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Control-Oriented Modeling of an Air-Based Electric Thermal Energy Storage Device.

INTRODUCTION

The main objective of this paper is to develop a simple model for an electric thermal storage (ETS) device, a particular kind of thermal energy storage (TES) system. The model is intended to be used in model-based control applications. One of the distinctive characteristics of Quebec's load from residential and commercial buildings is the large penetration of electrical heating (e.g., electric baseboards), largely a result of low electricity prices made possible by hydroelectric power generation (Hydro-Quebec, 2016). As electricity is frequently used for space heating, electrical thermal storage is an attractive technology in Quebec and elsewhere in Canada.

ETS systems can consume electrical power and store heat during low electricity price period (or when demand on the grid is low) and provide heat to the building during peak demand periods (Moffet, Sirois, Joos, & Moreau, 2012). They do not reduce the total energy consumption, but can provide a significant reduction of the electricity bill when there exists a demand charge in the utility pricing structure (Bedouani, Labrecque, Parent, & Legault, 2001; Syed, 2011). With a well-designed mix of on-peak and off-peak electric heating the load can be leveled and the addition of new generating capacity can be delayed (Cooke & Hardy, 1980). ETS systems use bricks as a medium to store heat during low price periods or off-peak times. In peak periods, heat is released from the bricks to the building with the help of a thermostat-controlled fan.

Thermal energy storage comes in both low- and high-temperature storage schemes. Water and solutions of water and sodium sulfate have been used for low-temperature (less than 100[degrees]C [212[degrees]F]) energy storage. Magnesite bricks have mainly been used for high-temperature schemes, where brick temperatures can go up to 900[degrees]C [1652[degrees]F]. A forced-air electric furnace using bricks as a heat storage material is the subject of this paper.

Electric Thermal Storage (ETS) Device

The focus of this study is the modeling for improved operation of an electric thermal storage device (ETS). The device consists of an insulated heat storage tank containing 3,121 kg [6,880 lbs] of magnesite bricks. Electric wire heating elements are placed between the rows of bricks. The bricks can be charged to a maximum temperature of 750[degrees]C [1,380[degrees]F]. The maximum storage capacity of this device is approximately 640 kWh [2,183,680 BTU]. A fan controls airflow and the air either passes through the bricks, or bypasses the device.

The control requirements of the ETS device are more complex than those of a typical heating system. Control is needed for three things: 1) control during the time when the storage medium in being heated, 2) control and adjustment of the peak temperature to be reached during the charging cycle, and 3) control of the total heat to be stored in the storage medium. During the thermal storage discharge cycle, control requirements include a means of maintaining consistent outlet air temperature under conditions of large variations in the storage medium temperatures.

The ultimate goal is to match the amount of stored thermal energy to the energy requirements during the following discharge cycle, thus, the implemented control scheme should anticipate to some extent the heat requirements of the building or conditioned zone during the following day. A common approach to anticipate heating requirements for the next day is to sense current outdoor temperature and use this measurement as an indication of the expected trend. However, in many parts of North America, the weather can change rapidly, rendering this method unreliable, especially during shoulder seasons when outdoor temperature fluctuations can be vast. Therefore, these devices are often equipped with a rather simple control strategy: owner-selectable set points to adjust the storage capacity (Cooke & Hardy, 1980). Thermocouples embedded in the thermal storage material are used for heat input control. During the discharge cycle, mixing of heated air with ambient air is controlled.

METHODOLOGY

ETS devices are capable of storing heat during off-peak electricity demand periods to meet daytime (on-peak) heating loads (or partially), thus they can reshape a building's heating electric load profile without impacting total energy consumption or occupant comfort, providing large amounts of thermal storage capacity to the grid. They can be modelled as a thermal battery with a standby loss and controllable discharge rate. Figure 1 shows schematics of the device and specifications for the ETS used in this study are shown in Table 1.

Measured data at 15-minute intervals was collected from a building equipped with a 640 kWh [2,183,680 BTU] ETS system. Data collection from various sensor points began in 2014 and is on going. The measured data has been used to identify and analyse control-oriented thermal models of varying resolutions of the ETS. The building, which is located in Sherbrooke, Canada, has a peak demand in February 2015 of 600 kW [2,047,285 BTU/h], with a consumption of 166 MWh [566,400 BTU] for that month. The on-site ETS has the ability to reduce the winter peak by 106 kW [361,687 BTU/h] by supplying hot air to a specific warehouse area within the building Focus has been placed on operation during the winter months at the end of 2016 and beginning of 2017.

The following proposed models of the ETS are based on two-dimensional lumped parameter equations for heat conduction and energy conservation. The modeling approach is gray-box modeling (in which physical models are combined with measured data to complete the model). Within the developed MATLAB modeling environment, the two-dimensional grid of brick thermal capacitance nodes can be easily adjusted by specifying how many rows and columns of brick nodes will be used. The resulting number of brick capacitance nodes is then the number of rows multiplied by the number of columns. An example is shown in Figure 2, where there are two rows and two columns of brick nodes, thus resulting in a four-capacitance thermal network model for the device. However, many more complex row and column configurations can be easily evaluated. Each brick node has an associated capacitance term and electric power input.

Thermal Energy Storage Charging Mode Model

The charging mode of the system can be modeled using the following general energy balance equation:

[mathematical expression not reproducible] (1)

A fully explicit finite difference approach was used to solve the energy balance equations at each node in the models. The general equations (2) and (3) were used for nodes with and without capacitance terms, respectively. The input to the charging model is electric power input and the model output is the resulting average brick temperature.

Due to very high temperatures, there is enough heat loss from the ETS device to the ambient air of the mechanical room that these losses cannot be neglected in the models. There are both convective and radiative losses from the ETS to the room which are calculated at each time step using equations (4) (Athienitis, 1994) and (5), where [T.sub.surface] is assumed to be the same temperature as room air temperature.

[mathematical expression not reproducible] (4), [mathematical expression not reproducible] (5)

Thermal Energy Storage Discharging Mode Model

The discharging model of the system was modeled using the equation for heat exchange through a channel (Lienhard Iv & Lienhard V, 1986):

[mathematical expression not reproducible] (6)

Tw in this case is assumed as the average brick temperature [T.sub.brick]. It can give the variation of air bulk temperature along the channel if [T.sub.bout] is replaced by [T.sub.b(x)], L is replaced by Z(i), and h is adjusted accordingly. Temperatures at each control volume would therefore be calculated as follows:

[mathematical expression not reproducible] (7), where[mathematical expression not reproducible] and [mathematical expression not reproducible]

The energy extracted from the bricks in the air channels is calculated as follows (which is then subtracted from the brick node energy balance equation):

[mathematical expression not reproducible] (8)

The air stream model is based on dividing the air channel lengthwise in 6 sections, assuming uniform temperatures at the surfaces. Temperatures and heat transfer rates are found using a 1-D thermal network between the air and the surfaces. The exit temperature of each channel section is used as the entrance temperature of the next section. Less than six channel sections produced inadequate outlet air temperature results.

Model Reset

The main purpose of these control-oriented models is the rapid simulation of the ETS device in order to assess load management strategies and help in decision-making. These control-oriented models are intended to be used, along with knowledge of future conditions (such as electricity pricing, occupancy, weather forecasts etc.), to plan ahead the operation strategies within the Building Automation System (BAS) to better regulate electrical loads. Thus, the concept of "model reset" was also investigated. As these models are designed for the use of short-term control (1-2 days) and optimization (hours), it is reasonable to assume that the model can "check" itself against the real measured values (of brick temperature, outlet air temperature etc.) periodically and correct or "reset" its parameters. For this reason, we compare a model running for an extended period versus the same model with model reset every 6 hours. The main reason a 6-hour model reset intverval was chosen is because that is how often the available weather forecasts are updated and released.

MODELING RESULTS

Three different thermal model resolutions of the ETS system have been studied. The model results are shown below. The most detailed model consists of 140 brick capacitance nodes (10 rows and 14 columns). This high-resolution model is compared to measured data from the BAS and two simplified control oriented models. The first simple model consists of four brick capacitances (2 rows and 2 columns) and second simple model consists of one single capacitance (1 row and 1 column).

Charging Mode Model Results

Figure 3 shows the results for three days of charging model results for the ETS. The model results (average brick temperature) are compared to the measured data obtained from the building automation system. The fan operation and power input are from measured data from the building automation system. Figure 3a) shows results for the model continuously running, while Figure 3b) has a reset of 6-hour intervals incorporated in the models.

The statistical indices of Coefficient of variation of the root-mean-square error (CV-RSME) and Normalized mean bias error (NMBE) were used to determine the accuracy of the models of varying resolutions. ASHRAE Guideline 14 (Gillespie et al., 2002) suggests that a CV-RMSE below 30% and NMBE below 10% on an hourly basis ensures a calibrated model (shown in Table 2 for the charging mode). The infinity norm, [||*||.sub.[infinity]], of the absolute error between modeled brick temperature [[bar.T].sub.model] and measured brick temperature [[bar.T].sub.measured] is also presented. The infinity norm is in effect the biggest difference between the model results and measured data.

The above results show that the very detailed charging model (140 brick node capacitances) provides accurate predictions of brick temperature when compared to the measured data, even without reset. When model reset at 6-hour intervals is introduced, all models perform well.

Discharging Mode Model Results

Table 3 shows the statistical indices of the discharge modelling with and without model reset at 6-hour intervals. We see that without model reset, the three models all perform quite well and have slight improvements when model reset is incorporated into the models.

Figure 4 shows the results for several hours of discharging model results for the ETS. The time frame for the discharging mode is much shorter than the charging mode. The model results (average brick temperature and outlet air stream temperature) are compared to the measured data obtained from the building automation system. The fan operation, power input and inlet air stream temperature are taken from measured data from the building automation system. Figure 4a) shows results for the model continuously running for the whole period, while Figure 4b) has model reset of 6 hour intervals incorporated in the models.

Table 3 shows the statistical indices of the discharge modelling with and without model reset at 6-hour intervals. We see that without model reset, the three models all perform quite well and have slight improvements when model reset is incorporated into the models.

Results for Several Days

Modeling results for December 30, 2016 to January 9, 2017 are shown in Figure 5. Brick temperature and outlet air temperature predictions from the three models show good agreement with measured values, and performance improves again with model reset. Table 4 shows the error analysis of the three models with and without model reset at 6 hours intervals.

CONCLUSION

This paper presented a control-oriented modeling technique for the enhanced operation of an electric thermal storage device (ETS). The modeling results from the charging mode, discharging mode, and several days of operation show that even a simple model with one capacitance representing the entirety of the bricks could be adequate for the control and optimized charging and discharging operation of the ETS device. The simple one capacitance model is capable of predicting the temperature of the bricks over several days with a CV-RMSE value of 14.5% and an average difference between modeled brick temperature and measured brick temperature of 47[degrees]C [117[degrees]F], while the detailed 140 capacitance model has an average difference of 21[degrees]C [70[degrees]F] and corresponding CV-RMSE value of 6.2%. Incorporating periodic model reset based on measured values improves the model performance significantly.

The next step in further studies will be to use these models to test different operating modes and control strategies. These control-oriented models will be used, along with knowledge of future conditions (such as electricity pricing, occupancy, weather forecasts etc.) to plan the operation strategies within the Building Automation System (BAS) to better regulate electrical heating loads at critical hours (for example in the morning between 6am and 9am).

ACKNOWLEDGMENTS

Support provided through a NSERC/Hydro-Quebec Industrial Research Chair in Optimized Building Operation and Energy Efficiency: Towards High Performance Buildings and by CanmetENERGY is gratefully acknowledged. Thank you also to researchers at LTE for their helpful collaboration and insight.

NOMENCLATURE

A = Area, [m.sup.2] [[ft.sup.2]]

avg(*) = Average value of a vector

C = capacitance,

[c.sub.p] = Specific heat capacity of node, J*[kg.sup.1]*[K.sup.-1] [BTU/[degrees]F]

[P.sub.in] = Power input, kW [BTU/hr]

P = air channel perimeter, m [ft]

UA = Conductance, W*[K.sup.1] [BTU*[h.sup.-1]*[degrees][F.sup.-1]]

Z(i) = Control volume of air stream, m [ft]

[U.sub.inf] = Conductance due to infiltration, W*[K.sup.-1] [BTU*[h.sup.-1]*[degrees][F.sup.1]]

DH = Hydraulic diameter, m [ft]

h = Heat transfer coefficient, W*[m.sup.-2]*[degrees]C-1 [BTU*[h.sup.-1]*[ft.sup.2]*[degrees][F.sup.-1]]

k = Thermal conductivity, W*[m.sup.-1]*[degrees4][C.sup.-1] [BTU*[h.sup.-1]*ft-1*[degrees][F.sup.-1]]

M = Mass, kg [lbs]

M(t) = Volumetric flow rate, [m.sup.3] * [s.sup.1] [[ft.sup.3] * [s.sup.1]]

[??] = Mass flowrate, kg*h-1 [lbs*[h.sup.1]]

Q = Heat energy, W [BTU*[h.sup.1]]

R = Resistance, [degrees]C*[W.sup.-1] [h*[degrees]F*[BTU.sup.1]]

T = Temperature, [degrees]C [[degrees]F]

[??] = Density, kg*[m.sup.3] [lb*[ft.sup.3]]

[sigma] = Stefan-Boltzmann constant, W*[m.sup.-2]*[K.sup.-4] [BTU*[h.sup.-1]*[ft.sup.-2]*[R.sup.-4]]

[epsilon] = Emissivity, unitless

Nu = Nusselt number

W = width of air channel, m [ft]

Subscripts

ins = insulation node

int = interior surface node

k = adjacent node

t = time step

i = node

amb = ambient air node

b = brick node

s = general heat source

conv = convection

rad = radiation

[b.sub.in] = bulk channel inlet

[b.sub.out] = bulk channel outlet

w = air channel wall surface

REFERENCES

Athienitis, A. K. (1994). Building thermal analysis. Boston,MA: MathSoft Inc.

Bedouani, B. Y., Labrecque, B., Parent, M., & Legault, A. (2001). Central electric thermal storage (ETS) feasibility for residential applications: Part 2. Techno-economic study. International Journal of Energy Research, 25, 73-83.

Cooke, W. B. H., & Hardy, R. H. S. (1980). Thermal Energy Storage in Forced-Air Electric Furnaces, I, 127-133.

Hydro-Quebec. (2016). Electricity Rates Effective April 1, 2016.

Lavigne, K. (2006). Etude de Mediums De Stockage Pour un Appareil de Stockage Thermique Hybride. Universite de Sherbrooke.

Lienhard Iv, J. H., & Lienhard V, J. H. (1986). A heat transfer textbook. Journal of Heat Transfer, 108, 198.

Moffet, M. A., Sirois, F., Joos, G., & Moreau, A. (2012). Central electric thermal storage (ETS) heating systems: Impact on customer and distribution system. Proceedings of the IEEE Power Engineering Society Transmission and Distribution Conference. doi:10.1109/TDC.2012.6281536

Syed, A. M. (2011). Electric Thermal Storage Option for Nova Scotia Power Customers : A Case Study of a Typical Electrically Heated Nova Scotia House. Energy Engineering, 108:6, 69-79.

Wong, S., & Pinard, J. P. (2017). Opportunities for Smart Electric Thermal Storage on Electric Grids with Renewable Energy. IEEE Transactions on Smart Grid, 8, 1014-1022.

Jennifer Date

Andreas Athienitis, Ph.D., P.E.

Fellow ASHRAE

Jose A. Candanedo, Ph.D

Karine Lavigne
Table 1. Electric Thermal Storage (ETS) Device Specifications

Parameter                   Value                       Metric

Charging Input                106 [361,687]             kW
Storage Capacity              640 [2,183,680]           kWh
Storage Material            High-density ceramic brick  --
Number of Heating Elements     24                       --
Maximum Brick Temperature     750 [1,380]               [degrees]C
Weight of Bricks            3,121 [6,880]               kg
Number of Bricks              384                       --

Parameter                   [Imperial]

Charging Input              [BTU/h]
Storage Capacity            [BTU]
Storage Material            --
Number of Heating Elements  --
Maximum Brick Temperature   [[degrees]F]
Weight of Bricks            [lbs.]
Number of Bricks            --

Table 2. Charging Mode (January 6 to 8. 2017)

Parameter              CV-RMSE   NMBE
                       (Bricks)  (Bricks)

1 Capacitance Model    18.2%     -17.4%
4 Capacitance Model    15.4%     -14.7%
140 Capacitance Model   5.8%      -5.2%
                        With Model Reset every 6 Hours
1 Capacitance Model     3.3%      -1.5%
4 Capacitance Model     3.1%      -1.3%
140 Capacitance Model   2.6%      -0.4%

Parameter              [mathematical expression not reproducible]


1 Capacitance Model    128[degrees]C [262[degrees]F]
4 Capacitance Model    109[degrees]C [228[degrees]F]
140 Capacitance Model   60[degrees]C [140[degrees]F]
                       With Model Reset every 6 Hours
1 Capacitance Model     63[degrees]C [145[degrees]F]
4 Capacitance Model     57[degrees]C [135[degrees]F]
140 Capacitance Model   53[degrees]C [127[degrees]F]

Parameter              [mathematical expression not reproducible]


1 Capacitance Model    98[degrees]C [208[degrees]F]
4 Capacitance Model    83[degrees]C [181[degrees]F]
140 Capacitance Model  30[degrees]C [86[degrees]F]
                       With Model Reset every 6 Hours
1 Capacitance Model    12[degrees]C [54[degrees]F]
4 Capacitance Model    11[degrees]C [52[degrees]F]
140 Capacitance Model  10[degrees]C [50[degrees]F]

Table 3. Discharging Mode (January 9, 2017)

Parameter              CV-RMSE   NMBE
                       (Bricks)  (Bricks)

1 Capacitance Model    12.2 %    10.5 %
4 Capacitance Model    13.2 %    11.7 %
140 Capacitance Model  11.4 %    10.7 %
                       With Model Reset every 6 Hours
1 Capacitance Model     8.0%      5.6%
4 Capacitance Model     8.5%      6.1%
140 Capacitance Model   8.1%      6.2%

Parameter              [mathematical expression not reproducible]


1 Capacitance Model    85[degrees]C [185[degrees]F]
4 Capacitance Model    93[degrees]C [199[degrees]F]
140 Capacitance Model  82[degrees]C [180[degrees]F]
                       With Model Reset every 6 Hours
1 Capacitance Model    74[degrees]C [165[degrees]F]
4 Capacitance Model    76[degrees]C [169[degrees]F]
140 Capacitance Model  82[degrees]C [180[degrees]F]

Parameter              [mathematical expression not reproducible]


1 Capacitance Model    51[degrees]C [124[degrees]F]
4 Capacitance Model    57[degrees]C [135[degrees]F]
140 Capacitance Model  52[degrees]C [126[degrees]F]
                       With Model Reset every 6 Hours
1 Capacitance Model    27[degrees]C [81[degrees]F]
4 Capacitance Model    30[degrees]C [86[degrees]F]
140 Capacitance Model  30[degrees]C [86[degrees]F]

Parameter              CV-RMSE       NMBE
                       (Outlet Air)  (Outlet Air)

1 Capacitance Model    12.3 %        8.0 %
4 Capacitance Model    12.8 %        8.5 %
140 Capacitance Model  11.4 %        7.7 %
                       With Model Reset every 6 Hours
1 Capacitance Model    10.3%         5.7%
4 Capacitance Model    10.4%         5.9%
140 Capacitance Model   9.5%         5.5%

Table 4. Several Days of Simulation (December 30, 2016-January 9, 2017)

Parameter              CV-RMSE   NMBE
                       (Bricks)  (Bricks)

1 Capacitance Model    14.5%     -7.4%
4 Capacitance Model    12.1%     -4.5%
140 Capacitance Model   6.2%      1.4%
                       With Model Reset every 6 Hours
1 Capacitance Model     4.8%     -0.1%
4 Capacitance Model     4.6%      0.1%
140 Capacitance Model   4.0%      0.6%

Parameter              [mathematical expression not reproducible]


1 Capacitance Model    118[degrees]C [244[degrees]F]
4 Capacitance Model     96[degrees]C [205[degrees]F]
140 Capacitance Model   79[degrees]C [174[degrees]F]
                       With Model Reset every 6 Hours
1 Capacitance Model     72[degrees]C [162[degrees]F]
4 Capacitance Model     68[degrees]C [154[degrees]F]
140 Capacitance Model   57[degrees]C [135[degrees]F]

Parameter              [mathematical expression not reproducible]


1 Capacitance Model    47[degrees]C [117[degrees]F]
4 Capacitance Model    41[degrees]C [106[degrees]F]
140 Capacitance Model  21[degrees]C [70[degrees]F]
                       With Model Reset every 6 Hours
1 Capacitance Model    13[degrees]C [55[degrees]F]
4 Capacitance Model    13[degrees]C [55[degrees]F]
140 Capacitance Model  12[degrees]C [54[degrees]F]

Parameter              CV-RMSE       NMBE
                       (Outlet Air)  (Outlet Air)

1 Capacitance Model    6.3%          1.9%
4 Capacitance Model    6.4%          2.1%
140 Capacitance Model  6.2%          2.3%
                       With Model Reset every 6 Hours
1 Capacitance Model    5.6%          1.8%
4 Capacitance Model    5.6%          1.9%
140 Capacitance Model  5.4%          1.7%
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Author:Date, Jennifer; Athienitis, Andreas; Candanedo, Jose A.; Lavigne, Karine
Publication:ASHRAE Conference Papers
Article Type:Report
Date:Jan 1, 2018
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