new buildings. In the second step, to accommodate building heterogeneity, we build the VBDD regression models separately for each building in the portfolio. These models are used to separate the base load energy consumption from the weather dependent usage. The results in this step consist of the base temperature estimates, as well as the estimated coefficients for the weather dependent variables, i.e., Heating Degree Days (HDD) and Cooling Degree Days (CDD) for all buildings. In the third step, we further conduct root cause analysis, by building the multivariate regression models for the base load and coefficient for HDD and CDD resulting from VBDD model, from which the performance scores can be derived for base load, heating, and cooling. Finally, in the last step, we model the dependent error structure through the ARIMA model. We also include seasonal factors in the model. The analytical method provides useful information to track and forecast the energy consumptions of the building portfolio, which will help facility staff and property managers achieve significant energy savings, greenhouse gas emission reductions and cost savings. INTRODUCTION Saving energy, improving efficiency of energy consumption, lowering energy cost, and reducing greenhouse gas emissions are key initiatives in many cities, municipalities and for building owners and operators. According to the World Business Council for Sustainable Development, buildings account for 40% of the worlds total energy consumption and, in 2005, nine gigatons of global carbon dioxide (CO2) emissions, well ahead of transportation and industry (WBCDS, 2009; DOE, 2008a). In the United States alone, commercial and residential buildings account for 38% of all CO2 emissions and 72% of electricity consumption according to the U. S. Department of Energy (DOE, 2008b,c). Furthermore, buildings use 13.6% of all potable water, or 15 trillion gallons per year, and 40% of raw materials globally (3 billion tons annually) (USGS, 2000; Roodman and Lenssen, 1995). Much of the energy consumption by commercial buildings is spent on lighting (twenty-six percent), followed by heating and cooling (thirteen percent and fourteen percent, respectively) (DOE, 2007). With the U. S. building sector’s energy consumption expected to increase by 35% between now and 2025 and commercial energy demand projected to grow at an average annual rate of 1.6% reaching 25.3 quads 1, or equivalently 25.3 × 10 British thermal units (Btu), in 2025, a critical need exists to develop and deploy emerging energy-efficient technologies that can deliver reliable energy demand reductions throughout a building’s lifespan while simultaneously satisfying the building occupants comfort, satisfaction and productivity (LBNL, 2009). Investing in energy efficient light bulbs and insulation materials and in automated shading has proven to reduce the energy demands on cooling and lighting (Lee et al., 2007). However, incremental improvements achieved by implementing individual energy efficient technologies alone are not sufficient to the successful achievement of the challeng1A quad is a unit of energy equal to 1015 BTU (British Thermal Units). The quad is commonly used when describing national or global energy budgets. A quad is approximately equal to 293, 071, 000, 000 kwh. http://www.aps.org/policy/reports/popareports/energy/units.cfm ing objectives set forth by the Intergovernmental Panel on Climate Change (IPCC) and other directives issued by cities, for example PLANYC 2030 in New York City (NYC) (IPCC, 2007; PLANYC, 2007). PLANYC aims to reduce the city government’s energy consumption and CO2 emissions by 30% by 2030 from 2005 levels. New York City’s government spends over $1 billion a year on energy on their approximately 4,000 buildings (e.g. public schools, prisons, court houses, administrative buildings, waste water treatment plants, etc.). NYC plans to invest, each year, an amount equal to 10% of its energy expenses in energy-saving measures over the next 10 years. The largest segment of NYC government buildings are the 1,400 K-12 public schools, serving 1.1 million students and covering about 150 million square feet. The New York City Department of Education was interested in understanding how energy efficient their buildings are, what factors contribute to inefficiencies, what are the opportunities for improvement given budget constraints, and how and how much can they contribute to saving energy and reducing GHG emissions toward NYC’s PlaNYC initiative. As an important component of the IBM smarter planetinitiatives (IBM, 2010b), the focus area of the smarter buildingsis the development of new technologies that may help us to improve building energy efficiency and reduce greenhouse gas emissions. According to IBMs Smarter PlanetPrimer (IBM, 2010a), “A smarter building integrates major building systems on a common network. Information and functionality between systems is shared to improve energy efficiency, operational effectiveness, and occupant satisfaction.” A smarter building is a complex system of systems that span heating and air conditioning, lighting, security, access control, entertainment, people movers, water, and monitoring and control and maintenance systems. Together, these systems have well managed and integrated physical and digital infrastructures that make the building safe, comfortable, and functional for its occupants and sustainable for the environment. A smarter building uses sensors, digital smart meters, digital controls, and analytic tools to automatically monitor and control services for its users. Thus, a smarter building is transforming into an instrumented, interconnected, and intelligent energy system which will help enable greenhouse gas reductions and lower costs while empowering building users, facility managers and building owner/operators. The advantages of installing smarter buildings on a massive scale are tremendous given that buildings account for 40% of the world’s total energy consumption. Developed along this effort is the IBM Building Energy and Emission analytics (i-BEE) Toolset, a new analytical tool which assesses, benchmarks, diagnoses, tracks, forecasts, simulates and optimizes energy consumption in building portfolios. Our focus in this paper is the statistical methodology in i-BEE, which is developed for detecting anomalies, forecasting and root cause analysis of monthly electricity, gas and steam consumption. The problem of analyzing and monitoring building energy performance is a key step to improve energy efficiency and to reduce environmental impact and cost. As an initial effort of this initiative, IBM collaborates with the City University of New York (IBM, 2011) to analyze the energy use in the portfolio of K-12 public school buildings in New York City. We use this building portfolio as our test bed example in this paper. The building portfolio consists of about 1400 public school buildings, covering 150 million square feet. In addition, we collect relevant information such as weather, energy and building characteristics. Our objective is to develop a statistical methodology to help understand the energy use patterns throughout the school portfolio. We develop a multi-step statistical analysis procedure, which combines the multivariate regression model, the Variable Base Degree Day (VBDD) regression model (Kissock et al., 2003) and the Auto Regressive Integrated Moving Average (ARIMA) model, to assess energy use and identify energy saving opportunities for large portfolios of buildings. In the first step, we build a regression model which correlates the energy consumption with building characteristics. The energy related building characteristics are then identified through the stepwise variable selection technique. The results are valuable in providing building energy performance scores for the whole portfolio. Additionally, it offers insights for the energy consumption level of new buildings. In the second step, to accommodate building heterogeneity, we build VBDD regression models separately for each building. These models are used to separate the base load energy consumption from the weather dependent usage. The results in this step consist of the base temperature estimates, as well as the estimated coefficients for HDD and CDD for all buildings. In the third step, we further conduct root cause analysis, by building the multivariate regression models for the results from VBDD model, from which the performance scores can be derived for base load, heating, and cooling. The VBDD regression model is a popular approach to analyze energy consumption, which assumes an independent error structure for the regression model. The assumption may not be realistic in practice because serial correlations exist for building energy time series data, especially for our application with a large portfolio of buildings. To overcome this shortcoming, in the last step, we model the dependent error structure through the ARIMA model. We also include seasonal factors in the model. From our experience, the VBDD model, combined with the ARIMA model for the error structure, typically provides improved statistical performance compared to using VBDD alone. The results are used for detecting abnormal energy use and forecasting energy consumption for a portfolio of buildings. The proposed technique provides an integrated analysis for building heterogeneity, the weather dependent patterns and the temporal dependent patterns. It has wide applicability in anomaly detection, forecasting and root cause analysis for building energy portfolios. In the remainder of this paper, we will first describe the general modeling framework, followed by the application of using the test bed example of the NYC school building portfolio. DEVELOPING THE STATISTICAL TOOLKIT To motivate the approach we take to model energy use of building portfolios, it is useful to begin at the end, and consider the type of outputs that will result from the methodology. From the statistical toolset to be developed, we wanted to be able to answer the following questions: 1. Which building parametric data (e.g., building characteristics, operational activities and occupant behavior) is the most useful for predicting building energy use? 2. How can we benchmark the relative building energy performance within the portfolio? 3. What percentages of the total energy use are due to base load, heating use and cooling use, respectively? 4. What are the potential improvement opportunities / root causes for less efficient buildings? 5. How can we offset the weather dependent factors, and perform improvement tracking and energy savings from retrofit activities? 6. How can we detect abnormal energy use in the historical energy use data? 7. How much energy do we expect to use in the future? To address these questions, we develop a multistep statistical modeling strategy. The statistical models utilize typical data collected about the building energy portfolio, such as • energy use data for each building; • building characteristics such as the gross floor area (GFA), age of the building, occupant density, and number of each equipment type (e.g., refrigerator, freezers, etc); • building operation and activity; • weather data such as outside temperature and relative humidity. The statistical modeling strategy we developed consists of the following three major modules • Variable Based Degree Day (VBDD) model with building effect for each building; • Multivariate regression models (Multiregress): one for the overall energy use of the whole portfolio, and ones for base load, heating, cooling which utilize the outputs from VBDD of each building; • Time series models (TS-model), which utilize the outputs from VBDD. The system is best described by the schematic given in Figure 1. We will discuss the modeling details in the rest of this section. We note that these three modules can be integrated, in order to answer the aforementioned questions, as follows. • Multi-regress module is used to answer questions 1, 2. • VBDD module is used to answer questions 3, 5. • VBDD module and Multi-regress module are combined together to answer question 4. • VBDD module and TS-model module are combined together to answer questions 6 and 7. BUILDING EFFECTS VBDD MODEL To better manage the energy portfolio of the New York public school buildings, it is very important to first understand the energy usage patterns for all buildings. The overall energy consumption for commercial buildings like the NYC public school buildings can typically be divided into the following three categories of usage: base load, heating and cooling. Here, the base load refers to the energy consumption that does not depend on outside temperature. Typical usage that falls into this category includes cooking, lighting and hot water usage, and plug loads such as computers. In contrast, the heating and cooling usage depend on the outside temperature. Specifically, there exists some balance-point temperature such that the space-heating energy usage increases as the outdoor temperature decreases below the balancepoint temperature, whereas the space-cooling energy use increases as the outdoor temperature increases above the balance-point temperature. We use the following notations to describe the model development. Denote the total number of buildings in the portfolio by n, the total number of months of the billing cycle by m, and the number of days in month t by dt, respectively. Let Titd be the average outdoor temperature for building i on day d of month t, i ∈ {1, . . . , n}, t ∈ {1, . . . ,m}, © 2010 IBM Corporation IBM Confidential 3 Energy Data