A practical artificial intelligence-based approach for predictive control in commercial and institutional buildings

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A practical Artificial Intelligence-based approach for predictive control in commercial and institutional buildings N. Cotrufo , E. Saloux , J.M. Hardy , J.A. Candanedo , R. Platon PII: DOI: Reference:

S0378-7788(19)32243-1 https://doi.org/10.1016/j.enbuild.2019.109563 ENB 109563

To appear in:

Energy & Buildings

Received date: Revised date: Accepted date:

23 July 2019 8 October 2019 27 October 2019

Please cite this article as: N. Cotrufo , E. Saloux , J.M. Hardy , J.A. Candanedo , R. Platon , A practical Artificial Intelligence-based approach for predictive control in commercial and institutional buildings, Energy & Buildings (2019), doi: https://doi.org/10.1016/j.enbuild.2019.109563

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A practical Artificial Intelligence-based approach for predictive control in commercial and institutional buildings N. Cotrufoa,1, E. Salouxa, J.M. Hardya, J.A. Candanedoa and R. Platona

a

1

CanmetENERGY, Natural Resources Canada, Varennes, Québec, Canada

Corresponding author: e-mail [email protected]

ABSTRACT This paper presents a methodology for the development and implementation of Model Predictive Control (MPC) in institutional buildings. This methodology relies on Artificial Intelligence (AI) for model development. An appropriate control-oriented model is a critical component in MPC; model development is no easy task, and it often requires significant technical expertise, effort and time, along with a substantial amount of information. AI techniques enable rapid development and calibration of models using a limited amount of information (i.e. measurements of few variables) while achieving relatively high accuracy. In this study, the MPC algorithm targets the reduction of natural gas consumption by optimizing the transition between night setback and daytime indoor air set-point values as a function of the expected weather. This MPC strategy was implemented in an institutional building in Varennes (QC), Canada, during the heating season 2018-19. A significantly better performance was achieved when compared with “business as usual” control strategies: the natural gas consumption and greenhouse gas (GHG) emissions were reduced by approximately 22%, and the building heating demand by 4.3%. The proposed strategy is scalable and can be replicated in other buildings.

Nomenclature ANN

Feedforward Artificial Neural Network

DT

Decision Tree

E[]

Expected value from the Gauss Process Regression model

EBL

Building Electric Baseload, (kW)

EDM

Building Electric Demand Margin, (kW)

GPR

Gauss Process Regression

HD

Building Heating Demand, (kW)

KWlim

Building electric demand limit, set at 230 kW

NG

Building Natural Gas demand, (kW)

OAT

Outdoor Air Temperature, (℃)

RF

Random Forest

SVM

Support Vector Machine

Tsp

Indoor air temperature set-point, (℃)

X

Model inputs dataset

Y

model output vector

k()

Kernel function used by the Gauss Process Regression model

m()

Mean function used by the Gauss Process Regression model

t

Time, (hourly time steps are used in this study, t = 3,600s)

u

Vector of inputs to the Gauss Process Regression model

Greek letters ΔTsp

Indoor air temperature set-point variation between two consecutive time steps, (℃)

1. INTRODUCTION Buildings often perform below expected energy efficiency levels; it has been estimated that building operation improvements could lead to energy savings as high as 30% [1]. Significant opportunities to reduce building operational costs and resources deployment may thus be reached through advanced control strategies [2]. Among these, MPC is a promising approach. MPC uses a model of the system, along with forecasts of the disturbances (i.e. weather, occupancy, etc.) to predict the future building thermal behavior and select an optimal set of actions (for example, set-point profiles, energy storage charging/discharging steps, operation of pumps and fans, etc.). These control actions target the minimization of a cost function (i.e. total energy consumption, peak demand, utility bill, etc.), within a set of constraints. Typically, the model used in MPC is a control-oriented model, i.e., a model that is accurate enough for decision-making for a specific goal, but simple enough to be easily developed and incorporated in further calculations. In the 1980s and 1990s, research efforts were carried out in the area of optimal building operation [3-7]. Over the last decade, MPC – to some extent an offshoot of these earlier studies – has emerged as a very active research area in building engineering [8-11]. Given the flexible and general nature of the MPC basic principle, it may be applied at different scales and for many diverse purposes. For instance, studies on MPC for buildings have included: 

Optimal control of district heating and cooling systems [12, 13].



Management of ice banks for cooling applications [14, 15].



Provision of ancillary services (e.g. voltage and frequency regulation) to the grid [16-18].



Control of radiant heating and cooling systems [19, 20].



Short-term office temperature control [21-23].



Demand response schemes [24, 25].

An exhaustive review of the vast number of publications on MPC in buildings is beyond the scope of this paper. Nevertheless, it is worth pointing out that field implementations remain rare. MPC studies consistently report significantly better performance than traditional control strategies. However, there are hurdles for the widespread adoption of MPC. Arguably, the most important one is the lack of a method for rapid development of control-oriented models [26-28]. Today, each building needs developing a customized model; model development is a step which requires time, technical expertise, and often information which might be difficult to obtain (such as details on the construction of the building, mechanical system layout, etc.). Although AI has emerged in the last decade as a powerful tool in diverse fields (e.g. medical diagnosis, genetics, transportation, etc.), its application in building control is still in its early stages. Nevertheless, numerous exploratory research papers have been published in this area. A review paper by Afram et al. [29] discusses several applications of AI in building operation, including MPC. For instance, machine learning methods have been applied for the determination of simplified control rules [30]. AI techniques offer new opportunities for the rapid development of models for control applications. The calibration of purely physically-based models (“white-box” models) is quite challenging. A recent study [31] focuses on the calibration of an EnergyPlus model; a key challenge in this case is the determination of the capacitance zone multiplier (CZM). This parameter – essential to characterize the thermal dynamics of a space – is difficult to estimate a priori. Conversely, the use of AI techniques to create data-driven grey-box and black-box models offers an alternative and promising pathway for the development of models.

Over the last decade, efforts have been made to facilitate the creation of “grey-box” loworder Resistance-Capacitance (RC) based thermal networks, where equivalent or effective RC parameters are identified. Several methodologies and tools have been proposed [32-35] for this purpose. While low-order RC models preserve a certain physical insight, the structure of the circuit is more rigid than that of black-box approaches. There are numerous examples of the application of AI for load prediction [36]. However, the field implementation of these techniques in a control scheme is less common. Li and Wen [2] discuss models used in control applications, such as autoregressive models with exogenous inputs (ARX) for short-term predictions (of a few hours) [37, 38], and Artificial Neural Network (ANN) for longer-term cooling load prediction [39]. More recently, Deep Learning algorithms (an extension of the concept of ANN) were applied to predict the cooling load of an 11,000-m2 building over the next 24 h [40]. Deep Learning outperformed six other AI methods: multi-linear regression (MLR), elastic net (ELN), random forests (RF), gradient boosting machines (GBM), support vector regression (SVR), extreme gradient boosting trees (XGB). This study presents a general methodology, based on Artificial Intelligence (AI) techniques, to facilitate the development of MPC strategy. Machine learning models are applied within a multiple-model architecture intended to capture the energy behaviour of buildings with more than one energy source. Such a configuration is common, for instance, in the Province of Québec, Canada, where it is not rare to use both electricity and natural gas to supply the heating needs of commercial and institutional buildings. The development of machine learning techniques requires less time and technical expertise than white-box and hybrid (grey-box) models and optimization algorithms. Furthermore, the proposed strategy needs only a limited amount of information from the Building Automation System (BAS).

The paper is organized as follows: firstly, the case study building is described. The proposed AI-based methodology is then addressed by presenting the development of the controloriented model and the MPC optimization problem. The developed MPC strategy is implemented in the real building, and results are presented in terms of energy savings and GHG emission reduction as well as thermal comfort and operation trends. Finally, potential replicability of such an approach is discussed.

2. CASE STUDY The CanmetENERGY Centre, located in Varennes (Québec, Canada) was considered as case study. This is a single-storey building hosting around 120 workstations and 10 meeting rooms. The building heating needs are fulfilled by an electric boiler with a nominal power of 200 kW and two 470-kW natural gas boilers. When heating is required, the electric boiler starts first. The natural gas boilers are turned on only when the heating load exceeds the power provided by the electric boiler. In Québec electricity has a competitive price compared to natural gas. Furthermore, electricity in Québec is produced by hydroelectric plants, and thus has a low associated GHG factor. The local utility company applies charges to both the electric energy (kWh) and the power (monthly peak demand, kW). Thus, in order to reduce the peak demand charge component, the building operators set a limit on the electric power at 230 kW. Therefore, a trade-off on the use of electricity and natural gas is required to limit operation costs while limiting GHG emissions. The limit on the electric power supplied by the grid, which is set by the building operators, includes both the electric boiler and the electric baseload (e.g. workstations, lighting, appliances, etc.). The electric baseload is mainly due to occupancy, and it thus has the priority.

The electric boiler power is dynamically adjusted in order to remain within the electric demand margin, i.e. the difference between the 230 kW limit and the baseload power (Figure 1). When the electric power limit is reached, the electric boiler cannot provide more hearing. Therefore, the gas boilers are started to provide the portion of heating load not supplied by the electric boiler. The strategy described above to limit electric peak demand is given by Eqs1 and 2. EDM = KWlim – EBL

(1)

NG = HD – EDM

(2)

where EDM is the Electric Demand Margin; KWlim is the electric demand limit (set at 230 kW by the building operators); EBL is the building Electric Baseload; NG stands for Natural Gas; and HD is the building Heating Demand. A typical electric baseload profile is shown in Figure 1 for a week in January 2018. During the night of January 22 th the electric baseload was about 60 kW. In such conditions the electric boiler power should not exceed 170 kW (i.e. 230 kW minus 60 kW) at night; likewise, the electric boiler should not be used at all when the baseload reaches the 230 kW power limit.

Figure 1: Building electric baseload for a typical week in January 2018.

Figure 2 shows building power profiles – including building electric demand, electric boiler power and natural gas boiler power demand – for two consecutive days in January 2018. It can be seen that the natural gas boilers are turned on when the building electric demand (electric boiler + electric baseload) reaches the 230 kW limit value and there is no margin left to increase the electric boiler power input. During the night, the total electric demand is far below the electrical power limit; thus, the electric boiler has enough electric power margin to fulfill the heating load, without the need to start the gas boiler.

Figure 2: Building power profiles for two consecutive days in January 2018. The CanmetENERGY building is divided into four main Sections, served by four different secondary loops from the central plant. Although the activities hosted in the four Sections are similar, the indoor air set-point profiles differ slightly from one Section to another. This is the result of the monitoring and maintenance effort of building operators, who continuously adjust the system operation, aiming at maximizing occupant thermal comfort and

building energy efficiency. Since the occupancy pattern was approximately the same for all Sections, only one average indoor air temperature and one average indoor air temperature setpoint were considered for the whole building (Figure 3). These average values have been derived by weighting temperatures from each Section with their corresponding floor surface area.

(a)

(b) Figure 3: (a) Indoor air temperature set-point, and (b) indoor air temperature: Sections and weighted average values for a typical week in January 2018.

Building operation measurements (e.g. temperature, flow rate, power, etc.) are controlled by a BAS that collects measurements of operational variables at 10 minutes intervals. On a typical workday, the average indoor air temperature set-point is kept at 23.0℃ during working hours (i.e. from 7:00 to 17:30), while a night set-back of 19.6 °C is applied from 17:30 to 7:00 to reduce energy use (Jan 18th-19th in Figure 3-a). In this paper, this “conventional” control strategy is called Business As Usual (BAU).

3. METHODOLOGY This Section presents the development of the AI-based control-oriented model, and defines the MPC optimization problem. This is followed by a discussion on the MPC routine in the building and the strategy to assess energy savings.

3.1 The control-oriented model A multi-model architecture is used for modelling buildings with more than one energy source. Models at each node predict specific features of the building load (i.e. the total load, the portion of load fulfilled by a given equipment, the effect of occupancy on the heating/cooling load, etc.). The multi-model architecture should enable accounting for interdependency among loads, and for any energy sources limit and usage priority (i.e. control rules from Eqs. 1 and 2). For the considered case study, a three-model architecture was considered (Figure 4). This includes prediction models of i) the heating demand, ii) the electrical baseload, and iii) the natural gas consumption (Eqs. 3-5). Once the models are individually trained with historical operation data, the three-model architecture is expected to reproduce the building operation given by Eqs. 1 and 2, which estimate the natural gas consumption from the heating demand and the electric

baseload. The inputs used to predict the heating demand (Eq. 3) and the electric baseload (Eq. 4) were selected based on a correlation analysis and thermodynamic considerations. =

(

) = =

Where

,

, and

( (

) )

(3) (4) (5)

are the machine learning models developed to predict the heating

demand, the electric baseload and the natural gas consumption, respectively. The heating demand (red module in Figure 4) is predicted from the outdoor air temperature (OAT) at current and previous time step, the indoor air set-point (Tsp), and the indoor air set-point variation at consecutive time steps (ΔTsp) (Eq. 3). Using the OAT at the previous time step and the set-point variation from the previous time step as model inputs, allow accounting for the thermal mass and the thermal behavior of the building. No strong correlation was found between the building heating load and the solar radiation; therefore, solar radiation was not included among the inputs for this model. The indoor air temperature set-point (Tsp) has been used as control variable, and thus included among the model inputs. On the other hand, the indoor air temperature profile over the prediction horizon is unknown. Since for the considered case study the indoor air temperature follows the set-point value quite closely (effective heating system and low thermal inertia), T sp and ΔTsp remain good approximations of actual indoor air temperature and temperature variation. Furthermore, thermal comfort was guaranteed by following a conservative approach based on ramps, anticipating the transition from night setback to daytime set-point (Sections 3.2 and 4.3). The electric baseload (green module in Figure 4) is predicted using the outdoor temperature and the hour of the day at the same time t. The models from Eqs. 3 and 4 were developed using average hourly values. The control rule from Eqs. 1 and 2 was set for values collected every 10 minutes, and thus cannot be directly

used with the hourly values predicted by models from Eqs. 3 and 4. Therefore, a third model (blue module in Figure 4) was trained to predict hourly values of the natural gas consumption from the predicted building heating load (HD) and electrical baseload (EBL) at the same time t. Through Eq. 1, EBL is linearly correlated with the electric demand margin (EDM), which is used in Eq. 2 to derive the consumption of natural gas. Therefore, the prediction model from Eq. 5 reproduces this rule, predicting the hourly consumption of natural gas from the total heating load (HL) and the electrical baseload (EBL).

Figure 4: Schematic of the proposed data-driven three-model architecture. Five machine learning techniques were considered for the development of models: i) Artificial Neural Networks (ANN), ii) Gauss Process Regressions with squared exponential Kernel function (GPR), iii) Support Vector Machines (SVM), iv) Decision Trees (DT), and v) Random Forests (RF). The selection of one of those five techniques was based on the analysis of models accuracy. Using statistical indices, such as the Root Mean Squared Error (RMSE), models predictions were compared to historical measurements from the building plant. Results from Section 4.1 proved that GPR models were the most accurate ones for the considered case study building, and were thus used for the development of a control-oriented model. Applying the proposed methodology to a different building will require the re-evaluation of the accuracy of

models based on techniques listed above, and the selection of the most accurate ones for the new case study. In the last years, Gaussian Process (GP) modelling techniques raised interest on topics such as building modeling [41, 42] and advanced control [43]. The capability of GPs to capture complex nonlinear and multivariate interactions among building and environment variables was leveraged by [42] to perform measurements and verification of savings after energy efficiency measures. In [41] GPs were developed to predict the day-ahead profile of the indoor air temperature within a single thermal zone by using different combinations of regressors, such as outdoor air temperature, solar gains, hour of the day, and zone temperature. The GP-based models developed in [41] proved to be more accurate than traditional Resistance-Capacitance models (e.g. 3R3C). However, grey-box models require shorter datasets and less information compared to GPs to be calibrated. Furthermore, Jain et al. [43] developed a GP-based controloriented model for energy consumption prediction of large buildings, and proved its effectiveness within an advanced control strategy aiming at shaving peak demand over several hours. Jain et al. [43] highlighted the importance of informative content within datasets for model learning, and presented a procedure to select the relevant information for model update. GPR is a non-parametric modelling technique that relies on a stochastic process which determines Gaussian probability distributions for random subsets of input variables. Every random subset of variables have a joint Gaussian distribution [41]. GPR models provides a distribution that contains both the mean value and its confidence interval rather than a specific point estimate [42]. In such a process, a mean function m(u) (Eq. 6) and a covariance (Kernel) function k(u,uˈ) (Eq. 7) must be specified to properly consider the interdependence between variables. From two input sets (u and uˈ), the covariance function defines the degree of

correlation between the outputs of the two input sets [41]. The GPR output is finally given by Eq. 8 [41]. m(u) = E[

]

k(u,uˈ) = E[ Y= where E[

(6) ]

(7) (8)

[

]

] is the expected value of a certain system

, Xtrain and Ytrain are the inputs and

output with which the GPR model has been trained, I is an identity matrix, and

the output

noise’s variance.

3.2 The optimization problem The objective of the proposed MPC is the reduction of natural gas consumption in the building. As described in Section 2, the gas boilers start when the electric demand margin does not suffice to fulfill the building heating demand. Under the BAU control strategy this is likely to occur in the morning, when the indoor temperature set-point rises from 19.6°C to 23.0°C, which causes a peak in the heating demand. At the same time of the day, the electric baseload increases as well because of occupancy, thus reducing the electric demand margin available to feed the electric boiler. Therefore, the optimization strategy consists of using pre-defined set-point profiles designed to shift the building heating load to hours of the day when the electric demand margin is larger. For each of the pre-defined set-point profiles the model runs a simulation using forecast weather data to estimate the associated natural gas consumption over the next 24 hours (Eqs. 9). The set-point yielding the lowest natural gas consumption is selected as the optimal control

strategy for the next 24 hours. Equations 9 and 10 describe the set-point selection problem to be solved by the MPC algorithm. ∫ = min(

(9)

dt )

(10)

where i is the index of the pre-defined set-point profiles; f3-M stands for the ensemble of the three control-oriented models (Figure 4 and Eqs. 3-5); h is the prediction horizon, h = 24 hours; NG(i) is the natural gas consumption over one day using the i-set-point profile; k is the index of the setpoint profile identified as optimal control. Several pre-defined set-point profiles with different ramps were considered (Figure 5). The use of ramps allows to gradually heat the building over several hours at night, instead of keeping it cold (night set-back value) until 7:00 (BAU). A gradual, smooth transition from the night set-back to the day-time temperature value can shave the heating peak demand in the early morning (Figure 2). As a result, the portion of heat demand provided by the gas boilers is expected to decrease, while the increase in the heating demand at night can be fulfilled by the electric boiler. The use of pre-defined set-point ramps is also beneficial for occupant’s thermal comfort, as the use of ramps at night would rise the temperature gradually from the night set-back to the daytime value. The impact of MPC on thermal comfort was evaluated in terms of indoor air temperature at 7:00 and 8:00 in the morning. Results are presented in Section 4.3.

Figure 5: Several pre-defined set-point profiles used to reduce natural gas consumption.

3.3 MPC routine Once GPR prediction models were developed, and the set-point profiles were pre-defined, the MPC routine targeting the minimization of the natural gas consumption could be implemented. The MPC routine consists of the following steps: 1- Weather forecasts with a prediction horizon of 24 hours are retrieved before 18:00; 2- Weather forecasts are used along with the control-oriented model to estimate the building heating demand, the electric baseload and the natural gas consumption from 18:00 to 18:00 the next day for all the considered pre-defined set-point profiles; 3- The set-point profile achieving the lowest natural gas consumption is identified as “optimal control strategy” and sent to the BAS; 4- From 18:00 to 18:00 the next day, the building is operated under the identified optimal control set-point. The state of the building thermal mass at the beginning of the optimization horizon (18:00) is considered to be the same every day. This is possible because each day, during the 11 hours before 18:00 (from 7:00 to 18:00), the building set-point is kept constant at 23.0℃.The thermal

state of the building is then taken into account by the prediction AI-based model that predict the building energy consumption using information on future disturbances. The MPC routine was written in MATLAB®, and automatically run every day. Weather forecasts were retrieved using CanMETEO® [45, 46], a free software tool developed by Natural Resources Canada.

3.4 Assessment of energy savings In order to assess the energy savings from the MPC implementation, benchmarking models of the building loads (heating load and natural gas) under BAU control were developed. These benchmarking models predict the daily natural gas consumption and heating load using the daily average outdoor air temperature as an input. Historical data from three previous heating seasons (2015-18) were used for model development. Several statistical modelling techniques, such as linear regression, ANN, GPR, and SVM, were considered for benchmarking. Finally, a GPR model with a Matérn kernel function with a coefficient of 3/2 was used to benchmark the natural gas consumption; a simple linear regression model was found to be accurate enough for the building heating demand. Details on the development of these models are given in Annex 1. An economic and environmental assessment of the savings was performed and presented in the next Section. Electricity and natural gas prices were assumed to be 0.049 CAD$/kWh and 0.051 CAD$/kWh, respectively. Energy price values were derived from utility bills from the implementation period in winter 2019. They refer to the cost of delivered energy; costs related to peak demand charge were not considered in this study (the pre-set demand limit is intended to target this issue). In terms of GHG emissions in Québec, values of 0.00036 t CO2eq/GJ and 0.0507 t CO2eq/GJ were used for electricity and natural gas, respectively.

4. RESULTS This Section presents the results from control-oriented model development and MPC implementation. Also, the impact of MPC on thermal comfort is discussed, and trends in building operation are highlighted.

4.1 Model development The five considered machine learning techniques were applied to develop models of the three building loads used within the three-model architecture: the heating load, the electric baseload, and the natural gas consumption. Hourly measurements from October 1 st, 2017 to March 31st, 2018 were used for model learning. The dataset was randomly divided into two non-stratified sub-datasets: 50% of the dataset was used for training, while the remaining 50% was kept for validation purposes. The performance of models was assessed by comparing model predictions with BAS measurements. The accuracy was evaluated in terms of Root Mean Square Error (RMSE). Table 1 shows the results from each of the three prediction models for both training and validation periods. Figure 6 illustrates, over one week in January 2018, the goodness of fit of the three prediction models developed using Gaussian Process Regressions, for (a) the building heating demand, (b) the electrical baseload, and (c) the natural gas consumption.

Table 1 – RMSE of the control-oriented models developed with five AI techniques. Heating demand

Electric baseload

Gas boiler power

(kW)

(kW)

(kW)

AI technique train

val

train

val

train

val

ANN

30.1

32.6

13.1

13.2

10.1

10.4

GPR

24.3

32.1

9.5

13.1

3.3

11.2

SVM

30.2

33.9

14.7

13.9

10.2

11.7

DT

27.6

34.3

12.3

13.9

8.3

12.2

RF

22.3

32.7

21.4

21.9

8.5

12.1

(a)

(b)

(c) Figure 6: Prediction models over one week in January 2018: (a) heating load, (b) electrical baseload, and (c) natural gas consumption.

4.2 Energy savings and GHG emission reduction The MPC strategy was implemented in the building during ten weeks in the 2019 winter (Jan 15th – Mar 31st). The performance of the MPC strategy was evaluated in terms of daily gas consumption by comparing measured values with those that would be expected with the BAU strategy. The daily consumption of natural gas registered under MPC control (Jan 15th – Mar 31st 2019) was compared to the values expected by the benchmarking model (which predicts the consumption under the BAU scenario). From Figure 7-a, it appears that most of the daily average measurements under the MPC strategy are below the benchmarking model, which means that, for the same average outdoor temperature, MPC led to a lower consumption of natural gas compared to the BAU strategy. Table 2 summarizes the estimated savings over the period Jan 15th – March 31st. Although the objective function of the proposed approach is the reduction of natural gas consumption (MWh) and the total GHG emissions (t CO2eq), the total energy cost ($) is reported as well, in order to

assess the economic viability of the implemented strategy. The measured natural gas consumption (48.2 MWh) was 22.2% lower than the benchmark model (BAU control, 61.9 MWh), which corresponds to a reduction of GHG emissions of 2.5 t of CO2eq (21.9% reduction). Moreover, the building heating demand observed under MPC (147.5.0 MWh) is 4.3% lower than what would be expected under the BAU scenario (154.1 MWh) (Figure 7-b). In conclusion, the proposed MPC, reduced the natural gas consumption and the associated GHG emissions, without increasing the total building heating demand. Since the MPC aims at using the electric boiler instead of the gas boilers, higher electric consumption was expected. Results show an increase of 7.7% compared to BAU control.

(a)

(b) Figure 7: Results from MPC implementation: (a) natural gas boiler consumption, and (b) building heating demand. It is worth highlighting that the daily natural gas consumption was used as the cost function in this study (Eqs. 10), without applying any other constraints to the building heating demand. Under these conditions, it is possible for the daily building heating demand to occasionally exceed the BAU heating demand (Figure 7-b). In the future, in order to guarantee the MPC cost-effectiveness, additional constraints could be included in the MPC routine (e.g. the electric energy consumption, the heating demand or the energy bill). Table 2: Building performance under MPC and BAU operation with an estimation of savings. Variable

BAU

MPC

Savings

Building heating demand

154.1 MWh

147.5 MWh

4.3 %

Electric boiler consumption

92.2 MWh

99.3 MWh

- 7.7 %

Natural gas boiler consumption

61.9 MWh

48.2 MWh

22.2 %

Total energy cost

6,178 $

6,183 $

+ 0.1 %

GHG emissions

11.4 t CO2eq

8.9 t CO2eq

21.9 %

4.3 Thermal comfort The use of ramps is a conservative approach with respect to the thermal comfort of the occupants. Sudden variations of the set-point profile (typical of BAU control) require the heating system to raise the indoor air temperature by several degrees in a short period of time. Since increasing the indoor temperature implies a certain delay, some thermal discomfort is to be expected (i.e. indoor air temperature colder than the daytime set-point value of 23.0 ℃). In contrast, a set-point gradual variation by using ramps would not only reduce the building power demand at 7:00, but it would also help guarantee that thermal comfort is achieved by that time. In summary, the use of ramps is not expected to compromise the level of thermal comfort

provided by BAU; ramps would provide at least the same thermal comfort level of the BAU control or even improve it. The thermal comfort level under MPC was evaluated for the entire period of the strategy implementation (Jan 15th – Mar 31st, 2019). Measurements from a previous heating season (Oct 1st 2017– Apr 30th 2018) were used to assess thermal comfort under BAU control. Figure 8 shows results for each of the four building Sections. The curves in the figure show the occurrence of the minimum value of the indoor air temperature at 7:00 am and 8:00 am, i.e. the number of times, as a percentage, when the indoor air temperature is equal to or higher than the corresponding temperature value on the y axis. For example, during the heating season 2017-18 the indoor temperature in Section 3 at 7:00 was higher than 21.0℃ for about 80% of the time (top-left of the figure). When comparing BAU (top-left) and MPC (top-right) conditions at 7:00, indoor air temperatures for Sections 2 and 3 are closer to the daytime set-point when the building is controlled with MPC. At 8:00, MPC (bottom-right) appears to significantly improve the air temperature conditions in Section 3 when compared to the BAU control (bottom-left): the indoor air temperature was higher than 22.0℃ 70% of the time under BAU while this percentage raised up to 100% under MPC. Under MPC the air temperature from the other Sections at 8:00 was higher than 22.0℃ for at least 80% of the time. In general, the implementation of MPC did not compromise the thermal comfort provided with BAU control and in some cases, MPC even provided better indoor conditions than BAU.

Figure 8: Analysis of the indoor air temperature under BAU in 2017-18 (left) and MPC in 2019 (right), operation at 7:00 (top) and 8:00 (bottom).

4.4 Operation trends The optimal set-point profiles recorded during the MPC implementation period, and the corresponding outdoor temperature and natural gas consumption were analyzed in order to identify patterns and operation trends. During the MPC implementation in winter 2019, it was observed that lower average outdoor air temperatures correspond to steeper set-point transition slopes between night and daytime conditions (higher ramp number from Figure 5). On the other hand, when the outdoor temperatures were near or above 0.0°C, the selected set-point ramp was flat at night (no night set-back) or nearly flat (ramps #1-4 from Figure 5).

A coarse decision tree was calibrated with the results obtained along the MPC implementation period (Jan. 15th – March 31st, 2019), to highlight the building operation trends under predictive control (Figure 9). The decision tree from Figure 9 identifies sub-groups of similar set-point profiles (similar slope) as function of the daily average outdoor air temperature. Two nodes, corresponding to two critical-temperature values were identified. 

For average outdoor air temperatures lower than -5.4°C, ramp #20 was selected by the MPC routine. Ramp #20 has a night set-back value of 19.6°C, and it starts only two hour before occupancy starts.



For average OAT higher that -5.4°C, a second node was identified at -3.7°C. When the average predicted OAT was below -3.7°C (but still above -5.4°C), the MPC routine selected ramps between #11 and #14, which are ramps with a night set-back value of 19.6°C and duration between eight and eleven hours. When the average OAT was above -3.7°C, ramps between #1 and #4 were selected. Those are flat or nearly flat ramps, with a night set-back value higher than 21.6°C and twelve hours duration.

Figure 9 – Decision three from MPC implementation: optimal set-point profile as function of the average outdoor air temperature. The observed trend was studied by running the control-oriented models with weather data corresponding to two different days of the MPC implementation period: a) a colder day (-10.5℃ daily average OAT), and b) a warmer day (2.7℃ daily average OAT). Two profiles were tested on both days: i) a set-point with a very steep transition from the night set-back and daytime value, and ii) a nearly flat set-point. In the case of the colder day (-10.5°C), simulations showed that when the outdoor air temperature is very low, it is necessary to burn natural gas at night, and it is thus beneficial to maintain lower night set-back value to avoid excessive consumption (Figure 10). The sudden expenditure of natural gas consumption resulting from the abrupt set-point variation (peak load in the morning) is still expected to be smaller than the gas saved at night by lowering the setpoint. Conversely, on a warmer day (2.7℃ daily average OAT), an almost flat set-point allows

shifting the building heating load from the morning to the night, when the electric boiler suffices to supply it because the electric demand margin is larger (Figure 11). Although the conclusions on the building thermal dynamics presented in this paragraph can be used for the development of predictive, rule-base control strategies, they cannot be generalized to other buildings, for which a dedicated modelling and simulation analysis should be carried out.

(a)

(b) Figure 10: Natural gas consumption during a cold winter day (daily average OAT of -10.5℃) in January 2018 with: (a) a sudden change of the set-point value; (b) a smooth ramp.

(a)

(b) Figure 11 – Natural gas consumption during a warm winter day (daily average OAT of 2.7°C) in January 2018 with: (a) a sudden change of the set-point value; (b) a smooth ramp.

5. DISCUSSION The development of control-oriented models for MPC applications using AI techniques (along with a judicious selection of inputs), requires less time, information, and technical expertise than an approach based on detailed white-box or grey-box models (such as RC models). Using a multi-model architecture enables to easily arrange building operation, considering different energy sources and accounting for their simultaneous utilization. The multi-

model approach proposed in this paper can be used to model buildings whose heating systems are based on several energy sources, or in which specific constraints are applied to a particular energy source (e.g. electric power limit). The models were calibrated and the strategy was developed using measurement data from a few variables: power input to electric and natural gas boilers, building electric consumption, indoor air temperature and indoor air temperature set-point, outdoor air temperature. Although the calibration of models based on machine learning generally requires more observations than grey-box models, it can be done with fewer variables. Measurements of these variables are commonly available from the BAS, or can be derived from other monitored variables. A judicious selection of models inputs is a crucial step for the proper development of control-oriented models. In order to be considered “control-oriented”, a model should allow to investigate the effect of the controlled variable (in this study the indoor air set-point) on the parameter to be optimized (in this study the natural gas consumption). Thus, the controlled variable must be included among the model inputs. Furthermore, the inputs of the model should include information on the past demand history and/or thermal behavior of the building through time (e.g. set-point variation or outdoor air temperature at previous time steps). Herein lies an important advantage of using machine learning models as compared to white-box and grey-box models: as long as information on the building thermal behaviour is properly provided through data, the calibration process of the machine learning technique will attempt to identify the hidden patterns between these data and the controlled variable (e.g. the indoor air set-point profile). In contrast, white-box and grey-box modelling techniques need an explicit formulation of the thermodynamic phenomena which characterize the building behavior.

Once the building model is properly developed, a set of set-point profiles can be defined along with an objective function (i.e. natural gas, peak demand, total energy, etc.). Since this objective function can be customized, MPC strategies can be tailored for other energy markets. For instance, where Time-Of-Use energy rate structures are used (e.g. in Ontario, Canada), the MPC objective function may target the reduction of the energy bill, moving the load from hours of the day in which an high price is applied to energy, to hours in which the energy price is lower. Overall, this approach aims to provide a general methodology for load management in commercial and institutional buildings, thus facilitating replicability in other buildings. This is a first step towards the development of practical solutions for MPC strategies targeting optimal energy management of integrated energy systems – including among others boilers, chillers, heat pumps using various sources, photovoltaic panels, connection with district heating and cooling as well as energy storage devices of different nature – in buildings and communities. The presented methodology includes the selection of an appropriate AI technique and the training of the prediction model using operational data from the building case. A new model should be trained for each new building application. On the other hand, the considered predefined set-point profiles could be applied to the majority of commercial and institutional buildings, as these buildings are usually occupied during the same period of the day, from 7:00 to 17:00, while thermal comfort could be guaranteed with pre-defined ramps.

6. CONCLUSIONS A novel approach for the development and implementation of MPC in buildings was presented. The development of a control-oriented model is a crucial step in predictive control strategies. To

this end, AI techniques and a multi-model architecture were used to model an institutional building. The MPC strategy was implemented in an institutional building in Varennes, Québec, from January 15th to March 31st, 2019. Results revealed that MPC achieved a 22.2% reduction of natural gas consumption (2.5 tons of equivalent CO2 avoided) and a 4.3% reduction in building heating demand. The proposed AI-based approach allows for the development of MPC strategies that reduce the required amount of time and information, as well as technical expertise, compared to detailed first-principle based and grey-box models, while still remaining easily replicable on a large portfolio of buildings. Furthermore, MPC improved occupant’s thermal comfort by gradually increasing the indoor temperature during night, rather than applying abrupt set-point variations just before occupancy starts. AI-based MPC can effectively support the widespread adoption of advanced control strategies in buildings. Further improvements of the MPC strategy developed and presented in this paper will include the integration of constraints on the building heating demand within the MPC routine objective function and additional indoor set-point profiles to be considered when targeting optimal control.

AUTHOR DECLARATION None. Acknowledgments The financial support of Natural Resources Canada through the Office of Energy Research and Development (OERD) is gratefully acknowledged. The authors would also like to thank Mudasir Ahmed from CanmetENERGY for his technical assistance to implement the MPC strategy.

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5th International High

ANNEX 1: ENERGY SIGNATURE MODELS The accuracy of energy signature models was assessed by using the RMSE for both training and validation periods. Results are shown in Table A-1. Table A1: RMSE of the energy signature models based on the five AI techniques. Modelling

Heating demand

Gas boiler consumption

(MWh)

(MWh)

technique train

val

train

val

Linear regression

0.272

0.260

-

-

ANN

0.258

0.258

0.229

0.288

GPR

0.269

0.255

0.241

0.283

SVM

0.273

0.259

0.242

0.283

DT

0.241

0.271

0.233

0.304

RF

0.228

0.270

0.209

0.304

As shown in Table A1, GPR was the best candidate for natural gas benchmarking (Figure A1-a), while linear regression was accurate enough for modelling the daily average building heating demand (Figure A1-b).

(a)

(b) Figure A1: Building energy signature for: (a) natural gas boiler consumption and (b) heating demand.

ANNEX 2: STATISTICAL ANALYSIS OF RESULTS The 22.2% savings of natural gas were estimated by comparing the measured daily natural gas consumption under MPC with the GPR-based energy signature model developed using historical data collected when the building was operated under BAU. A statistical analysis of those results is here provided. GPR are probabilistic models, whose predictions come in the form of probability intervals. For practical purposes, usually the mean value of the probability interval is taken as the predicted value. In other words, the distribution of predicted probability is characterized by a mean value (prediction) and an associated prediction interval that follows a Gaussian distribution. By considering a 95% prediction interval, four regions (a, b, c, d) can be identified across the model prediction (Figure A2), each one with its associated probability distribution (Figure A2). The daily average natural gas consumption under MPC was plotted in Figure A2 (dots), and the distribution of those values across the four regions is given in Table A2. Percentage values in Table A2 indicate that the relocation of the dots (MPC operation) below the energy signature model (BAU operation) is statistically relevant and that the new distribution of MPC operation dots is a different event with respect to historical data used to develop the energy signature model. These results prove that the MPC strategy had a tangible impact on the building operation, and its effect was the reduction of the NG consumption compared to the previous heating seasons.

Figure A2: Distribution of the daily average NG consumption under MPC (dots) against the energy signature model (blue line) and its 95% confidence interval (dot black lines).

Table A2: Distribution of the probability distribution across the four regions for energy signature predictions (Gaussian distribution) and measured daily average gas consumption under MPC. a

b

c

d

Energy signature (BAU)

2.5%

45.0%

45.0%

2.5%

MPC

23.5%

66.7%

7.8%

2.0%