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FTC 2016 - Future Technologies Conference 2016 6-7 December 2016 | San Francisco, United States

701 | P a g e 978-1-5090-4171-8/16/$31.00 ©2016 IEEE

Prediction of Energy Consumption in Buildings by System Identification

Darrion Long Department of Computer Science,

Technology and Mathematics

Lincoln University Jefferson City, MO, USA

[email protected]

Nabil Nassif, Ph.D. PE Department of Civil and

Architectural Engineering North Carolina A&T State

University Greensboro, NC

[email protected]

Andrew Scott Ours Department of Mathematics

Capital University Columbus,

Ohio [email protected]

Abstract—This paper presents modeling methodologies for predicting energy consumption using system identification. The models discussed will predict the systems performance using the measured input and output. To test and train the models, data was gathered from an existing building. State space, nonlinear, and polynomials models based mathematical functions and tested with different parameters such are temperature, time, and dew point. The results show that the proposed models can output similar energy results. The developed model can be used for energy assessment and diagnosis.

Keywords—black box modeling; system identification; energy; energy management; buildings; data driven modeling; models

I. INTRODUCTION According to U.S Energy Information Administration

(EIA) [1], today’s building in the U.S. consume 72 percent of electricity produced, and use 55 percent of U.S. natural gas. Of this energy consumed the heating, ventilation, and air conditioning (HVAC) system contributes as the largest percentage of the overall energy usage in a building. If current energy use trends continue, building will become the largest consumer of global energy by 2025. In order to diminish the amount of energy consumed by building, several energy efficient strategies have been explored [2]. The black-box models are developed by measuring the data of the system input and output and fitting a mathematical function to the data. However, the development of black-box models does not require the understanding of system physics and they have high accuracy compared to the physics-based models though they suffer from not being able to form conclusion based on the data [3]. These models, propose that the incorporation of computational approaches along with real time data can help generate optimal control strategies as well as energy saving for system designers [4, 5]. Utilizing the system identification (SID) process, various model structures along with different time delays are investigated to determine the best structure yielding satisfactory accuracy in terms of mean square errors (MSE), root mean square error, and coefficient of variances (COV). The MSE, RMSE, and COV are employed to evaluate the approximating capability of the identification models [6].

The necessary development of energy management tools to prevent wasteful consumption. The use of modeling based on mathematics and computational methods imitating the

energy consumption, can help predict and avoid mismanaged use of energy in short-term analysis.

Using SID, a form of black-box modeling, to handle mathematical models using dry bulb temperatures, dew point, and number of days. The building selected is a commercial- sized building in Greensboro, North Carolina. The results of the SID models are compared to determine the most effective model by using Coefficient of determination (COD), MSE, COV.

II. METHODOLOGY To conduct the proposed study, the following methodology

is used (1) data collection, (2) data analysis and preprocessing, (3) model development, (4) model testing. The data is collected from an existing building and used for the training and testing of the model. The models are developed from using data-driven modeling standards by analyzing trends within the data, and trends found within the data. This modeling based on data and mathematics is known as black box modeling such as system identification where we fit a mathematical equation to the system that is modeled after. The objective of this overall research, as shown in Figure 1, is having a precise mathematical model that predicts energy consumption and how well that prediction fits to the system.

Fig. 1. A schematic of the methodology

FTC 2016 - Future Technologies Conference 2016 6-7 December 2016 | San Francisco, United States

702 | P a g e 978-1-5090-4171-8/16/$31.00 ©2016 IEEE

III. PREPROCESSING AND DATA ANAYLSIS

A. Data Collection The data used for this research came from two sources.

First, the buildings energy consumption that is converging into a spreadsheet by smart meter readings of kilowatts every 15minutes. Then, the weather data that is recording hourly and is in the form of comma separated value (.csv) files, which consist of possible conditions that affect the output of the energy consumption such as time of weather recording, temperature, wind-chill, heat index, dew point, humidity, pressure, visibility, wind direction, wind speed, gust speed, precipitation, events, and conditions from the weather records of a local airport within the area of Greensboro, NC. After collection of hourly data sets for each month, then the data was merged into a single spreadsheet by assembling each of the .csv files together chronologically from March 2014 to May 2016 using command line operations. Hourly data of each month was then inserted into the spreadsheet with the energy consumption data.

B. Preprocessing Now, in the preprocessing phase by duplicating the hourly

weather patterns into every 15minute segments of the hour. This is done by insuring that weather conditions were hourly consistent throughout the day to strengthen the creditability of the data. This is due to trying to reduce the most amount of noise as possible considering the possible main variable as inputs into the black-box modeling being temperature, hour of the day, and dew point. This is evident with data clustered from within the range shown Figures 2, 3, and 4.

Fig. 2. A graph of how the energy consumption changes over time

C. Data Anaylsis The spreadsheet had trends within the data in relation to

the energy consumption which revealed that the variables would be temperature, time of the day, and dew point (moisture within the atmosphere).

Fig. 3. A graph of how the energy consumption corresponds to temperatures

Fig. 4. A graph of how the energy consumption changes of moisture within the atomosphere

IV. MODELING EQUATIONS The data-driven techniques used to process the models

were based on black-box modeling method known as system identification. The purpose of this method, as depicted in Figure 5, was to focus on the measured input signal and measured output signal of the system by modeling it mathematically with equations.

Fig. 5. A schematic of how the system identificaiton method works

FTC 2016 - Future Technologies Conference 2016 6-7 December 2016 | San Francisco, United States

703 | P a g e 978-1-5090-4171-8/16/$31.00 ©2016 IEEE

The mathematical equations that were used for modeling the system were polynomial, nonlinear autoregressive (NLAR), and the state space model. This section will discuss the three model types of model.

A. Polynomial For a system of utilizing one output and multiple inputs,

the continuous-time ARMAX model can return a goodness-of- it to the system based specified polynomial order to determine estimated parameters and covariance. The continuous-time ARMAX model is represented by the following equation: ( ) ( ) = ( ) ( − ) + ( ) ( )

Where A, B, and C are polynomials. y(t) is the output at time t, u(t) is the input, e(t) us the white-noise disturbance value ,and is the number of input samples that occur before the input affects the output.

B. State Space(SS) The continuous-time models are represented by the

following equation: ( ) = ( ) + ( ) + ( ) ( ) = ( ) + ( ) Where A, B, C, D, and K are state-space matrices. u(t) is

the input, y(t) is the output, e(t) is the disturbance and x(t) is a vector based on the order of the estimated model.

C. Nonlinear Autoregressive(NLAR) The nonlinear autoregressive model is represented by the

following equation: ( ) = ( ( − 1), ( − 2), ( − 3), … , ( ), (− 1), ( − 2), .. Where ( − 1), ( − 2), ( − 3), … , ( ), ( −1), ( − 2), .. are delayed input and outputs known as

regressors, ( ) is the prediction of the output as a sum of weight regressors, and is a nonlinear function.

V. BLACK BOX MODELING System Identification is a black box modeling method.

According to Afram [3], the black-box models are developed by measuring the data of the system input and output and fitting a mathematical function to the data. This is also depicted in Figure 6 with the idea of system identification towards this research.

Fig. 6. Example of a black-box model

In regards to this research, the data set of the system

mainly focused on the year of 2014 as there were difficulties of fitting a mathematical model to the year of 2015 and 2016 as the building received upgrades in the Heating, Ventilation, and Air Conditioning (HVAC) system. The year of 2014, prior to the upgrades allow for the data to be fit with a mathematical function without the unknown factors of the upgrades. The different mathematical functions that were available to fit the data were transfer functions, state space models, process models, polynomials models, nonlinear models, spectral models, and correlation models. As stated previously, for the sake of this research the mathematical functions used for fitting the energy consumption data were state space models, polynomials models, and nonlinear models. The data used is divided into two time series sets (1) training set with inputs and outputs, from March 17th to October 17th in the year 2014 and the (2) testing set with inputs and outputs from October 18th to December 31st in the year of 2014. State space, nonlinear, and polynomials models were based on the training set and were validated with the testing set with five polynomial models, five state space models and six nonlinear models with different parameters regarding the inputs and outputs.

The inputs for the black-box models that will be discussed are temperature, hour of the day, and dew point for having the most impact on the output, energy consumption. First, temperature due to the constant change of throughout years that will affect the energy consumption of a building by the use of Heating, Ventilation, and Air Conditioning (HVAC) system for comfort. Second, the hour of the day due the different temperatures throughout the day that affect the use of the HVAC, lighting, and electric appliances. Third, dew point being moisture within the atmosphere would affect the temperature.

VI. RESULTS The 16 models used a function based on probability using

the history of the time series data, training and testing set, to make a prediction of the outputs referred to as the K-step ahead prediction. The K-step ahead prediction method was done by focusing on the measured outputs of the model to see similarities of the system measured output, so a prediction horizon was set to 3 which became a multiple of the data sample-time. This allows for a K step prediction to become a 3 step prediction to give a prediction of the measured output, mean square error (MSE) defined as with the following equation MSE = ∑ (y − y ) , coefficient of variance (C ) defined as C = , and coefficient of determination ( ) defined as = ∑ . The fitting of the mathematical functions brought about the different goodness- of-it measures based on statistical approach using the COV, MSE, and COD. The difference between the training and testing sets shows improvement among the COV, MSE, and COD that is reflected in Figures 7, 8, and 9.

FTC 2016 - Future Technologies Conference 2016 6-7 December 2016 | San Francisco, United States

704 | P a g e 978-1-5090-4171-8/16/$31.00 ©2016 IEEE

Fig. 7. Comparsion of the training and testing data COV results

Fig. 8. Comparsion of the training and testing data MSE results

Fig. 9. R-squared values that determines how well the model fits the system

VII. CONCLUSION The few mathematical models offer excellent feedback

showing that the coefficient of determination had high

percentages around 70% such as ss2, ss3, and nlarx3. While model ss2 has the best result there is still room for improvement to obtain a more accurate model with reduced MSE and higher COV and R-squared value while using K- step prediction method to predict a model’s performance with further predictions to determine if the models can perform long-term analysis rather than short-term analysis.

The findings in the results came to the most efficient model that meets the output of the system while maintaining the least amount of error. The model that shows the most precession is the State Space models, but specifically ss2 with results of an R-squared value of 74.77% with the training data being 0.10075 for COV and 55.454 for MSE. Then, the results of the testing data being 0.1273 for COV and 89.347 for MSE. This is represented within Figure 10 and 11 with a fitting of the model “ss2” against the system with measured inputs (temperature, hours of the through the days, and dew point) and measured output (energy consumption).

Fig. 10. The fitting of state space model “ss2” to the testing data

VIII. FUTURE WORK Additional approaches based on results and conclusion

will be implemented in upcoming revisions of this research that will consist of optimization and further analysis of inputs that affect energy consumption for more defined models. The optimization approach is a method that will be an application of machine learning that will be a autonomous task that to determine the most effective model out of the developed models, and construct a model of best fit that can best match the buildings energy consumption based on analysis of trends in data using polynomials, state space, and nonlinear auto regression. In relation to the previous method mentioned the approach of further analysis of models with fewer inputs that can determine if less inputs such as temperature, dew point, and other weather conditions to allow for accurate results of energy consumption within a building. In addition, the analysis of inputs mentioned will allow for forecasting into the unknown periods of time based on the most effective models predictions based on the known data.

FTC 2016 - Future Technologies Conference 2016 6-7 December 2016 | San Francisco, United States

705 | P a g e 978-1-5090-4171-8/16/$31.00 ©2016 IEEE

Fig. 11. The fitting of state space model “ss2” to the training data

REFERENCES

[1] U.S. Energy Information Adminstration EIA,www.eia.gov [2] ASHARE. 2011. ASHARE Handbook-Applications. Chapter 41.

Atlanta: American Society of Heating Refrigeration and Air Conditioning Engineers.

[3] Afram, A. and Janabi-Sharifi,F. 2015 Black-box Modeling of Residential HVAC System and Comparison of Gray-box and Black- box Modeling Methods. Energy and Buildings 94(1):121-49

[4] Nassif,N. 2014. Modeling and Optimization of HVAC systems using Artifical Neural Network and Genetic Algorithm. International Journal of Building Simulation 7 (3):237.245.

[5] Nassif,N. 2008. Self-Turning Dynamic Models of HVAC System Components. Energy and Buildings 40:1709-1720.

[6] Buford J. N. Nassif. 2016. The Dynamic Modeling of Chilled Water HVAC Systems Using System Identification Methods. 2016 ASHRAE Annual Conference, St Louis, Missouri.

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/HRV (Za stvaranje Adobe PDF dokumenata pogodnih za pouzdani prikaz i ispis poslovnih dokumenata koristite ove postavke. Stvoreni PDF dokumenti mogu se otvoriti Acrobat i Adobe Reader 5.0 i kasnijim verzijama.) /HUN <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> /ITA (Utilizzare queste impostazioni per creare documenti Adobe PDF adatti per visualizzare e stampare documenti aziendali in modo affidabile. I documenti PDF creati possono essere aperti con Acrobat e Adobe Reader 5.0 e versioni successive.) /JPN <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> /KOR <FEFFc7740020c124c815c7440020c0acc6a9d558c5ec0020be44c988b2c8c2a40020bb38c11cb97c0020c548c815c801c73cb85c0020bcf4ace00020c778c1c4d558b2940020b3700020ac00c7a50020c801d569d55c002000410064006f0062006500200050004400460020bb38c11cb97c0020c791c131d569b2c8b2e4002e0020c774b807ac8c0020c791c131b41c00200050004400460020bb38c11cb2940020004100630072006f0062006100740020bc0f002000410064006f00620065002000520065006100640065007200200035002e00300020c774c0c1c5d0c11c0020c5f40020c2180020c788c2b5b2c8b2e4002e> /NLD (Gebruik deze instellingen om Adobe PDF-documenten te maken waarmee zakelijke documenten betrouwbaar kunnen worden weergegeven en afgedrukt. De gemaakte PDF-documenten kunnen worden geopend met Acrobat en Adobe Reader 5.0 en hoger.) /NOR <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> /POL 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<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> /ENU (Use these settings to create Adobe PDF documents suitable for reliable viewing and printing of business documents. Created PDF documents can be opened with Acrobat and Adobe Reader 5.0 and later.) >> >> setdistillerparams << /HWResolution [600 600] /PageSize [612.000 792.000] >> setpagedevice