Antoine Garnier

Julien Eynard

Matthieu Caussanel

Stéphane Grieu
email: stephane.grieu@promes.cnrs.fr

Predictive Control of Multizone HVAC Systems in Non-residential Buildings

Keywords: Multizone HVAC system, non-residential buildings, predicted mean vote, predictive control, optimization problems, feedforward neural networks, genetic algorithms

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INTRODUCTION

Within non-residential buildings, almost half of the energy consumption is due to Heating, Ventilation and Air-Conditioning (HVAC) systems [START_REF] Pérez-Lombard | A review on buildings energy consumption information[END_REF]. Older, oversized or poorly maintained systems may be using more energy and costing more to operate than necessary. As a result, new approaches dealing with energy ressources management are needed to make HVAC systems more efficient. First, energy efficiency can be improved in central heating and cooling systems by introducing zoned operation. This allows a more granular application of heat and HVAC sub-systems can be controlled independently. Another key point is thermal comfort. Thermal comfort is mainly related to indoor conditions and impacted by both the effectiveness of the building envelope and the way the centralized or zoned HVAC system is used.

Many works focusing on both the control of HVAC systems and the management of thermal comfort have been conducted over the last few years. [START_REF] Bermejo | Energy consumption: 224.2 Wh/day•m 2 . Discomfort criterion: 1.8%. (b) S2. Energy consumption: 86.7 Wh/day•m 2 . Discomfort criterion: 1.0%[END_REF] used artificial intelligence tools to develop interesting approaches. However, these approaches require to turn the HVAC systems on at a fixed time and, as a result, this can impact thermal comfort negatively if these systems are started too late, or energy consumption if triggering happens too soon. As it has been highlighted by many studies, predictive control can take advantage of the intermittent use of non-residential buildings and allows the behaviour of the considered system to be anticipated [START_REF] Paris | Heating control schemes for energy management in buildings[END_REF] In this sense, we proposed a new approach allowing energy consumption to be significantly reduced and the HVAC sub-systems of a non-residential building to be turned on and off at the right time [START_REF] Garnier | Low computational cost technique for predictive management of thermal comfort in non-residential buildings[END_REF]. Only heating has been considered. We used the PMV (Predicted Mean Vote) index as a thermal comfort indicator and focused on satisfying constraints. The algorithm we developed offers very good performance and does not require on-line optimization. As a result, it is computationnaly tractable and can be implemented in an embedded system whose resource is limited. Its main drawback lies in the simultaneous engaging and stop of all of the HVAC sub-systems. That is why the present paper focuses on improving this predicitive approach by optimizing for each room the operation time of its HVAC sub-system. Both heating and cooling operation modes are now considered. We decided for a Genetic Algorithm (GA) in order to solve the optimization problem [START_REF] Holland | Adaptation in Natural and Artificial Systems[END_REF] and used artificial neural networks to develop the controller's internal models. Such algorithms are commonly used in energy resources and thermal comfort management [START_REF] Attia | Computational optimisation for zero energy buildings design: interviews results with twenty eight international expert[END_REF]. [START_REF] Berthou | Optimal control for building heating: an elementary school case study[END_REF] used a GA to manage thermal comfort into a unique room of a building, without considering interaction (i.e. heat transfer) with the other rooms. Thermal comfort has been defined on the basis of temperature thresholds. [START_REF] Liu | Simulation-based receding-horizon supervisory control of HVAC system[END_REF] also used a GA to optimize the operation of HVAC systems by searching for optimal control settings. The controllable variables include supply air and chilled water temperatures.

The paper is organized as follows: section 2 is about the non-residential building we modelled using the EnergyPlus software. Section 3 deals with the Predicted Mean Vote (PMV) we used as a thermal comfort indicator. Next, the predictive strategy as well as the low-order ANN-based models we developed and used as controller's internal models are described (section 4). Finally, the management results are analyzed and compared with the results given by standard strategies (section 5). The paper ends with a conclusion and an outlook to future work.

NON-RESIDENTIAL BUILDING

In order to evaluate the proposed strategy, a reference building has been modelled using the EnergyPlus software, which is able to perform accurate building simulations. The considered building is a real two-storey building of 1000 m 2 , built in 2008 and located in Perpignan (south of France). It is facing south and agrees with the French Thermal Regulation of year 2005. This non-residential building is divided into 3 main areas of 340 m 2 each (Fig. 1), with different uses. About a dozen employees work in offices at the ground and first floors (green and yellow areas). The red area in the first floor is a manufacturing room where about 6 persons work seated or in a standing position. The last room of the ground floor is a warehouse (blue area) that is not heated. For both the warehouse and the manufacturing area, ceiling is 3.90 m. In the offices, a suspended ceiling stands at 2.70 m. The materials used in the building are listed in table 1: l is the thickness (cm), λ is the conductivity (W•m -1 •K -1 ), ρ is the density (kg•m -3 ) and, finally, C is the specific heat (J•kg -1 •K -1 ). The exterior walls consist of several layers. From the outside to the inside are juxtaposed a brick layer, heavy weight concrete, an insulation board, and finally a gypsum board. The interior walls are composed of two gypsum boards, for a total thermal resistivity of 2.2 m 2 •K•W -1 . The south face and a part of the west face of the building are made from glass. Glass has been treated to filter infrared radiation and avoid overheating in summer. The other glasses consist in 3 mm double glazed bays. The present study focuses on the three following (occupied and equipped with sensors) rooms: the offices on both floors (R1 and R2) and the manufacturing area (R3), that is composed of an open space of 230 m 2 and three storage rooms of 110 m 2 (not heated). Heating is handled in the building by a zoned electrical HVAC system consisting several sub-systems, one for each area, where only the temperature set-point can be adjusted. Each sub-system is managed by a local controller. The characteristics of the different HVAC sub-systems for each area are listed by table 2. All units have a coefficient of performance (CoP) equal to 3.8. As previously stated, the management approach is based on a model predictive controller that will supervise the HVAC sub-systems (Fig. 2).

THERMAL COMFORT

The Predicted Mean Vote (PMV) index is used as a thermal comfort indicator. This indicator was developed by [START_REF] Fanger | Assessment of man's thermal comfort in practice[END_REF], before to be standardized by international organizations. The PMV index quantifies the thermal sensation felt by people in a room. This sensation is described by a scale ranging from -3 (cold) to +3 (hot).

The exchange of heat between the human body and its environment strongly governs thermal comfort. It is highly subjective and can be considered as perfect when the sum of exchanges is zero. Equation 1 depicts the way one can compute the PMV index, for the room j, ∀j ∈ 1; 3 :

P M V j = [0.303exp -0.036Mj + 0.028] × L j (1)
with L j the difference between the heat produced and the heat lost:

L j = M j -W j -H j,1 -H j,2 -H j,3 -H j,4 -H j,5 -H j,6 (2)
M j is the metabolism (described below). W j is the external work. H j,1 , ..., H j,6 are the heat loss coefficients (W•m -2 ). H j,1 is the heat loss by diffusion through the skin and H j,2 is the heat loss by sweating. H j,3 and H j,4 are the losses by latent and dry respiration, respectively. Finally, H j,5 is the heat loss by radiance and H j,6 is the heat loss by convection. To calculate these heat loss coefficients, several parameters about environment and occupants are taken into account: indoor air temperature (T a j ), radiative temperature (T r j ), relative humidity (HR j ), air speed (v a j ), metabolic activity, as well as clothing thermal insulation (ICL j ). Let us note that air speed is not calculated by the EnergyPlus software. However, this missing information is not critical at all because air speed has no influence on the PMV index as long as it remains below 0.1 m•s -1 . This is mostly the case within the non residential building we considered. Moreover, metabolic activity is supposed to be constant and only depends on the considered area. In offices (R1 and R2), people work in a sitting position most of the time and, as a result, M j is set to 70 W•m -2 (i.e. 1.2 met). Activity in the manufacturing area (R3) is more dynamic and M j is set higher to 116 W•m -2 (i.e. 2 met). Moreover, depending on climatic conditions, people dress differently. So, clothing thermal insulation in the room j (ICL j ) varies over time and is defined from the outdoor temperature observed at 6 a.m. [START_REF] Schiavon | Dynamic predictive clothing insulation models based on outdoor air and indoor operative temperatures[END_REF].

MULTIZONE PREDICTIVE CONTROL

As previously stated, each room has its own HVAC subsystem, handled by a local controller (Fig. 2). Simulation is carried out using the EnergyPlus building model we developed and the predictive control strategy is implemented thanks to Matlab R . The MLE + interface enables both tools to communicate in real time [START_REF] Nghiem | MLE+: a Matlab-EnergyPlus co-simulation interface[END_REF].

Low-order ANN-based models

We used a total of six feedforward (multi-layer) artificial neural networks with only one hidden layer in order to model at time step k + 1 (∀j, l, m ∈ 1; 3 such as j = l = m) the air (T a j ) and radiative (T r j ) temperatures as well as the electrical power consumed by the HVAC sub-systems (P j ) for both operation modes (heating and cooling) and the three considered rooms in the non-residential building (the offices on both floors and the manufacturing area). Estimation is carried out from several inputs: outdoor temperature (T out ), solar radiation (SR), room occupancy (O j ), T a j , T r j , T sp j and, finally, the HVAC temperature set-points in the two adjacent rooms (T sp l and T sp m ) of room j at time step k (Fig. 3). These ANN-based models (used as controller's internal models) perform a one-stepahead forecast and their outputs are reinjected as inputs, along the horizon. We identified their parameters through a training phase, thanks to the Levenberg-Marquardt Algorithm (LMA) [START_REF] Hagan | Training feedforward networks with the marquardt algorithm[END_REF] as well as data generated by the EnergyPlus model. The LMA is accurate, very fast and uses matrix decomposition. We optimized the topology of the feedforward artificial neural networks and considered from 18 to 24 hidden neurons. Validation has been carried out using a 2-month database and we obtained correlation coefficients higher than 0.9 and mean relative errors lower than 5%, whatever the operation mode. Using equation 1 (section 3), P M V j (k + 1), ∀j ∈ 1; 3 , is computed among others from T a j (k + 1) and T r j (k + 1). Let us note that M j do not change over the simulation period (i.e. from June 1 to September 30 then from November 1 to March 31, 2011) while HR j is supposed to be constant over the forecast horizon and equal

Feedforward

ANN j

PMV index computation

Fig. 3. ANN-based model for the room j, ∀j, l, m ∈ 1; 3 such as j = l = m (heating and cooling modes).

to the value measured at the beginning of the optimization process. Indeed, changes in relative humidity are low and a parameter has a limited impact on the PMV index. ICL j is considered as constant from 6 a.m. (day d) to 6 a.m. (day d + 1). v a j and W j are considered to be null.

Control strategy

Fig. 4 depicts the predictive control strategy we developed first to search for the right time t j to turn the HVAC subsystem on then off in the room j, ∀j ∈ 1; 3 , with the aim of minimizing the total consumption of electrical power (equation 3). The strategy deals also with the temperature set-point T sp j (its value is fixed over the forecast horizon) allowing thermal comfort constraints to be met during periods of occupancy (i.e. leading to P M V sp j = 0). t is about the optimal switching times (integer values) for the three HVAC sub-systems we consider (equation 4). In addition, outdoor temperature (T out ) and solar radiation (SR) have been forecasted over an horizon (N ) set to 8 hours, using previous day values corrected by current values. Room occupancy (O j ) is regular and, as a result, known in advance. Finally, T sp j is chosen by the decision block (Fig. 4), according to t j and T sp j :

J( t) = min t∈N   N k=1 3 j=1 (P j (t j , k))   (3)    t = [t j , t l , t m ], ∀j, l, m ∈ 1; 3 s.a. j = l = m t0 < t < tN , with N the forecast horizon P M V min j < P M V j (k) < P M V max j , ∀O j (k) = 0 (4)
P M V min j and P M V max j are thermal comfort thresholds defined for the room j, ∀j ∈ 1; 3 . These thresholds can be adapted to users' preference. For the simulations we decided for P M V min j = -0.5 and P M V max j = 0.5.

Genetic algorithm for problem resolution

In order to solve the problem we formulated, we decided for a numerical optimizer able to deal with integer values and known to be efficient in the search for the optimal solution, by testing a reasonable number of possible solutions. As a result, we used the Genetic Algorithm from the Matlab R Global Optimization Toolbox [START_REF] Palonen | Mobo a new software for multi-objective building performance optimization[END_REF]. At each step of the process, the best individuals are selected from the current population (the initial population is generated randomly) and serve as parents in order to produce the children for the next generation. Each individual is a vector t = [t j , t l , t m ], ∀j, l, m ∈ 1; 3 such as j = l = m. Selection is based on performance (typically, the genetic algorithm is more likely to select parents with better fitness values), that is why the thermal behaviour of the three considered rooms (R1, R2 and R3) in the non-residential building is simulated for each individual in the current population. Over successive generations, this population evolves toward an optimal solution topt allowing electrical power consumption in the room j of the building to be minimized (P j , ∀j ∈ 1; 3 ) and thermal constraints to be met (equation 4). As a key point, we performed crossover (recombinations of individuals) and mutation (random alterations of individuals) operations during the optimization process. We decided for a crossover fraction equal to 0.8 and a rate at which the average amount of mutation decreases equal to 1. The process ends if the maximum number of generations is reached or the solution found is not improved for 10 successive generations. The parametric analysis we performed also allowed the impact on performance of both the population size and the number of successive generations to be highlighted. Taking a look at Figure 5, one can observe that the higher both the number of individuals in the population and the number of generations, the higher the percentage of optimal solutions related to the minimization of P j , ∀j ∈ 1; 3 , while meeting thermal constraints. Figure 6 shows how a given solution is related to overconsumption of electrical power (reference is the optimal solution). One can clearly observe that with a too low number of individuals, the search for an acceptable solution is not successful. In opposition, starting from 10 individuals and with a sufficient number of successive generations, a solution in the neighbourhood of the optimal one can be found. So, we decided for 15 individuals and 40 successive generations. In this case, overconsumption of electrical power is insignificant and the number of tested solutions is reduced.

RESULTS

Non-predictive strategies

We considered two non-predictive strategies in order to highlight the benefits of the predictive approach we propose for multizone HVAC systems in non-residential buildings. The first strategy (S1) is basic: all the sub-systems operate all the time. The second strategy (S2) is a scheduler used to stop the sub-systems during periods of nonoccupancy and to turn them on in the morning, two hours before people arrive at the building (i.e. at 6 a.m.). The sub-systems are turned off when people leave (i.e. at 6 p.m.). S2 is the strategy currently used in the real nonresidential building located in Perpignan (south of France) we modelled. For both strategies, heating and cooling setpoints are set to 22 • C (only during occupancy periods for S2) and the PMV is near zero, whatever the room. Let us remember that the predictive strategy we propose allows the right time to turn the HVAC sub-systems on then off to be found in each of the considered rooms of the building while meeting with thermal comfort requirements (S3). As a result, energy consumption can be significantly reduced.

Analysis of the results

In order to evaluate performance regarding thermal comfort, we considered the percentage of time for which the PMV value is out of the desired interval during occupancy periods [-0.5; +0.5]. Moreover, an average value (per day and square meter) is used for energy consumption. Tables 3 and4 summarize the results we obtained for two simulation periods, from November 1 to March 31 (heating mode) and from June 1 to September 30, 2011 (cooling mode).

Taking a look at these results, one can clearly observe that the predictive strategy (S3) allows energy consumption to be significantly reduced, whatever the operation mode and the period of the year, in comparison to what can be observed with the non-predictive strategies (S1 and S2). In addition, thermal comfort is better (heating mode) or similar (cooling mode) with S3 than when using S1 or S2. Considering the results we obtained using S2 as reference results, energy consumption and thermal dis-comfort are reduced from 80.9 to 69 Wh/day•m 2 (-15%) and from 14.4% to 6.4% (-56%), respectively (heating mode). In cooling mode, energy consumption and thermal discomfort are reduced from 122.6 to 116.2 Wh/day•m 2 (-5%) and from 0.2% to 0.1% (-50%), respectively. Table 5 gives the optimal on/off switching times computed by the predicitive controller (S3) in heating mode. The simulation period is from January 6 to January 12, 2011. One can highlight that the operation time of the HVAC subsystems is most of the time significantly reduced, whatever the room (comparison is between S2 and S3). The daily time saved can reach up to 5 hours. Fig. 7(a), 7(b) and 7(c) describe the way energy consumption and thermal comfort evolve from January 6 to January 12, 2011, whatever the strategy. With S1, overheating may happen during the afternoon and alters thermal comfort (heating mode).

Using the scheduler (S2), overheating is delayed or even avoided, whatever the mode. As a result, thermal comfort is improved during cold periods. In cooling mode, thermal comfort is slightly worse (0.2 % vs. 0.1%) because of HVAC sub-systems being turned on later in the morning than with S1 when outdoor temperature is high. In addition, turning the HVAC systems off during non-occupancy periods allows energy consumption to be significantly reduced. With S3, heating is stopped sooner and overheating is completely avoided (heating mode). During hot periods, the benefits of using S3 are less important. Indeed, in cooling mode, the HVAC sub-systems can not be turned off as soon as during cold periods.

CONCLUSION

The present work deals with the predictive control of multizone Heating, Ventilation and Air-Conditioning (HVAC) systems in non-residential buildings. Such systems account for a large part of the energy consumption. Heating and cooling modes have been considered. In order to test the proposed approach, a real non-residential building located in Perpignan (south of France) has been modelled using the EnergyPlus software. We used the PMV (Predicted Mean Vote) index as a thermal comfort indicator and developed low-order ANN-based models to be used as controller's internal models. The optimization problem has been solved using a genetic algorithm. The proposed strategy allows the operation time of each HVAC subsystem to be optimized (i.e. the right time to turn the HVAC sub-systems on and off to be found) and thermal comfort requirements to be met. In comparison to what is observed when using a standard (non-predicitive) strategy, energy consumption is significantly reduced and thermal comfort is improved, whatever the operation mode and the period of the year. Future work will focus on implementing and validating the predictive strategy in the real building. Finally, natural ventilation will be considered in cooling mode with the aim of reducing energy consumption.

Fig. 1 .

 1 Fig. 1. Topology of the non-residential building.

Fig. 2 .

 2 Fig. 2. The three considered rooms (R1, R2 and R3) equipped with sensors and HVAC sub-systems.

Fig. 4 .

 4 Fig. 4. Block diagram of the predictive control strategy.

Fig. 5 .

 5 Fig. 5. Optimal responses percentage.

Table 1 .

 1 Properties of the materials used in the exterior walls.

	Layer	l	λ	ρ	C
	Brick	10 0.89 1920	790
	Heavy weight concrete 20 1.45 2000 1000
	Insulation board	5	0.03	43	1210
	Gypsum board	2	0.16	800	1090

Table 2 .

 2 Characteristics of the three considered rooms.

Table 3 .

 3 Performance of the different strategies, ∀j ∈ 1; 3 . The simulation period is from November 1 to March 31, 2011 (heating mode).

	Occupancy	Non-occup.	Consumption	Discomfort
	period	period	(Wh/day•m 2 )	criterion
	S1 S2 S3 P M V sp T sp j = 22 • C T sp j = 22 • C j = 0	T sp j = 22 • C Off Off	209.5 80.9 69.0	19.4% 14.4% 6.4%

Table 4 .

 4 Performance of the different strategies, ∀j ∈ 1; 3 . The simulation period is from June 1 to September 30, 2011 (cooling mode).

	Occupancy	Non-occup.	Consumption	Discomfort
	period	period	(Wh/day•m 2 )	criterion
	S1 S2 S3 P M V sp T sp j = 22 • C T sp j = 22 • C j = 0	T sp j = 22 • C Off Off	198.5 122.6 116.2	0.1% 0.2% 0.1%

Table 5 .

 5 On/off switching times using strategy S3. The simulation period is from January 6 to January 12, 2011 (heating mode).

		Day	Jan. 6	Jan. 7	Jan. 8-9
		Starting time	6:15 a.m.	7:15 a.m.	n.a.
	R1	Stopping time	2:00 p.m. 2:30 p.m.	n.a.
		Time saved (h)	4:15	4:45	n.a.
		Starting time	5:15 a.m.	6:15 a.m.	n.a.
	R2	Stopping time	5:00 p.m. 2:00 p.m.	n.a.
		Time saved (h)	0:15	4:15	n.a.
		Starting time	6:15 a.m.	7:00 a.m.	n.a.
	R3	Stopping time	2:00 p.m. 2:00 p.m.	n.a.
		Time saved (h)	4:15	5:00	n.a.
		Day	Jan. 10	Jan. 11	Jan. 12
		Starting time	6:30 a.m.	6:15 a.m.	7:00 a.m.
	R1	Stopping time	2:15 p.m. 2:00 p.m. 1:45 p.m.
		Time saved (h)	4:15	4:15	5:15
		Starting time	5:00 a.m.	5:45 a.m.	6:15 a.m.
	R2	Stopping time	6:00 p.m. 2:00 p.m. 1:00 p.m.
		Time saved (h)	-1:00	3:45	5:15
		Starting time	6:30 a.m.	6:15 a.m.	7:00
	R3	Stopping time	2:15 p.m. 2:00 p.m. 2:00 p.m.
		Time saved (h)	4:15	4:15	5:00


Aurélie Chabaud
email: aurelie.chabaud@univ-perp.fr

Julien Eynard
email: julien.eynard@univ-perp.fr

Stéphane Grieu
email: grieu@univ-perp.fr

LOAD MANAGEMENT IN MULTI-ENERGY BUILDINGS: A SIMULATION CASE STUDY

This paper presents a comprehensive approach about energy resources management in buildings connected to the electricity grid and equipped with energy production and storage systems. The aim of the work is to find interesting configurations that favour energy self-consumption while minimizing the impact of the local production on the grid. Energy and economic criteria are proposed to evaluate the proposed strategy. A parametric study allowed the local systems to be optimally designed. So, we used first the TRNSYS software to model the thermal behaviour of a singlestorey house, inhabited by four persons and equipped with photovoltaic solar panels, a vertical-axis windmill and batteries for electricity storage. The results we obtained in simulation prove that one can design in an optimal way the just-mentioned systems and find configurations that offer a very good compromise between energy self-consumption and renewable energy coverage rate while limiting the negative impact of the local production on the electricity grid.

INTRODUCTION

Changes in climate due to greenhouse gas emissions, the rarefaction of fossil energy resources and an increasing energy demand, mainly caused by population growth and economic development, are worldwide concerns. In addition, power breakdowns due to grid disturbances or overloading are important issues impacting networks safety. As a result, the energy market is being deregulated and decentralized energy production systems become more and more popular. That is why one needs to develop tools to improve safety and ensure a good balance between electricity supply and demand. In addition, spikes in electricity demand are forcing power companies to invest money in "peaking facilities" that are rarely used. Smart building automation approaches capable of trimming demand for electricity in response to real-time variations in prices could shave many peaks and help to improve generation and distribution networks reliability, in particular if penetration of intermittent energy resources in the power system is high, as well as cost effectiveness. Initially, electricity networks were designed in a radial and unidirectional way to carry out electricity from centralized power plants to consumers [START_REF] Carrive | Réseaux de distribution -Structure et planification[END_REF][START_REF] Puret | Les réseaux de distribution publique MT dans le monde, Schneider Electric[END_REF]. However, distribution networks are no more passive networks and adapt to a massive penetration of renewable energy. This penetration requires dramatic changes in planning and operation practices because it affects the physical operation of the grid. In particular, it affects short circuit, transient and voltage stability, electromagnetic transients, protection, power levelling and energy balancing as well as power quality. As a result, load forecasting becomes highly valuable while managing reactive power consumption in an efficient way is critical to grid stability. This also includes dynamic reactive power requirements of intermittent resources [START_REF] Alvarez-Herault | Architecture des réseaux de distribution du futur en présence de production décentralisée[END_REF][START_REF] Courtecuisse | Supervision d'une centrale multisource à base d'éoliennes et de stockage d'énergie connectée au réseau électrique[END_REF][START_REF] Garcia | Interaction des réseaux de transport et de distribution en présence de production décentralisée[END_REF][START_REF] Pham | Influences de la production décentralisée sur la gestion des infrastructures critiques des réseaux de puissances[END_REF]. In this sense, new and "intelligent" tools allowing decentralized energy production and storage systems to be managed while taking into account the status of the grid are needed to minimize the impact of such production. In France, the residential sector is the largest sector of energy consumption. It accounts for 28.7% of the final energy consumed. Besides, more than 60% of this consumption are due to heating systems (Ministère de l'écologie, 2011). That is why we propose in this paper a multi-criteria approach for energy resources management in buildings equipped with energy production and storage systems [START_REF] Kolokotsa | Implementation of an integrated indoor environment and energy management system[END_REF][START_REF] Mathews | Developing cost efficient control strategies to ensure optimal energy use and sufficient indoor comfort[END_REF]. The impact of the local energy production on the grid as well as the way multi-energy buildings and the grid interact are taken into account. Dynamic pricing is also considered. The first part of the paper describes the management strategy we propose for a gridconnected house equipped with energy production and storage systems. The second part is dedicated to the modelling of a single-storey house inhabited by four persons and equipped with photovoltaic solar panels, a vertical-axis windmill and batteries for electricity storage. The end part focuses on the optimal design of the just-mentioned systems and the results we obtained in simulation using the proposed strategy.

ENERGY MANAGEMENT STRATEGY

Systems and objectives

We address a single-storey house, located in Perpignan (south of France) and connected to the grid. This house is equipped with photovoltaic solar panels, a vertical-axis windmill and batteries for electricity storage. Batteries favour energy self-consumption (because of a better balance between supply and demand) and allow the impact on the electricity grid of a local production of energy to be minimized.

Performance criteria

In order to evaluate the proposed energy management strategy, several criteria about energy and economic performance have been defined.

Renewable energy coverage rate

is the ratio of the renewable energy produced and consumed in situ to the total energy consumed (equation 1). The total energy consumed is the sum of the amount of energy produced and consumed in situ (

) and the amount of energy extracted from the electricity grid (

). and are both expressed in kWh. This criterion has to be maximized to decrease the dependency on the grid of a building:

(1)

Energy self-consumption
is the ratio of the renewable energy consumed in situ (

) to the renewable energy produced ( ) (equation 2). and are both expressed in kWh. This criterion has to be maximized to promote energy self-consumption:

(2)

Use of renewable energy

In order to find a reasonable compromise between the renewable energy coverage rate (

) and the energy self-consumption criterion (

) and, as a result, to avoid the optimization process to lead to non-realistic configurations (highly undersized or oversized systems), both criteria are combined in a single criterion ( ) (equation 3):

(3)

Dynamic pricing and economic cost

A criterion dealing with economic cost (€) is also defined, not according to the purchase and sale prices currently charged by EDF (Electricité de France) but based on a future application of dynamic pricing in the coming years. Dynamic pricing is already in use in the energy market and consists in adjusting energy prices dynamically, with a short time step. Dynamic pricing reflects variations in electricity production costs as well as daily and seasonally variations in the grid load. So, a polynomial energy price model ( ) has been identified from both the grid load ( ) and outdoor temperature ( ) (equation 4, with ). The mean square error is about 16%.

(4) The economic cost criterion is then calculated as the difference between the cost related to the purchase of energy and the gain resulting from the sale of energy.

is the amount of energy injected to the grid and is the electricity price (equation 5):

(5)

Impact of a building on the electricity grid

The grid load varies in daily (several peaks of consumption) and seasonal (demand is higher in winter than it is in summer) cycles (Figure 2).

Figure 1: Load of the Perpignan grid in 2006

In order to define the status of the electricity grid, taking into account the daily and seasonal variations in its load, a daily load normalization is firstly done. Then a daily threshold is defined to highlight a limit beyond which injecting energy to the considered grid is not appropriate. The difference between this threshold and the load allows ascertaining if injecting energy is more or less favourable. This difference is normalized between 0 and 1 when the load is higher than the threshold and from -1 and 0 when the threshold is higher than the load. When the threshold is high, the electricity grid is in need of energy only during peaks of demand. In opposition, when it is low, energy can be appropriately injected to the grid most of the time. So, the impact of the local production on the grid is defined from as well as the normalized deviation between the threshold and the status of the grid ( ) (equation 6):

(6)

The impact on the grid related to energy extraction (equation 7) is defined in the same way as for , with the amount of energy extracted from the electricity grid:

(7)

Finally, an overall impact criterion is defined as the sum of and (equation 8). With a positive criterion, electricity is injected to the grid when demand is high while electricity is extracted from the grid when demand is low:

(8)

Energy resources management strategy

Figure 2 describes the strategy we propose to manage energy resources in multi-energy buildings connected to the grid and equipped with energy production and storage systems. The status of the grid is taken into account. One can highlight the following three main cases based on :

① The local systems overproduce. Energy production is higher than instantaneous consumption. Thus, the renewable energy production covers 100% of the instantaneous consumption and, as result, no energy is extracted from the grid. The surplus of energy is managed, taking into account the status of the grid. If energy demand is high ( close to ), the surplus of energy is injected to the grid. Otherwise, if the batteries are not already fully charged, the surplus is stored in whole or in part.

② Energy production and local energy demand are balanced. All the renewable energy produced is so consumed locally and there is no interaction with the grid and the batteries.

③ The local systems under-produce. So, energy consumption is higher than the renewable energy production. As a consequence, this local production of energy is completely auto-consumed and energy is released from the batteries, if they are charged. Otherwise, the missing amount of energy is supplied by the electricity grid.

BUILDING AND SYSTEMS MODELLING

This section of the paper focuses on the model of the building equipped with energy production (PV panels and, possibly, a vertical-axis windmill) and storage (batteries) systems we considered to test the proposed management strategy. Occupancy scenarios are also defined and presented.

Building model

The TRNSYS software has been used to model the thermal behaviour of a 150 m 2 single-storey house located in Perpignan (south of France), facing south and inhabited by four persons (TRNSYS 17, 2010). The building can be equipped with photovoltaic solar panels, a vertical-axis windmill and batteries for electricity storage. Perpignan experiences a warm and windy Mediterranean climate, similar to much of southern France. Figure 3 presents the plan of the house and the volume of the different rooms. This single-storey house (TRNSYS model 56) features a living room, a kitchen, three bedrooms, a bathroom, a corridor and a garage. Table 2 depicts the materials used in that house as well as their characteristics. Common materials were considered and the overall thermal insulation of the structure agrees with new French standards. U is the heat transfer coefficient of the materials used while U RT2005 is the French thermal regulation RT2005 value (Legifrance, 2006). The photovoltaic solar panels (TRNSYS model 194) and the vertical-axis windmill (TRNSYS model 90) have also been modelled. The TRNSYS model 194 is based on the calculation method presented by DeSoto [START_REF] Desoto | Improvement and validation of a model for photovoltaic array performance[END_REF] and allows determining both the current and power of a photovoltaic array at a specified voltage. This method uses various semiempirical equations. The TRNSYS model 90 is based on the work of Quinlan [START_REF] Quinlan | A time-series wind turbine array simulator[END_REF] and allows the power output of wind energy conversion systems to be calculated on the basis of a power versus wind speed characteristic. The impact of air density changes as well as wind speed increases with height is also considered in the model. The way energy is consumed in the house has been also studied. Because of its significant impact on energy consumption, the inhabitants' lifestyle has been also considered via occupancy scenarios fixed by the French thermal regulation RT2005 (CSTB, 2006).

The zoned HVAC (Heating, Ventilation and Air-Conditioning) system (maximum power is 1kW) is properly managed thanks to local regulators (TRNSYS model 56). Indoor temperature regulation is based on set-point profiles and the above-mentioned occupancy scenarios. Inhabitants are at home during working days from 0 a.m. to 10 a.m. and from 6 p.m. to 12 p.m. During weekends, they are present from 0 a.m. to 12 p.m. So, the indoor temperature set-point is defined as follows: 19°C for heating and 28°C for cooling during occupancy periods and 16°C for heating and 30°C for cooling if people are out the house (non-occupancy periods). Figure 4 depicts the annual power consumption of the considered 150 m 2 single-storey house for heating and cooling. When consumption is negative (respectively positive), heating (respectively cooling) mode is on. Finally, we used real data collected on site to validate the models. As a key point, one can note that energy production and consumption is impacted by climatic, geographical and physical conditions. Such conditions are part of the models. The meteonorm software provided meteorological data (meteonorm 7, 2012). Monthly, hourly and minute values are available for any location worldwide.

Figure 4: Annual power consumption for heating and cooling

Batteries modelling

The model describes the functioning of the batteries, i.e. the charge and discharge processes. At time t, the status of the batteries is related to their status at time t-1 and the production/consumption of energy at time t. Equations 9 and 10 are about charging mode and discharging mode, respectively:

(9) (10) with the inverter performance, the charge performance, the amount of energy available to charge the batteries, the amount of energy stored, the amount of energy produced by the local production systems after taking into account the energy losses due to the controller and the hourly self-discharge rate (equal to 10 -4 ). Performance is supposed to be constant and equal to 85% in charging mode while it is equal to 1 in discharging mode. The amount of energy stored in the batteries is used when the local production is not sufficient to meet demand. In opposition, energy is stored when the power supplied by the renewable energy systems exceed the house demand. However, it should be noticed that the amount of energy one can store in the batteries is related to and (equation 11):

(11)

Here, the maximum batteries capacity, , is equal to the rated capacity. The minimum capacity, , is determined from the Depth of Discharge (DoD), as shown in equation 12. DoD is used to describe how deeply the batteries are discharged: (12) According to the various specifications given by the manufacturer, life of the batteries can be extended if the DoD is between 30% and 50% [START_REF] Yang | Computer-aided design of PV/Wind hybrid system[END_REF]. So, we considered a conservative DoD of 50%.

ENERGY RESOURCES MANAGEMENT AND DESIGN OF ENERGY PRODUCTION AND STORAGE SYSTEMS

Parametric study and optimal design

The management strategy presented in the first part of the paper has been applied to the single-storey house whose model is presented in part two. Using this model and the models of the energy production and storage systems, a parametric study has been carried out to optimize the power of both the PV solar panels (power is related to the available surface on the roof and its orientation; maximum power is so 8 kWp) and the vertical-axis windmill (maximum power is 25 kWp) as well as the capacity of the batteries (capacity is related to size; maximum capacity is so 200 kWh what is equivalent to batteries of 2 m 3 ). The optimization process aims at maximizing an objective function, according to different values of the grid threshold. We choose as function to be maximized. Let us remember that is a compromise between the renewable energy coverage rate and the energy self-consumption criterion. We highlight in the next section the most remarkable configurations we obtained, with or without energy storage. Let us remember that we want energy self-consumption to be promoted and the impact of the local production on the electricity grid to be limited.

Results analysis

Table 3 First, we highlight three configurations as well as the results we obtained in simulation (one year) (Table 3). In addition, Figure 5 shows the impact of the sizing of the local energy production systems on . Configuration 1 is based on standard photovoltaic solar panels of 3 kWp only (no vertical-axis windmill and no energy storage). Configurations 2 and 3 are based on optimally designed systems: photovoltaic solar panels of 6.9 kWp for configuration 1 and PV panels of 3.8 kWp as well as a vertical-axis windmill of 11 kWp for configuration 2. At this time, energy storage (using batteries) is not considered. Taking configuration 1 as a reference, configuration 2 allows energy self-consumption to be increased by 61.7% and energy extraction to be reduced of 7.8%. In addition, energy costs are reduced of about 25% (3 0 €). With configuration 3, energy self-consumption is increased by 50% while energy extraction is reduced of about 11% (in comparison to configuration 2). Moreover, from configuration 1 or 2 to 3, increases in a significant way (from 8.38 or 9.53 to 20.45%). Figure 6 depicts the way energy is managed annually in the considered house when using configuration 3. Tables 4 and5 present new configurations as well as the results we obtained in simulation (one year). Configurations 4A, 4B, 5A, 5B, 6A and 6B (Table 4) are based on optimally designed photovoltaic solar panels and batteries. With this design, the criterion is maximized. Results are given for three thresholds allowing the status of the electricity grid to be taken into account: 30%, 50% and 70%. A threshold of 30% is representative of a grid able to accept most of the time the decentralized production (configurations 6A and 6B). In opposition, a threshold of 70% is typical of a grid having a preference for injection of energy during peaks of demand (configurations 4A and 4B). Finally, a threshold of 50% is for a balanced electricity grid (configurations 5A and 5B). Whatever the threshold, the first configuration proposed (i.e. 4A, 5A or 6A) is based on photovoltaic solar panels of 6.9 kWp (design is from configuration 2) (Table 3) and optimized batteries. The second configuration (4B, 5B or 6B) is based on optimally designed PV panels and batteries. Configurations 7A, 7B, 8A, 8B, 9A and 9B (Table 5) are based on optimally designed photovoltaic solar panels, vertical-axis windmill and batteries. Configurations 7A, 8A and 9A derive from configuration 3 (PV panels of 3.8 kWp and a windmill of 11 kWp). Figures 7 and8 highlight the impact of the sizing of the energy production and storage systems on , for a grid threshold of 70%. In a general way, optimally designed batteries favour energy self-consumption (approximately +25% for a threshold of 70%, with or without vertical-axis windmill) and allow injection to the grid to be reduced (for example, for a threshold of 50%, energy injection is reduced of about 35% in case of windmill and about 15% without windmill). In addition, with optimally designed batteries, the amount of energy supplied by the electricity grid is also generally reduced (considering PV panels as well as a verticalaxis windmill, this amount is reduced of about 10% for a threshold of 70% and 2% for a threshold of 50%; amount is almost the same for a threshold of 30%). Clearly, optimally designed batteries allow interaction between the single-storey house and the grid to be minimized. However, batteries increase and reduce . In some cases, for example when considering a threshold of 70%, the overall impact of the considered house on the grid is increased. Periods of interaction seem to be less favourable for the grid when considering a storage system. Figures 9 and 10 depict the way energy is managed annually when using configuration 4B or 7B. Furthermore, batteries do not reduce economic costs. Depending on both the configuration and the threshold, one can observe a slight increase in costs when using batteries. As a key point, the lowest the threshold, the lowest the impact of the batteries on the management of the available energy resources. Finally, as highlighted by the results we obtained, energy storage is one of the best ways to overcome intermittency in local production and allows a better match between production and demand.

CONCLUSION

The paper focuses on a multi-criteria approach for energy resources management in buildings equipped with energy production and storage systems. This approach takes into account the way the building and the electricity grid interact. The aim of the proposed strategy is to favour energy self-consumption while minimizing the negative impact the local production can have on the grid. Energy and economic criteria are proposed to evaluate this strategy we applied in simulation to a single-storey house inhabited by four persons. This house can be equipped with photovoltaic solar panels, a vertical-axis windmill and batteries. We used the TRNSYS software to model the thermal behaviour of the building. A parametric study allowed the design of the local production and storage systems to be optimized. We obtained several configurations allowing energy self-consumption to be promoted while avoiding the impact of the house on the grid to be clearly negative. With the proposed management strategy, a good equilibrium between decentralized energy production, energy needs and integration into the grid can be found. Future work will focus on improving the strategy using a predictive approach. We want the availability of the renewable resources, variations in energy demand and the status of the grid to be anticipated and the storage system management to be refined. We will also consider the impact of the geographical situation, insulation and lifestyle habits on energy resources management. (-977.20) -927.33 (-901.44) -982.12 (-977.20) -909.55 (-901.44) -978.44 (-977.20) -905.67 (-901.83) 1034 ( 616 4)

Figure 10: Energy management with configuration 7B (Table 5)

Figure 2 :

 2 Figure 2: Energy management algorithm (see sections "Performance criteria" and "Batteries modelling")

Figure 3 :

 3 Figure 3: Plan of the 150 m 2 single-storey house. Windows are represented in blue

Figure 5 :

 5 Figure 5: PV panels and vertical-axis windmill sizing. Impact on

Figure 6 :

 6 Figure 6: Energy management with configuration 3 (Table3)

Figure 9 :

 9 Figure 9: Energy management with configuration 4B (Table4)

Table 1 :

 1 Coefficients of the energy price model

		0	1	2	3	4	5
	0	6,58.10 1 -0,38.10 1 7,67.10 -2 -5,12.10 -4 3,48.10 -7 6,37.10 -9
	1	-1,77.10 1 9,27.10 -1 -1,64.10 -2 1,30.10 -4 -4,04.10 -7	-
	2	6,04.10 -2 -3,12.10 -3 4,41.10 -5 2,29.10 -7	-	-
	3	-5,16.10 -4 -1,96.10 -4 2,38.10 -6	-	-	-
	4	4,11.10 -4 1,19.10 -5	-	-	-	-
	5	2,01.10 -5	-	-	-	-	-

Table 2 :

 2 Characteristics of the materials used in the considered single-storey house

	Element	Material	Thickness [m]	U [W.m -2 .K -1 ]	U RT2005 [W.m -2 .K -1 ]
		BA13	0.013
	External wall	Rockwool Cinderblock	0.06 0.2	0.602	0.45
		Surface coating	0.02
		BA13	0.013
	Internal wall	Glass wool	0.04	0.845	/
		BA13	0.013
		Tiles	0.022
		Mortar	0.05
	Floor	Heavy concrete	0.16	0.415	0.4
		Expanded polystyrene	0.08
		BA13	0.013
	Ceiling	Glass wool Air knife	0.1 0.5	0.196	0.34
		Terracotta	0.01
	Garage ceiling	BA13 Terracotta	0.013 0.2	2.37	0.34
	Window	Double glazed	0.2	1.43	2.6

Table 4 :

 4 Configurations 4A, 4B, 5A, 5B, 6A and 6B with or without (in brackets) energy storage

	Threshold (%)	70		50		30
	Configuration (-)	Config. 4A	Config. 4B	Config. 5A	Config. 5B	Config. 6A	Config. 6B
	PV panels (kWp)	6.9	8	6.9	8	6.9	7.9
	Batteries (kWh)	40 (-)	50 (-)	20 (-)	50 (-)	10 (-)	50 (-)
		7117 (5345)	7959 (5746)	5626 (5345)	6199 (5746)	5326 (5345)	5748 (5711)
		2695 (4860)	3370 (6087)	4191 (4860)	5476 (6087)	4561 (4860)	5861 (5974)
		22266 (24038)	21425 (23638)	23757 (24038)	23184 (23638)	24058 (24038)	23635 (23672)
		2166 (-)	2717 (-)	452 (-)	611 (-)	82 (-)	112 (-)
		69.74 (52.38)	67.26 (48.56)	56.08 (52.38)	52.39 (48.56)	52.99 (52.38)	49.19 (48.88)
		24.22 (18.19)	27.09 (19,55)	19.48 (18.19)	21.10 (19.55)	18.41 (18.19)	19.56 (19.44)
		16.89 (9.53)	18.22 (9.49)	10.92 (9.53)	11.05 (9.49)	9.75 (9.53)	9.62 (9.50)
		-997.27

Table 5 :

 5 Configurations 7A, 7B, 8A, 8B, 9A and 9B with or without (in brackets) energy storage

	Threshold (%)	70		50		30
	Configuration (-)	Config. 7A	Config. 7B	Config. 8A	Config. 8B	Config. 9A	Config. 9B
	PV panels (kWp)	3.8	5.8	3.8	4.2	3.8	3.5
	V.-a. windmill (kWp)	11	15	11	18	11	20
	Batteries (kWh)	200 (-)	200 (-)	190 (-)	200 (-)	100 (-)	200 (-)
		14251 (10994)	17313 (12917)	12659 (10994)	16000 (13162)	11868 (10994)	15305 (13688)
		4621 (9124)	9373 (15431)	6645 (9124)	12669 (16774)	7848 (9124)	15190 (19327)
		15132 (18390)	12070 (16466)	16725 (18390)	13383 (16222)	17515 (18390)	14079 (15696)
		4504 (-)	6058 (-)	2479 (-)	4105 (-)	1276 (-)	2997 (-)
		70.84 (54.65)	61.07 (45.57)	62.92 (54.65)	53.45 (43.97)	59.00 (54.65)	48.53 (41.46)
		48.50 (37.41)	58.92 (43.96)	43.08 (37.41)	54.45 (44.79)	40.39 (37.41)	52.09 (46.58)
		34.36 (20.45)	35.99 (20.03)	27.11 (20.45)	29.10 (19.69)	23.83 (20.45)	25.28 (19.31)
		-531.54 (-468.52) -136.38 (-52.35) -509.71 (-468.52)	-34.81 (26.89)	-488.84 (-468.52)	55.02 (106.62)
		942 (-662)	911 (-1166)	2755 (1551)	3920 (3574)	3978 (3208)	6901 (4013)
		3790 (4634)	3036 (4326)	844 (1024)	677 (-583)	-2413 (-2459)	-1995 (-525)
		4732 (3972)	3947 (3160)	3599 (2575)	4598 (2991)	1565 (749)	4906 (3488)


Antoine Garnier
email: a.garnier@pyres.com

Julien Eynard

Matthieu Caussanel

Stéphane Grieu
email: stephane.grieu@promes.cnrs.fr

HVAC CONTROL AND COMFORT MANAGEMENT IN NON-RESIDENTIAL BUILDINGS

Keywords:

In France, non-residential buildings account for a significant part in energy consumption. Moreover, a large part of this consumption is due to Heating, Ventilation and Air-Conditioning (HVAC) systems, which are generally badly handled. So, the present work deals with an efficient approach allowing energy consumption to be minimized while ensuring thermal comfort. In this sense, a predictive control strategy is proposed for existing zoned HVAC systems considering the Predicted Mean Vote (PMV) index as a thermal comfort indicator. In order to test the developped strategy in simulation, a non-residential building located in Perpignan (south of France) has been modelled using the EnergyPlus TM software. The aim is to limit the times during which the HVAC sub-system is turned on and to ensure a satisfactory thermal comfort during working time. This approach, computationally tractable, allows thermal comfort requirements to be met without wasting energy.

INTRODUCTION

Almost half of the electricity consumption in nonresidential buildings is due to Heating, Ventilation and Air-Conditioning (HVAC) systems [START_REF] Pérez-Lombard | A review on buildings energy consumption information[END_REF]. As a result, new approaches are needed to make (central or zoned) HVAC systems more efficient. In addition, thermal comfort requirements must be met but thermal comfort is subjective, hard to define and even harder to achieve in non-residential buildings. As an interesting work, [START_REF] Endravadan | Régulation des systèmes de chauffage et de climatisation basée sur la sensation thermique humaine. Impact sur la consommation d'énergie dans les bâtiments[END_REF] has developed a method to achieve a good thermal comfort in buildings using a Local Heating System (LHS) for each occupant. This technique allows significant energy savings but is not well adapted in case of occupants moving frequently. Moreover, such a technique needs additional heating equipments to be installed, whereas our objective is to develop an efficient solution for existing HVAC systems. Moros ¸an et al. (2010) have proposed a predictive approach, what is a very interesting solution, but on-line optimization is needed. Otherwise, the Pyrescom Company, our industrial partner, has developed a monitoring system that carries out meteorological parameters and energy measurements to improve energy efficiency in nonresidential buildings (Batnrj project, www.pyres.com). The collected data are sent to a remote server with a significant computational power. These data are used to find out possible ways to finalize an efficient HVAC control strategy. Several buildings are instrumented with the Pyrescom monitoring system, including a 1000 m 2 non-residential building located in Perpignan (south of France). This reference (pilot) building has been modelled using the EnergyPlus TM software and allowed the proposed strategy about HVAC management to be tested and evaluated. As a first approach, only the manufacturing area is considered. In the other rooms of the building, the HVAC sub-systems are all turned off. Energy consumption, thermal comfort and computation time are considered as performance indicators. Thermal comfort is evaluated on the basis of the Predicted Mean Vote (PMV) index, which is a standardized indicator designed to estimate the thermal sensation of occupants (NF EN ISO 7730, 2006). This index allows temperature to be adjusted in a building according to the period of the year or work activities and behaviours. So, we propose in this paper a predictive strategy for managing zoned HVAC systems without on-line optimization. This strategy is computationally tractable and the developed algorithms will be implanted in an embedded system. In order to develop the predictive controller allowing the strategy to be implanted, a linear model that mainly links the PMV index with solar radiation, outdoor temperature and internal heat gain has been identified. With this model, the PMV index can be used as a set-point and thermal comfort can be maintained in a desired interval which can be adjusted by people working in the considerd non-residential building. The paper is organized in the following way: first, the reference building modelled using the EnergyPlus TM software is described. The following section focuses on thermal comfort as well as on the way the PMV index can be controlled using the proposed strategy. Next, the PMV linear model and its identification process are described. Then, the predictive control strategy we propose and the results we obtained in simulation are presented. We compared these results with the results given by various standard (non-predictive) strategies. The paper ends with a conclusion and an outlook to future work.

REFERENCE BUILDING

In order to evaluate the proposed strategy, a reference building has been modelled using the EnergyPlus TM software, which is able to perform accurate building Franc ¸aise, 2006). This non-residential building features three main areas of 340 m 2 each (figure 1), with different uses. About a dozen employees work in offices at the ground and first floors (green and yellow areas). The red area in the first floor is a manufacturing area where about 6 persons work seated or in a standing position. The last room of the ground floor is a warehouse (blue area). This room is not heated.

(cm) (W•m -1 •K -1 ) (kg•m -3 ) (J•kg -1 •K -1 )

Figure 1: Topology of the reference building

For both the warehouse and the manufacturing area, ceiling is 3.90 m. In the offices, there is a suspended ceiling at 2.70 m. The materials used in the building are listed in table 1. Exterior walls consist of several layers of different materials. From the outside to the inside, there is a brick layer, heavy weight concrete, an insulation board, and finally a gypsum board. Interior walls are composed of two gypsum boards. The south face and a part of the west face of the building are composed of a large glazed area. These glasses were treated by filtering infrared beam to avoid overheating due to excessive solar radiation exposure in summer.

The other glasses in the building consist in 3 mm double glazed bays. Heating is handled in the building by a zoned electrical HVAC system consisting in several sub-systems, one for each area. Only the temperature set-point (with a thermostat for heating and another one for cooling) can be adjusted. As previsously mentioned in the paper, only the manufacturing area and the process of heating are considered to test the proposed approach about HVAC system management. This manufacturing area is composed of an open space of 230 m 2 and three storage rooms of 110 m 2 . HVAC power is 10 kW. Coefficient of Performance (CoP) is 3.8 while maximum air flow rate is 0.6 m 3 •s -1 , which represents 2.4 vol•h -1 .

Weather data (outdoor temperature, solar radiation, wind speed) are required to perform the simulation. So, we used real data from year 2011 provided by the Pyrescom monitoring system. Since atmospheric pressure measurements were missing, we used data from the Perpignan airport which is located 7 km away from the building. Measurements were carried out with a time step of 30 seconds while averaged values were saved every 15 minutes and stored in a database. As a consequence, the time step of the simulation is 15 minutes. A Mediterranean climate, relatively mild, can be found in Perpignan. Figure 2 shows how outdoor temperature evolves at 6 a.m., from January to December 2011 (the simulation period). THERMAL COMFORT

Predicted Mean Vote

The Predicted Mean Vote (PMV) index is used as a thermal comfort indicator. This indicator was developed by [START_REF] Fanger | Assessment of man's thermal comfort in practice[END_REF], before to be standardized by international organizations (NF EN ISO 7730 (2006) and ANSI/ASHRAE Standard 55 ( 2010)). The PMV index quantifies the thermal sensation felt by people in a room and is described by a scale ranging between -3 (cold) and +3 (hot) (Table 2). The exchange of heat between the human body and its environment impacts on thermal comfort. Thermal comfort is highly subjective and can be considered as perfect when the sum of exchanges is zero. Equation 1 depicts the way one can compute the PMV index:

P M V = [0.303exp -0.036M + 0.028] × L (1)
with L the difference between the heat produced and the heat lost.

L = M -W -H 1 -H 2 -H 3 -H 4 -H 5 -H 6 (2)
M is the metabolism, which is described below. W is the external work and is considered to be null. H n are the heat fluxes (W•m -2 ). H 1 is the heat loss by diffusion through the skin and H 2 is the heat loss by sweating. H 3 and H 4 are the losses by latent and dry respiration, respectively. Finally, H 5 is the heat loss by radiation and H 6 is the heat loss by convection. To calculate these heat losses, several parameters about environment and occupants are taken into account: indoor air temperature (T air ), radiant temperature (T wall ), relative humidity (HR), air speed (v air ), metabolic activity and clothing thermal insulation. It can be noticed that air speed is not calculated by the EnergyPlus TM software. However, this missing information is not critical because air speed has no influence on the PMV value as long as it remains below 0.1 m•s -1 . This is mostly the case within the non-residential building we considered as reference building. Moreover, metabolic activity is supposed to be constant and only depends on the considered area. In offices, people work in a sitting position most of the time and, as a result, M is set to 70 W•m -2 (i.e.

INTERVAL ICL VALUE (clo) t 6 < -5 • C 1 -5 • C ≤ t 6 < 5 • C 0.818 -0.0364t 6 5 • C ≤ t 6 < 26 • C 10 -0.1635-0.0066t6 t 6 ≥ 26 • C 0.46
According to theses equations, clothing thermal insulation varies from 0.58 clo, during winter time, to 0.46 clo, during summer time. Figure 3 depicts the way clothing thermal insulation evolved between January and December 2011. Usual clothes for summer are a pant with a short-sleeved shirt, while during winter, usual clothes are a trouser with a long-sleeved shirt. Looking at figure 2, the result seems to be realistic. We can highlight that the 2011 winter was mild, so the clothing thermal insulation was moderate. At the end of January, temperature has strongly decreased and the algorithm has automatically adjusted the clothing thermal insulation value.

Control of thermal comfort

The air temperature set-point T sp air is adjusted by the HVAC sub-system to maintain an adequate thermal comfort in the manufacturing area. A desired value for the PMV index (P M V sp ) has to be reached, that is why we need to estimate the necessary air temperature T air from T wall , HR, v air and M . Because of the complexity as well as the nonlinearity of the PMV equation, one can not solve this equation in an analytical way to find the appropriate air temperature. Thus, numerical methods are used to solve equation 3. Next, T sp air is set according to the computed value of T air .

P M V (T air , θ) = P M V sp (3)
with θ bringing together T wall , HR, v air , and M and P M V sp the PMV set-point from which we computed the air temperature set-point T sp air .

Comfort level controller

Figure 4: Control of thermal comfort

Different iterative methods have been tested with the aim of finding the fastest and the most efficient one. The standard algorithms we tested will not be detailed here. The stopping criterion is a tolerance of 0.05 • C for T air . First, we used the binary search algorithm. The number of iterations is related to the desired accuracy, given that convergence is linear. The initial values of the minimal and maximal thresholds were set to 15 and 30 • C, respectively. At each iteration, the gap around the solution is reduced until it is lower than the desired accuracy. The second algorithm used is the Newton-Raphson method. The solution is computed, applying a correction term defined as the ratio between the function and its derivative. Since it is not possible to find the derivative analytically, it is approximated. The initial value was set to 20 • C. The main advantage of the Newton-Raphson method lies in its quadratic convergence. The third algorithm we considered is the secant method. It is quite similar to the Newton-Raphson method, but uses a specific equation to approximate the derivative, based on the two previous values. The initial values were 20 • C and 25 • C. Table 4 summarizes the performance results we obtained using these three methods. Although the Newton-Raphson method needs three time less iterations to reach the solution than the binary search algorithm, computation time is similar. Slowness is due to the PMV index being calculated three times per iteration instead of only one time with the binary search algorithm. With the secant method, convergence is slightly slower but the PMV index is computed only once per iteration. As a consequence, computation time is reduced by half and the secant method has been chosen among the three methods we tested.

IDENTIFICATION OF A LINEAR MODEL

PMV model of reduced order

In order to maintain the PMV index in the desired interval using a predictive control approach, a model of the system to be controlled is required. So, a real-time model that links the PMV index and (i) outdoor temperature (T out ), (ii) solar radiation (SR) and (iii) internal heat gain (IG) has been identified. Internal heat gain deals with the heat generated by people in a room (metabolism) and devices (mainly lighting and electrical devices). The heating system is indirectly taken into account via the air temperature set-point (T sp air ). Figure 5 depicts the input/output model we proposed.

Linear PMV model

Figure 5: PMV linear model

State-space model

As previously mentioned, the proposed management solution has to be computationally tractable. Indeed, it will be implanted in an embedded system that will control the different areas of a building (let us remember that we focus here on the manufacturing area). So, a model with reduced order is needed to carry out simulation on such a platform. However, identification will be realized using a remote server, which has more powerful computing capabilities. The chosen model is a state-space model which is equivalent to a linear transfer function. We considered a n-order space model, i.e. a discrete MISO (Multiple Input/Single Output) system defined as follows:

x k+1 = Ax k + Bu k y k = Cx k (4)
where A ∈ R n×n , B ∈ R n×r and C ∈ R 1×n . n is the system order and r the number of inputs. u k ∈ R r×1 is the command vector at instant k while x k ∈ R n×1 is the state vector. y k ∈ R is the system output.

Identification

To find the optimal parameters of the model (matrix A, B and C), an identification phase is necessary. So, a dataset has been generated using the EnergyPlus TM model of the considered non-residential building. Let us note that in a real building, identification will be carried out directly from measurements provided by the Pyrescom monitoring system, without using the thermal model of the building. Using generated (or measured) data, identification is achieved using Matlab R and the N4SID (Numerical algorithm for Subspace State Space System IDentification) algorithm, based on the work of [START_REF] Overschee | N4SID subspace algorithms for the identification of combined deterministic-stochastic systems[END_REF]. In the present work, we used eight weeks of data to identify the model parameters. We obtained the best fitting results with a 4-order model. Models of a higher order of complexity led to over-estimated parameters, oscillations and a decreasing accuracy. In opposition, models of a lower order of complexity led to under-estimated parameters and a low accuracy. The identification process was performed in 21 seconds, so it can be handled by a remote server. Figure 6 shows PMV values given by EnergyPlus TM and the developed linear model. The temperature set-point is set to 22 • C during occupancy.

The FIT is 73.8%, the Mean Relative Error (MRE) is 6.6% and the Mean Absolute Error (MAE) is 0.11. Table 5 shows the time constant of each pole and zero of the identified linear model.

State observer

In order to perform a simulation with the state-space model (a forecasting of the PMV index over the prediction horizon), the model has to be initialized correctly. That is why we used a state observer to keep the model as close as possible to the state of the real system. By using a state observer, one can avoid divergence due to perturbations or non-modelled dynamics. So, the observer allows estimating the state vector xk from measured inputs (u k ) and outputs (y k ) (equation 5):

xk+1 = Ax k + Bu k + K(y k -ŷk ) ŷk = C xk (5)
with ŷk the output rebuilt by the observer and K ∈ R n×1 its gain matrix. The gain matrix K is computed to obtain a new system with poles 10 times faster than those of the identified linear model. The proposed predictive strategy is summarized by figure 7. EnergyPlus TM is used to simulate the behaviour of the real non-residential building we considered as reference building. The controlled output is the PMV index. The proposed Model Predictive Controller (MPC) uses the identified linear model to perform some predictions and to optimize the way the heating system will operate (when it will be turned on and off), taking into account the constraints about thermal comfort during occupancy. The controller computes the HVAC air temperature set-point (the manipulated input). The state observer is used to initialize correctly the state vector of the internal model before each prediction. Based on previous day values, the forecasting unit estimates the considered exogenous disturbances (T out , SR and IG). As previously mentioned in the paper, thermodynamic simulations are carried out using EnergyPlus TM with MPC set-point values computed by Matlab R . These two softwares are interfaced using the MLE+ toolbox [START_REF] Nghiem | MLE+: a Matlab-EnergyPlus co-simulation interface[END_REF]. In real buildings equipped with HVAC systems, EnergyPlus TM simulations are no more needed. As a first approach, only the manufacturing area is considered. In the other rooms, the HAVC sub-systems are turned off. To assess performance, energy consumption and thermal comfort during occupancy periods are considered. The main objective is to satisfy thermal comfort requirements when people work in the manufacturing area and to avoid enegy waste during the rest of the time. The thermal comfort interval is defined on the basis of a PMV value ranging between -0.5 and 0.5. The temperature set-point is so computed with a PMV index equal to zero. In real buildings, these parameters will be adjusted in real time, according to the thermal sensation of the workers. With the proposed strategy, one can optimize the way the HVAC sub-system switches from one operation mode to another. Figure 8 depicts the predictive algorithm used. As mentioned above, the sampling time is 15 minutes. First, the air temperature set-point is computed to set the PMV setpoint (P M V sp = 0). Moreover, the state of the statespace model is defined by the observer. Depending on occupancy, two cases are possible:

PREDICTIVE CONTROL STRATEGY

(i) When the manufacturing area is occupied (Z(k) = 1), we want to turn off the HVAC sub-system as soon as possible while ensuring that thermal comfort will meet requirements until all the people leave the room, taking into account its thermal inertia.

The HVAC sub-system is considered to be turned off (HV AC(k : k + p/k) = 0) along the forecasting horizon while outdoor temperature, solar radiation and internal gain (exogenous disturbances) are estimated on the basis of previous day values. The PMV index is forecasted using the proposed linear model. As long as the manufacturing area is occupied, the predictive algorithm checks if thermal comfort requirements are satisfied (P M V (k :

k + i/k) > -0.5) ∧ (P M V (k : k + i/k) > 0.5).
If the constraints are not met, it means that the HVAC sub-system must not be turned off now and, as a result, the air-temperature setpoint is set to the value initially computed. When the manufacturing area is no more occupied (Z(k+i/k) = 0), thermal comfort is necessarily satisfied and the HVAC sub-system is turned off (HV AC(k) = 0).

Action to do

Test phase

Yes No

We look if HVAC system should be turned on, right now, to satisfy future thermal comfort constraints

We look if HVAC system could be turned off, right now, but satisfying thermal comfort constraints until the end of occupancy

No

No Yes (ii) When the manufacturing area is empty (Z(k) = 0), the algorithm searches for the last moment to turn on the HVAC sub-system. The optimal instant to switch on the system is defined as the instant allowing thermal comfort requirements to be met at the time the first worker arrives in the manufacturing area. If thermal comfort is ensured at least two sample times before the first worker arrives, decision is delayed and the sub-system is switch off for now (HV AC(k) = 0). If thermal comfort is not ensured at least one sample time before the first worker arrives, the sub-system is switched on (HV AC(k) = 1) and the air temperature set-point initially computed is used.

Yes

RESULTS

This section of the paper focuses on the results we obtained with the predictive strategy we proposed to manage zoned HVAC systems in non-residential buildings. To evaluate performance dealing with thermal comfort, we considered the percentage in time for which the PMV value is between -0.5 and 0.5, the manufacturing area being occupied. This percentage is directly related to constraints satisfaction. The average value of the PMV index is already computed to evaluate the thermal sensation of people in the manufacturing area. Moreover, energy consumption is calculated. With these criteria, one can compare the proposed predictive strategy with non-predictive ones. Finally, the time needed to compute the air temperature set-point is recorded and allows computation requirements to be evaluated. The results are grouped in table 6.

Non-predictive strategies

In the real building, for now, the zoned HVAC system is always turned on and the air temperature setpoint remains the same (T sp air = 22 • C) during daytime, nighttime and week-end periods. This is the reference scenario (S1). With this scenario, thermal comfort is good (the average PMV index is very close to zero) and constraints are always met. Figure 9 (a) depicts the way the PMV index (top) and power consumption (bottom) evolves. S2 allows the same strategy to be applied but using a PMV set-point, instead of an air-temperature set-point. So, T sp air is adjusted at each time step, what requires 2.4 ms to be calculated. Again, the average PMV index is very close to zero and the percentage in time for which the PMV value is between -0.5 and 0.5 (the comfort criterion) is 100%. As an other option, we used a scheduler to turn off the HVAC sub-system during the night and week-ends and to turn it on in the morning, two hours before people arrive in the manufacturing area. Two hours is a standard amount of time for heating the building. On this basis, we defined two more scenarios: S3 (air temperature set-point) and S4 (PMV set-point). The results we obtained highlight a significant decrease in energy consumption: -49% (-204 Wh/day•m 2 ) with S3 and -42.5% (-177 Wh/day•m 2 ) with S3, taking as a reference the results we obtained with S1. However, comfort is not quite as good (-2%). As it can be no-

Predictive strategy

With the proposed predictive strategy (scenario S5), the above-mentioned problem is solved. Indeed, as it can be seen in figure 9, anticipation is related to the considered day. During cold days or after week-ends, anticipation time is longer than in case of warm days. Thermal comfort requirements are just met when the first worker arrives at the building in the morning. As a result, energy waste is low and thermal comfort is very good. The HVAC sub-system is switched off at the end of the day, some hours before occupancy ends. This allows energy savings without impacting (negatively) thermal comfort. During warmer weeks, the predictive strategy has other advantages. Anticipation time is shorter than when using the scheduler and the HVAC sub-system is often turned off at the end of the morning, what allows big energy savings during the afternoon. Thermal comfort requirements are met until the last worker leaves the building. Energy consumption is reduced of about 44.5% (-185 Wh/day•m 2 ) and 43.9% (-181 Wh/day•m 2 ), in comparison to the results we obtained with strategies S1 and S2, respectively. Thermal comfort is quite identical. In addition, energy consumption is similar than when using the scheduler but thermal comfort is always better. Finally, this predictive strategy has a low-computational cost. Only 3 to 5 ms more are needed than with S1 or S3. As a result, the algorithm can be implanted in an embedded system.

CONCLUSION

This paper focuses on a predictive strategy used to manage energy consumption as well as thermal comfort in non-residential buildings. In order to test the proposed strategy in simulation, we modelled a building located in Perpignan (south of France). As a first approach, only the manufacturing area has been considered. We used the Predicted Mean Vote (PMV) index as a thermal comfort indicator. The strategy is computationally tractable and the developped algorithms can be implanted in an embedded system, what is the main objective of the Batnrj project (supported by the Pyrescom company). As a key point, it clearly appears, when comparing the results we obtained in simulation with the proposed predictive approach and the results given by different standard (non-predictive) strategies, that predictive control offers a significant gain in energy consumption reduction and thermal comfort satisfaction. The predictive strategy allows the HVAC sub-system to be turned on and off at the right time. As a result, the system is turned on a few hours before the next occupation period to satisfy thermal comfort requirements (when people come to the building) and is turned off before people leave the building to reduce energy consumption. Future work will focus on applying the proposed predictive strategy to all the occupied rooms of the building. Then, this strategy will be tested in real buildings. Finally, a predictive controller with on-line optimization carried out by a dedicated remote server will be developed.

Figure 2 :

 2 Figure 2: Outdoor temperature at 6 a.m., from January to December 2011

Figure 6 :

 6 Figure 6: PMV index estimation. The red solid line is the PMV index given by EnergyPlus and the blue dashed line is the fitted PMV index (linear model)

Figure 7 :

 7 Figure 7: The proposed predictive control strategy

Figure 8 :

 8 Figure 8: Predictive control algorithm

Table 1 :

 1 Properties of the materials used in exterior walls

	LAYER	THICKNESS CONDUCTIVITY DENSITY SPECIFIC HEAT

Table 2 :

 2 Thermal sensation scale

	PMV VALUE THERMAL SENSATION
	+3	hot
	+2	warm
	+1	slightly warm
	0	neutral
	-1	slightly cool
	-2	cool
	-3	cold

Table 3 :

 3 Clothing thermal insulation

Table 4 :

 4 Evaluation of the tested algorithms

	METHOD	NUMBER OF	COMPUTATION
		ITERATIONS	TIME (ms)
	Binary search	9	4.6
	Newton-Raphson	2-3	5
	Secant	4-5	2.4

Table 5 :

 5 Poles and zeros of the identified linear model (*: two conjugated roots)

		TIME	TIME
	ROOTS	CONSTANT CONSTANT
		(seconds)	(hh:mm:ss)
	Poles	830 * 29221 *	0:13:51 8:07:02
	Zeros (T out )	786 2543596 *	0:13:06 706:33:16
	Zeros (S R )	7767 37055 *	02:09:28 10:17:35
		1485	0:24:45
	Zeros (T sp )	1801	0:30:01
		21125	5:52:05
	Zeros (I G )	704 700152 *	0:11:45 194:29:13

Table 6 :

 6 Results for the strategies performance from January to February 2011. (C) is Continuous strategy, (S) is Scheduler operating mode and (P) is Predictive strategyticed in figure 9 (b), S3 suffers from a lack of flexibility. Some days, thermal comfort is reached too early, what leads to energy waste. Sometimes it is reached too late. In this case, thermal comfort is not ensured.

		OCCUPANCY	VACANCY	CONSUMPTION	COMFORT	AVERAGE COMPUTATION
		SET-POINT	SET-POINT		CRITERION	PMV	TIME (ms)
	S1 (C) T sp air = 22 • C T sp air = 22 • C	416	99.8%	0.05	0
	S2 (C)	P M V = 0	P M V = 0	412	100%	0.01	2.4
	S3 (S) T sp air = 22 • C	OFF	212	97.7%	-0.20	0
	S4 (S)	P M V = 0	OFF	239	98.0%	-0.03	2.4
	S5 (P)	P M V = 0	OFF	231	99.3%	-0.05	3 to 5

(Wh/day•m 2 ) Figure 9: (a) Scenario S1, (b) Scenario S3, (c) Scenario S5. Simulation is from January 26 to February 1st, 2011. Top: Indoor temperature set-point (blue line), PMV index (red line) and thermal comfort constraints (green dashed line). Bottom: Power consumption (blue line)

ACKNOWLEDGMENT

The authors want to thanks the Pyrescom company for its financial support. Jean-Michel Cabanat and Cédric Calmon are acknowledged for their technical help.


Mouchira Labidi

Julien Eynard

Olivier Faugeroux

Stéphane Grieu

OPTIMAL DESIGN AND MANAGEMENT OF THERMAL STORAGE TANKS FOR MULTI-ENERGY DISTRICT BOILERS

Keywords: Multi-energy district boiler, thermal energy storage, stratification phenomenon, thermal losses, optimal design, management strategy

As part of the second phase of the OptiEnR research project, the present work deals with improving multi-energy district boilers operation, by adding optimally sized and controlled thermal storage tanks to the plants. Previous studies focused on both a sizing approach based on a parametric analysis and an operation strategy. The aim of the present work is to improve the design of the tanks, in particular by evaluating the thermal losses and finding the adequate insulating materials. We focused on the stratification phenomenon and highlighted that the effectiveness of a thermal storage tank is related to the time during which the stored energy can be kept without considerable degradation. A case study allows the impact of thermal energy storage to be quantified.

INTRODUCTION

Nowadays, the storage of energy in suitable forms is a scientific and technical challenge. A number of approaches have been investigated over the years to store thermal energy, including rock storage and phase change materials, but the most pragmatic solution is using water. Indeed, water is an excellent storage medium for low-to-medium temperature applications because of a high volumetric heat capacity, a low cost, very good security properties and widespread availability. Consequently, hot water tanks (for stratified thermal energy storage) are considered as an attracting technology and used in several industrial applications [1,2]. It should be noted that thermal stratification has a major influence on performance. Stratification can be impacted by turbulence inside the tank as well as thermal losses [3]. First, using discretization of time and space, a stratified tank has been modeled. The resolution of the resulting model allows the water temperature for each of the tank layers to be accurately estimated. Next, a design methodology based on a complete parametric analysis is proposed in order to optimize the tank shape and find the adequate insulating material. Then, we used the proposed methodology in order to design a 200 m 3 hot water storage tank that will be installed at a Cofely GDF-Suez multienergy district boiler located in Northeast France (Alsace region). We carried out simulations in order to highlight the impact of the geometrical characteristics of the tank, its insulation and the weather conditions on the thermal losses. As a result, we found that heat losses have to be considered as a key factor when designing thermal storage tanks. Indeed, the efficiency of such systems is mainly related to its design and insulation.

MODELING OF THE TANK

In order to investigate the main factors leading to thermal losses, a model describing the thermal stratification phenomenon in the hot water tank has been developed. Unlike simplistic models in which temperature is supposed to be uniform throughout the volume of the tank, the proposed discrete space model, adapted from the "turbulent mixing model" [4], takes into account the existing temperature gradient. The tank is divided into N equal volume layers. When energy is stored, hot water is allowed to enter by the top of the tank and is assumed to mix with the m first top layers. In discharging (release) mode, the process described above is reversed. So, cold water is allowed to enter by the bottom of the tank and is assumed to mix with the m first bottom layers. Heat loss by conduction through the walls and by convection with the ambient air, conduction between layers as well as inlet and outlet thermal mixing are taken into account. The resolution allows the water temperature for each layer of the tank to be calculated.

DESIGN OF THE TANK

As previously mentioned in the paper, the optimal volume of the thermal storage system can be defined on the basis of economic and energy criteria. However, a key point in the project is to design the tank by defining adequate geometrical characteristics as well as finding the insulating material allowing the thermal losses to be limited. To carry out this study, we used the model of the stratified water tank described in the previous section of the paper.

Case study

We selected as a case study a multi-energy district boiler managed by Cofely GDF-Suez. The plant, located in Northeast France (Alsace region), is connected to a heat network and equipped with a 4 200 kW biomass (wood) boiler and two gas boilers of 7 000 kW. A preliminary study, based on economic and energy criteria, has shown that 200 m 3 is the optimal size of the tank [5].

Geometrical characteristics.

In order to define the adequate geometrical characteristics of the thermal storage tank, we evaluated in static mode (no water is passing through the tank) the impact of the ratio of Height to Diameter (H/D) on the thermal losses. We supposed that the 200 m 3 thermal storage tank is not insulated at all and initially filled with hot water at a temperature of 105 °C. The tank is not used during 24 hours. Outdoor temperature is supposed to be equal to 0 °C and unchanged through the day. Figure 1 highlights the way the ratio H/D impacts on the thermal losses. As it can be noted, by choosing for the tank a height equal to its diameter (H/D = 1), the average water temperature is decreased by 44 °C at the end of the day. Thus, such a temperature is 16 °C higher than when considering a ratio H/D equal to 5. So, we designed the tank as follows: V tot = 200 m 3 , H = D = 6.33 m. Insulation. The insulating material used and its thickness play an important role in the minimization of the thermal losses and, as a result, in saving energy. Figure 2 shows the impact of both the material used and its thickness on the thermal losses. If the objective is to lose no more than 1°C per day, the possible choices are: a 100 mm layer of Rockwool, a 50 mm layer of rigid polyurethane foam or a 150 mm layer of foam glass granulate. A definitive choice based on market price can then be made. Weather conditions. Thermal losses are also influenced by the weather conditions, in particular outdoor temperature and wind speed. We carried out a parametric analysis in order to outline both the impact of the weather conditions on the tank operation during the cooling down phase and the way an appropriate insulation (e.g. a 100 mm thick layer of rock wool) can cope with unfavorable conditions. From Figures 3 and4, we can easily notice that for a given ambient temperature, the impact of wind, implicitly considered through the heat transfer coefficient of air (h out ), can be limited if the tank is well isolated. In addition, to limit the effect of forced convection created by the wind and prevent the tank to be subjected to very low ambient temperatures during cold days, it must be located in a place well sheltered from both the wind and cold (e.g. a place where it can be buried).

RESULTS AND DISCUSSION

Table 1 summarizes the characteristics of the designed thermal storage tank. Adding an appropriately shaped and correctly insulated storage tank to the plant can have economic and energy benefits. Insulation allows the thermal losses to be minimized, in particular when the tank is not used (static mode). Table 1. Characteristics of the thermal storage tank.

Figure 1 .

 1 Figure 1. Impact of the ratio of Height to Diameter (H/D) on the thermal losses (static mode, non-insulated tank).

Figure 2 .

 2 Figure 2. Impact of the insulating material used.

Figure 3 .

 3 Figure 3. Impact of the weather conditions in case of a non-insulated tank.

Figure

  Figure 4. Impact of the weather conditions in case of an insulated tank. Volume Height Diameter Insulating material Thickness of insulating material 200 m 3 6.33 m 6.33 m Rockwool 100 mm

[ 1 ]

 1 Dehghan A. A. and Barzegar. A. 2011. Thermal performance behavior of a domestic hot water solar storage tank during consumption operation. Energy Conversion and Management, 52, 1 (January 2011), 468-476. [2] Han Y. M., Wang R. Z., and Dai Y. J. 2009. Thermal stratification within the water tank. Renewable and Sustainable Energy Reviews, 13, 5 (June 2009), 1014-1026. [3] Kaloudis E., Grigoriadis D.G.E., Papanicolaou E. and Panidis T. 2013. Large eddy simulations of turbulent mixed convection in the charging of a rectangular thermal storage tank. International Journal of Heat and Fluid Flow, 44 (December 2013), 776-791. [4] Al-Najem N. M. and El-Refaee M. M. 1997. A numerical study for the prediction of turbulent mixing factor in thermal storage tanks. Applied Thermal Engineering, 17, 12 (December 1997), 1173-1181. [5] Labidi M., Eynard J., Faugeroux O., Grieu S. 2013. Optimal design of thermal storage tanks for multi-energy district boilers. In Proceedings of the 4th Inverse Problems, Design and Optimization Symposium (Albi, France, June 26 -28, 2013). IPDO 2013.


Mouchira Labidi

Julien Eynard

Olivier Faugeroux

Stéphane Grieu

Wavelet-based Decomposition and Artificial Neural Networks for Short-Term Prediction of Power Demand in District Heating

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Wavelet-based Decomposition and Artificial Neural Networks for Short-Term Prediction of Power Demand in District Heating

Mouchira LABIDI (1,2,3) , Julien EYNARD (1,2) , Olivier FAUGEROUX (1,2) , Stéphane GRIEU (1,2) (

Why a predictive controller ?

Generate optimal command sequences to manage the amount of thermal energy to be stored or released by the hot water tank.

To implement such a controller, one needs to forecast the heat network power demand.

Hourly forecast model (April to September) Impact of the predictive controller

Objectives

A model is developed to forecast the power demand as follows:

 Results highlight the ability of such an approach to achieve the task of forecasting with high accuracy  The proposed control scheme allows the fossil energy consumption to be significantly reduced  The same remark applies to the functioning costs and CO 2 emissions

  1) PROcédés, Matériaux & Energie Solaire Laboratory, PROMES-CNRS UPR 8521, Rambla de la thermodynamique, Tecnosud, 66100 Perpignan, France. (2) University of Perpignan Via Domitia, 52 avenue Paul Alduy, 66860 Perpignan cedex 9, France. (3) Cylergie, Centre de Recherche de Cofely GDF-Suez, 18 avenue Tony Garnier, 69007 Lyon, France. mouchira.labidi@promes.cnrs.fr, julien.eynard@promes.cnrs.fr, olivier.faugeroux@promes.cnrs.fr, stephane.grieu@promes.cnrs.fr is carried out to optimize the:  Number of observation sequences (M)  Decomposition level (N)  MLP topology (number of hidden neurons)

  The present work is directed towards improving the operation of multi-energy district boilers by adding to the plants optimally sized and controlled thermal storage tanks. The proposed strategy is based on a Model Predictive Controller (MPC).

	Multi-energy district boilers
		CASE STUDY
	Component	Description
	WB	Wood boiler [1050 ; 4200] kW
	GB1	Gas boiler [140 ; 7000] kW
	GB2	Gas boiler [180 ; 9000] kW
	OPTIMAL CONFIGURATION
	Parameter	Value
	Wavelet decomposition level	1
	Number of observation sequences	1
	Number of hidden neurons	17
	FIT (similarity criterion)	72.26
	MAE (mean absolute error)	299.57 kW
	MRE (mean relative error)	5.9%