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Heating control

Benjamin Paris, Julien Eynard, Stéphane Grieu

ELIAUS Lab., University of Perpignan Via Domitia, 52 Av. Abstract: because of both the global energy crisis and the necessary the use of renewable energy when heating schemes ( and on the co of PID and model predictive fuzzy controllers VPUMPHJ\·V UHTXLUHPHQPV especially reducing the consumption were defined with the aim of evaluating the control scheme adapting the strategy to the specific use of very good compromise, thanks to both but not PID and the efficient but hard

Keywords:

1. Introduction

largest s of energy consumption with the just GLUHŃPLYH·V recommendation and energy performance. Usually, the NXLOGLQJ·V Energy Performance Indicator (EPI) is calculated Unfortunately, this global indicat express the amount of energy consumption only without any explanation. It does not dissoci the various energy consumption (as well as allowing ensuring thermal comfort, while reducing significantly energy consumption, has become mandatory. theme is handled by researchers Mathews et al. (2008) [ Levermore et al. (1992) [ Bernard al. (1982) [ Kolokotsa et al. (2005) [ Ben et al. (2001 [1 Kalogiro et al. (2000) [1 and Gonzalez et al. (2005) [1 present works related to energy consumption forecast while Chen et al. (2006) [1 Calvino et al. (2004) [1 K predictive control of thermal conditions in buildings. However, energy management the specific use of a given building buildings) I temperature control schemes were developed with the aim of both energy savings a increasing the renewable energy contribution while ensuring thermal comfort.

PID control are

commonly used in buildings engineering basis of a PID controller performance of this controller This allows implementing these schemes in buildings even if a control the aim of (about describing the w were d with the aim of evaluating both the energy management strategy

2. Energy

2.1. Strategy fundament

both the "Thermal Regulation 2005 and the "Energy Performance Diagnosis" allowed one can define various energy consump components such as cooling, water heating, lighting, cooking, ventilation or electronics. O can highlight and this on outside temperatures) which account for about 60% the proposed strategy focuses on managing heating systems considering multi

NXLOGLQJ·V

" MV

Co we want the proposed strategy to be easily and

use of a As most of "Thermal Regulation 2005 is NXLOGLQJ·V Energy Performance Indicator-.year-) this global indicat express the amount of energy consumption only without explain energy consumption and global performance, were defined (section 2.2) Although thermal comfort is to live or to work in a particular environment. proposed strategy

2.2. C

7RROV MUH QHHGHG IRU ŃRPSMULQJ POH ŃRQPUROOHUV· SHUIRUPMQŃHB As previously

NXLOGLQJ·V

that common criteria for human consumed com with the total energy used Then, the comfort criterion , based on temperature set tracking, specifies the mean relative error b proposed controller comparing the two just criteria, and the way the contr scheme impacts energy consumption (Equation 1).

Fossil energy consumed kWh.m-2.year-1

Renewable energy consumed kWh.m-2.year-1

Total energy consumed kWh.m-2.year-1

Percentage of the fossil energy consumed

compared with the total energy used %

Comfort criterion %

Performance criterion %

%XLOGLQJ·V LQGRRU PHMQ PHPSHUMPXUH °C

Temperature set-point °C

2.3. Simulation: set

Because both the use and occupancy of a building impact on the French " 2005 [2 were used This allows testing in several ways the POH NXLOGLQJ XVH VŃOROMU ORVSLPMO"B )RU H[MPSOH MQ RIILŃH NXLOGLQJ OMs

3. Simulation dynamic models

Dynamic models are necessary to test the

In both models, two heat s are considered: the main

3.1. Theoretical model

The theoretical model [2

Thermal diffusivity m-2.s-1

Thermal conductivity W.m-1.K-1

Density kg.m-3

Specific heat capacity J.kg-1.K-1

Heat transfer coefficient W.m-2.K-1

Power density of the jth heat source W.m-3

Time s

Space coordinate m

Temperature °C

To simplify

The three right

temperature and the walls temperature Using th theoretical dynamic model, preliminary results about heat control were promising [2 That is why another dynamic model, describing the thermal behavior of a

3.2. Mock

Having the possibilit to instrument real buildings with a set of sensors and to test temperature is not easy That is why a building mock with a mock inertia favors reactivity and avo energy waste; a small amount of electricity is consumed the power of the two resistor and time periods. Figure 1 presents an example of temperature

Figure 1. Mock

The study of the mock

with: Indoor temperature measured by the ith sensor °C

Outdoor temperature °C

Experimental temperature data °C

Modeled temperature data °C

Power of the first heat source W

Power of the second heat source W

Inertia of temperature -

Influence of the first heat source on temperature - Influence of the second heat source on temperature - Influence of outdoor temperature on temperature -

Time index ( and 60s) -

Error criterion -

Sample number -

using Equation 7 A

Table 1. Parameters of the mock

The

4. Indoor temperature

Simulation were carried out for both testing the management strategy proposed (focusing on and evaluating performance of the indoor temperature control schemes developed using the two just models and a un set of outdoor temperatures. T evaluation IHP·V UHPHPNHU POMP NRPO GHYHORSHG PRGHOV LQŃRUSRUMPH PRR OHMP sources, model and 80W ( and 34W ( for the mock model.

As a consequence,

all the ŃRQPUROOHUV· parameters are optimized to way, various constrains and aditional parameters (they will be explained in the next sections cont schemes (based on PID or

4.1. PID

A standard PID controller is a control mechanism [26], widely used in buildings engineering for basic us remind its structure (Figure 2) for discrete time control with anti heat power) then both ( power of . Outdoor temperature impacts on indoor temperature and is as a consequence considered

Figure 2.

%XLOGLQJ·V LQGRRU PHMQ PHPSHUMPXUH °C

Temperature set-point °C

Proportional gain -

Integral gain -

Derivative gain -

Sampling time s

Anti-windup time constant s

Integration state -

Derivation state -

Unsaturated heat power (computed by the PID controller) W Saturated heat power (computed by the PID controller) W

Maximum heat power W

PID controller Heating system

Disturbance

With the aim of optimizing the performance criterion w

4.2. PID

A optimal command sequence To elaborate this sequence one needs both a linear model and a working point of the system to be controlled these disturbances. The MPC controller used estimates the way outdoor

30 minutes, = 10 minutes and = 5 minutes. Th advanced heating control scheme

proposed basic component of the

Figure 3.

Being a model

with the following constraints: , and ,

PID controller Heating

system

Forecasted MPC controller

Disturbance

Time index -

Prediction horizon index -

Command horizon index -

Command increment W

%XLOGLQJ·V LQGRRU PHMQ PHPSHUMPXUH °C

Temperature set-point °C

Weight assigned to -

Testing several values of , one can find the right value allowing maximizing of with the a of minimizing the consumption of fossil energy or favoring thermal comfort with:

4.3. PID

Both the structure of the control

using model predictive and PID controllers (Figure 4). Let us just remember that the concept to the concept underlying the set They preserve a gradual and smooth transition from one [ That is why the PID scheme is proposed for easily tak into the specific use of a building, thanks to the design of appropriate fuzzy rules [3 F the difference between the set temperature ( and the indoor mean temperature ( the PID controller estimates the power of ( while a 1st fuzzy module determines if this power needs to be ( From and , a 2nd fuzzy mod evaluate the power of (

Figure 4.

PID controller Heating

system

Disturbance

Fuzzy module

FLCRE

Fuzzy module

FLCFE The v

POH ŃRQPUROOHUV· JMLQV

with:

5. Results and discussion

This section

are similar when using the theoretical model, they will not be presented. the a of answering to the following PID control schemes are compared to the reference results fossilń 0 limiting the use of renewable energy, the lower are the

Table 2. Respective values of the

Offices Houses

PID 7494.29 521.02 6.50 72.03 65.53 7414.05 786.73 9.62 61.86 60.24

10 7303.86 338.03 4.42 71.06 66.64 7394.28 343.15 4.44 65.42 60.98

5 7303.86 338.04 4.42 71.06 66.64 7395.89 342.81 4.43 65.42 60.99

3 7303.86 338.06 4.42 71.06 66.64 7395.83 342.22 4.42 65.42 61.00

1 7303.78 338.19 4.43 71.08 66.65 7402.64 342.31 4.42 65.44 61.02

0.5 7305.36 338.38 4.43 71.12 66.69 7408.75 341.33 4.40 65.52 61.12

0.2 7304.83 341.73 4.47 71.44 66.97 7404.29 348.79 4.50 65.84 61.34

0.1 7300.59 351.82 4.60 72.32 67.72 7411.77 367.92 4.73 67.03 62.31

0.05 7339.24 381.16 4.94 73.63 68.70 7406.36 432.56 5.52 69.56 64.05

0.03 7341.20 429.50 5.53 74.12 68.60 7376.96 538.35 6.80 71.26 64.45

0.02 7349.52 485.72 6.20 74.37 68.17 7410.01 642.32 7.98 72.14 64.16

0.01 7313.96 561.85 7.13 73.98 66.84 7379.45 791.97 9.69 71.92 62.23

0.001 7239.58 626.28 7.96 73.55 65.59 7322.18 894.65 10.89 71.18 60.30

0.0001 7383.21 625.69 7.81 73.55 65.73 7395.39 903.41 10.89 71.19 60.30

So, whatever the set

Figure

Figure

of these perce seem to be weak, they are significant due to the average life of buildings.

Taking another look at Table 2

scheme one can also note that whatever the set the PID control scheme allows - -, while - -, while - -.

5.2. Impact on the

5.2.1. Universes of discourse

the difference between the set temperature and the indoor mean temperature ( of ( while a first fuzzy module determines if this power needs to be corrected ( )URP NRPO dž MQG , a second fuzzy module evaluates the power of mentioned, o POH IX]]\ PRGXOHV· LQSXP MQG RXPSXP param and their " of discourse using fuzzy sets triangular or trapezoidal functions ( functions are chosen to be bell with a minimum and maximum equal to 0 and 1 respectively and linguistic labels and, secondly, to de appropriate ). Because of the thermal inertia, heat transfer and heating system dimensioning, indoor temperatures in buildings may As previously mentioned t values of and are normalized between are obtained only results for offices will be presented in the following sections

5.2.2. Optimal c

Usually, one considers that energy consumption increases by 7% over a year if control scheme for implementing the proposed energy management strategy

PRGXOHV· the design of

the fuzzy Nine configurations are proposed from a starting ( the number of both the fuzzy sets (common triangular or trapezoidal membership us also note, first, that the shape of the triangular membership functions used for characterizing close to the performance of the optimal configuration E, but using less fuzzy rules) then from t fuzzy rules was modified from configuration E to configuration F then from configuration

Table 3.

Configuration Module FLCRE Module FLCFE

dž Rules dž Rules

PID - - - - - - - 7494.29 521.02 6.50 72.03 65.53

A 3 3 3 3 2 3 6 7236.19 473.99 6.15 59.69 53.54

B 5 5 5 5 2 5 10 7779.79 338.76 4.17 62.07 57.90

C 5 5 5 5 2 5 10 7504.92 480.95 6.02 72.14 66.12

D 5 5 5 5 2 3 10 7700.20 619.18 7.44 70.78 63.33

E 7 5 7 7 2 5 14 7731.35 470.66 5.74 72.38 66.64

F 7 5 7 7 2 5 14 7470.84 625.22 7.72 71.05 63.32

G 7 5 7 7 2 5 14 7426.40 654.02 8.09 71.08 62.98

H 7 5 7 7 2 4 14 7470.84 625.22 7.72 71.05 63.32

I 7 5 7 7 2 4 14 6709.86 760.13 10.2 69.48 59.31

Figure 7.

scheme ( considering the optimal configuration E) allows reducing from 65.53% to 66.64 respectively. L at Table 3, one can also note that

E provides the highest comfort criteri

is significantly reduced wh renewable energy consumption increases - -, while

8 9 10 and 1 present the respective fuzzifications of , , and while Tables

and 5 depict FE RE)

M NL (Negative Low), AZ (A

High),

NL (Negative Low), AZ (Approximately Zero), PL (Positive Low) and PH (Positive High) for

Figure

Figure

Figure

Figure

Table

Module

FLCRE

Rule 1 2 3 4 5 6 7

NH NM NL AZ PL PM PH

NH NH NL AZ PL PL PH

Table 5.

Module

FLCFE

Rule 1 2 3 4 5 6 7

NH NM NL AZ PL PM PH

Null Null Null Null Null Null Null

Rule 8 9 10 11 12 13 14

NH NM NL AZ PL PM PH

Null Null Null Weak Medium Strong Full

5.2.3. Design of new rules for improving the control quickness

As just

IX]]\ PRGXOHV·

input and output parameters

H) dž LV 10 7+(1 N" (rule

H) dž LV 30 7+(1 PL" (rule

H) dž LV 30 7+(1 is P" (when it is too cold, heating has to be significantly IF

dž LV 10 7+(1 is NL" (when it is too ho

dž LV 1I 7+(1 is

PM" (when it is slightly too hot, heating has to be significantly increased) or "IFdž LV 3I 7+(1 is NL" (when it is slightly too cold, heating

Figure 12. New configurations

5.2.4. Synthesis and temperature set

The present section

and one of the control schemes developed ( PID and PID when applying the buildings. Let us remember that, whatever the temperature set (for offices or houses) the respective performance of the

Table 6.

scheme ( 2 while increases by 3.2% with the schemes. T PID control is the best performer, mainly because than developing and testing a classical PID controller and as previously mentioned requires of the building not always easy to obtain. Furthermore, implementing this kind of advanced controller can observe specific behaviors the design of the fuzzy rules (PID03F·V objective function Figure 1 Temperature set tracking using the PID, PID and

6. Conclusion

into consideration the European energy context and according to the latest laws meeting widely strategy based on the specific use of a building and

Indoor temperature

control schemes were developed with the aim of favoring energy savings a increasing the renewable energy contribution, while ensuring thermal comfort.

PID control are commonly used in buildings

basis of a PID controller implementing these schemes in buildings even if a control system based on such a controller is already in use calcula an optimal command sequence while remarkably simp way t draw definite conclusions from vague, imprecise or missing information, the French " 2005 were used

In both models, two heat sources are

considered: the main Finally, NXLOGLQJ·V Energy Performance Indicator ( not dissociate the various energy consumption (about control performance describing the w energy is used and controlled in real were defined with the aim of evaluating both the Despite some limitations due to specific features, scheme, as a result of both the lowest and the highest comfort criterion ( consequently leading to the best performance criterion ( task. The PID sc also provided better results than the PID scheme.NRPO POH IX]]LILŃMPLRQ RI POH IX]]\ PRGXOHV· LQSXP MQG output parameters and consequently, of the two heat sources. So, w

·V POH PID

complex models and/or situations with the aim of being finally implemented in real buildings.

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pQHUJpPLTXH G·XQ NkPLPHQP ŃRQPU{OH IORX ,

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