IFAC WS ESC’06 ENERGY SAVING CONTROL IN PLANTS AND BUILDINGS, October 2-5, 2006 Bansko, Bulgaria
A HIERARCHICAL CONTROL STRATEGY FOR ENERGY OPTIMIZATION Giovanni Palmieri and Giovanni Fiengo Dipartimento di Ingegneria, Universit` a degli Studi del Sannio, Benevento. E-mail: {palmieri, gifiengo}@unisannio.it.
Abstract: A new hierarchical and adaptive control strategy, integrating the heating and lighting systems, is proposed combining the classical control techniques, such as LQ optimal control and PI regulator, with fuzzy logic rules. The strategy is aimed at guaranteeing the satisfaction of comfort objectives, both thermal and lighting, by using the minimum amount of energy. The main idea is to maximize (in winter) or reject (in summer) solar gain by acting on window blind and avoiding glare on working plane. The effectiveness of the strategy has been tested by using a purposely designed simulator, developed in Java language and Matlab/Simulink environment. It is chosen the simulation environment to test the benefits of optimization strategy and in future in the Grace’s laboratory will designed an hardware demonstrator. Keywords: Energy management systems, Home Automation, Optimal control, Kalman Filter, Adaptive Control.
1. INTRODUCTION
rooms, electronic devices presented inside, etc.), the simulator dynamically creates a panel reproducing the scheme of the environment (see Figure 1) capturing all the interactions occurring inside. Particular attention is set on the services realized to guarantee: comfort (air-conditioning, brightness, sonorous diffusion); safety (active and passive); supervision (energy optimization, control, management); maintenance (diagnostic and monitoring of the state).
Home and building automation is the science that studies the integration and the automation of the electronic devices present in an environment (domestic or industrial) aimed to improve mainly comfort and energy management. Even if this science is born from long time, it is possible to assert that it has really had large diffusion only in the last years, becoming a promising and challenging new industry.
In this paper, integrating the heating and lighting systems, we propose a new energy management strategy aimed to ensure a certain climate comfort minimizing the energy consumption. This topic has been widely investigated in literature, see Snoonian (2003), Wilson et al. (2005) and Al-Ali and Al-Rousan (2004). Among others, in Yonezawa (2000) the author eliminates the wasteful use of energy associated with its overuse without prejudicing the comfort; in Zuojun et al. (2002), a neural network approach is proposed to optimize the so called ”cooling preparation
Unfortunately, many requirements of this kind of systems (i.e. low cost, flexibility, ability to support various physical layer, facility to use, etc.) are in contrast and it has caused that the producers have developed extremely various solutions. In this scenario we worked at developing a simulator able to reproduce the dynamical behavior of the environment in which the home/building automation system is mounted. Given a detailed description of this environment through a guided procedure (e.g. number and displacement of the
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2.1 Temperature The thermal model (see Figure 2) is a two order dynamic system whose states are the inner temperature T1 and the thermal mass temperature T2 , representing the equivalent temperature evaluating the thermodynamic exchange with the contiguous rooms, according to Priolo et al. (2002) Ph − g3 (T1 − T2 ) − g1 (T1 − Tout ) dT1 (1a) +0.5αAw Gvglob τ fsun + Pint = C1 dt − g2 (T2 − Tout ) − g3 (T2 − T1 )+ (1b) dT2 + 0.5αAw τ (1 − fsun ) = C2 dt
Fig. 1. Simulator main panel.
where: gi , i = 1 . . . 3, are the thermal conductances; Ci , i = 1 . . . 2, are the thermal capacities; Aw is the glazed area of the window; τ is the window transmission factor; Tout is the ambient temperature; fsun is the fraction of solar gain warming T1 ; Pint is the internal thermal gain due to the electronic devices and human presence in the room; Ph and α are the control inputs, respectively the air-conditioning power and the fraction of the window blind opening; Gvglob is the global irradiance on window, function among others of the weather condition, the solar and zenith angle (see Olmo et al. (1999) for details).
period”; in Spasokukotskiy et al. (2001) the attention is focused on independent climate control of separated rooms by installing about 200 sensors into a area of approximately 50 m2 ; in Guillemin and Morel (2001), acting on the heating/cooling system, the ventilation, the blinds (shading devices) and the artificial lighting, the authors developed an innovative and self-adaptive integrated system for building energy and comfort management mainly based on fuzzy logic rules and genetic algorithms. In this work, a new hierarchical control strategy is developed integrating the classical control techniques, such as LQ optimal control and PI regulator, with fuzzy logic rules. This proposed strategy is aimed at guaranteeing the satisfaction of the comfort objectives, both thermal and lighting, by using the minimum amount of energy. The main idea is to maximize (in winter) or reject (in summer) solar gain by acting on window blind and avoiding glare on working plane. Different scenarios are considered, based on human presence. The effectiveness of the strategy has been tested by using the cited simulator.
Fig. 2. Thermodynamical model.
The paper is organized as follows. In the next section are introduced the models adopted both for simulation and control design. Then the proposed control strategy is described. Simulation results are reported in section 4. Conclusion and bibliography end the paper.
2.2 Illuminance The model of illuminance in the room is provided by a study of Tregenza (1995). Based on solar angular position, it calculates the illuminance on room surfaces (ceiling, walls and working plane) as function of three main components of illuminance on the external face, i.e. from sun and sky Ews , from the ground Ewg and from obstructions above the horizon Ewo , as follows
2. ROOM MODEL The system to be controlled is composed by the thermodynamic model of the temperature and the illuminance model. Since we are interested in capturing and controlling the dynamics occurring in the time scale of temperature, the fast illuminance dynamic can be neglected and, hence, modeled through a static model. For brevity reasons, in the following we will give just some hints and the corresponding reference for details.
αAw [Ews τsc + Ewo τoc + Ewg τgc ] (2a) Ac αAw Evi = [Ews τsv + Ewo τov + Ewg τgv ] (2b) Av αAw [Ews τsp + Ewo τop + Ewg τgp ] (2c) Epi = Ap Eci =
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where: Eci , Evi and Epi are respectively the mean direct illuminances on ceiling, walls and working plane; Ac , Av and Ap are respectively the equivalent area of ceiling, walls and working plane; τij are the window transmittance parameters corresponding to the relationship among the illuminance components on the external face and the illuminance on room surfaces. For details see Tregenza (1995).
Controller Tref season
Reference generator
E ref
Saving Energy
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Ep Room Model
Tin
(3) Fig. 3. General control scheme. Tout T1
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Energy Optimization
D
(5)
Pal is the percentage of electrical power and a, b, c and d are parameters to be set, depending by room geometry.
Ep
3. STRATEGY OF ENERGY OPTIMIZATION
Artificial Illuminance
Pal
Fig. 4. Proposed control strategy.
The proposed control strategy is aimed to guarantee the comfort objectives, in case of human presence in the environment, and minimizing at the same time the energy consumption of lighting and air-conditioning systems.
3.1 Glare Controller The Glare Controller has the goal to compute the maximum window blind opening αmax avoiding the glare on the working plane. To this aim, we adopt a fuzzy logic controller. The main idea is to take into account not only the incidence angle of the solar illuminance (altitude angle h) on the facade but the exact position of the sun relatively to the facade (azimuth angle af ). This allows to have different behaviors for different kinds of direct sun penetration. The inputs of controller are fuzzy values: total illuminance on facade Evglog ; solar altitude h; solar azimuth af (relative to the facade orientation). The output is a crisp value: maximum blind position (αmax ).
Based on the measurements of the working-plane illuminance Ep , the total illuminance on the external face Evglob = Ews + Ewo + Ewg , the inner T1 and ambient Tout temperatures, the controller computes the window blind opening α, the electric power Pal and the air-conditioning power Ph . In Figure 3 the general control scheme is reported. It is formed by a reference generator determining the temperature Tref and illuminance Eref references, function of season and human presence, and a switching control strategy based on the user presence in the room. In particular, the energy saving controller is always activated while the comfort controller is enabled only in case of human presence.
Table 1 reports the fuzzy rule when external illuminance Evglob is high. In this case, the position of blind depends by the relative azimuth and solar altitude angle. Conversely, if the external illuminance is low, or similarly if there isn’t human presence in the room, αmax is set to 1.
In both cases, it is possible to individuate four interactive modules composing the control strategy (see Figure 4): • • • •
Ph
presence
with Eal the artificial illuminance supplied by lighting system, Guillemin (2003), 4 3 2 Eal = aPal + bPal + cPal + dPal ,
Comfort
Saving Energy
where ρc , ρv and ρp are the reflectance of the three surfaces, ρ is the reflectance mean value and A is the total room surface, the final illuminance on the working plane is computed according to Ep = Epi + Er + Eal
Gvglob Pint
Present
Absent
Now, by modeling the mean illuminance Er over all room surfaces from inter-reflected light as follows (see Wilson and Brotas (2001, Bulgaria)) Eci Ac ρc + Evi Av ρv + Epi Ap ρp Er = A(1 − ρ)
Tout
Evglob
Table 1. Rule of controller when the external global illuminance is high
Glare Controller Natural Illuminance Artificial Illuminance Energy Optimization
af – h right center left
Each module will be described in the following.
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low 0.6 0.4 0.6
min 0.8 0.6 0.8
high 0.6 0.8 0.6
3.2 Natural Illuminance
alternatively, if α is limited by the glare controller and the inner luminance request is not satisfied.
The goal is to furnish the minimum window blind opening αmin necessary to satisfy the illuminance objective on working plane. To this aim we adopt an adaptive control strategy based on a simplified model of the working plane illuminance
The controller is realized by means of a PI regulator. Moreover, since Pal is bounded among 0 and 1, an anti wind-up scheme is realized.
Ep = [RI0 (1 − α) + RI1 α]Evglob
Finally, in case of user absence, the electric power is set to zero.
(6)
whose parameters RI0 and RI1 , function of the geometry of the room and windows, are identified on-line by means of a recursive least square procedure, measuring the working plane Ep and the external Evglob illuminance and the actuated window blind opening α.
3.4 Energy Optimization The key point of this strategy is the controller devoted to the optimization of the energy consumption guaranteeing the satisfaction of comfort objectives. The controller, acting on air-conditioning power Ph and window blind opening α, is aimed at minimizing the following LQ cost function Z 1 ∞ J= [q1 (T1 − Tref )2 + ρ1 Ph2 + ρ2 (α − α ˜ )2 ]dt 2 0 (8) where α ˜ is equal to αmax in winter and to αmin in summer and q1 , ρ1 and ρ2 are weighting factors.
The controller, shown in Figure 5, in case of human presence determines αmin by summing a feedforward action, obtained inverting the model (6) as follows (see Guillemin and Morel (2001)) αminF F =
Eref − Evglob RI0 , Evglob (RI1 − RI0 )
(7)
and a PI action based on the measurement of the error among the actual and the reference working-plane illuminance. The PI regulator is enabled only if the artificial illuminance controller in disabled, i.e. Pal = 0.
The reaching of comfort objectives are assured by the first term of (8) and by constraining the actuated α in the interval (αmin , αmax ), obtained respectively by the Natural Illuminance controller and by Glare Controller. In particular, if αmin is greater than αmax , the controller looses a degree of freedom and the blind opening is set to αmax and the illuminance goal is reached by enabling the Artificial Illuminance controller, as described in section 3.3. Similarly, the energy saving objective is guaranteed by the second term of (8).
Conversely, in case of user absence, since we don’t need to satisfy comfort objectives, αmin is imposed to be zero. Evglob On-Line Identification
D Ep
The problem (8) has been solved by means of LQ optimal control technique. To this aim, we consider the system (1) organized as follows
RIi RI Model Invertion
E ref
+ -
PI based controller
x(t) ˙ = Ax(t) + B(t)u(t) + Γ1 d(t) + Γ2 e(t)
+
D
(9)
where: x(t) is the state vector formed by the temperature T1 and T2 ; u(t) are the control inputs, respectively Ph and α; d(t) is the measurable disturbance Tout ; e(t) is the unmeasurable disturbance Pint ; A, B(t), Γ1 and Γ2 are the parameter matrices. In particular, B(t) is time varying since it is based on Gvglob .
min
+
Ep
Fig. 5. Natural Illuminance control scheme
Hence, the cost function (8) can be reformulated Z 1 ∞ [(x− x ˜)T Q(x− x ˜)+(u− u ˜)T R(u− u ˜)]dt J= 2 0 (10) where: x ˜ is the temperature reference vector; u ˜ is the control input vector reference, equal to (0, α ˜ ); Q, the state weighting factor, is a diagonal matrix whose element are respectively q1 and 0; R, the input weighting factor, is a diagonal matrix whose element are respectively ρ1 and ρ2 .
3.3 Artificial Illuminance If the Natural Illuminance controller is insufficient to guarantee the requested lighting, the artificial controller determines the quantity of extra electrical power Pal necessary to reach the reference. In other words, supposing to know the minimum value of external illuminance Evth necessary to provide the requested reference with the window blind full opened (α = 1), the artificial illuminance controller is enabled if the total illuminance on the external face Evglob is less then Evth or,
The control action has been obtained by solving the algebraic Riccati equation and, consequently, computing the feedforward action, according to (time dependencies are omitted for readability)
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In our simulation the window is placed in nordsud orientation, so its azimuth is zero degree. The temperature reference is set to 20◦ C if the user is present and 22◦ C if absent. Similarly, the illuminance reference is set to 380 lux if the user is present and this reference has been increased of 10% when satisfied with the Natural Illuminance controller.
AT P + P A − P BR−1 B T P + Q = 0 (11a) b(t) = −(A − BR
−1
T
−T
B P)
(P (B u ˜+
+ Γ1 d) − Q˜ x)
(11b)
u(t) = −R−1 B T P x − R−1 B T b + u ˜
(11c)
Now, since it is not possible to measure both state variables, a Kalman filter has been used to estimate it (see Figure 6 reporting the energy optimization control scheme). To this aim, considering as noise n(t) the air-conditioning power Ph and αGvglob , the Kalman filter is obtained according to x ˆ˙ (t) = Ae x ˆ(t) + Be u(t) + Ke (y(t) − yˆ(t)) (12)
The simulation results are reported in Figures 7– 10, showing the very good performance both in terms of comfort and energy saving. In particular in Figure 7 is shown the inner temperature (first plot), reference and measured signals, and the airconditioning power (second plot). In the first plot of Figure 8, it is reported the illuminance on the working plane. The dashed vertical line marks the activation of Artificial Illuminance controller (see second plot of Figure 8) due to the reduction of the external illuminance under the threshold Evth (see first plot of Figure 9). Moreover, during the illuminance regulation by acting on the window blind opening (see second plot of Figure 9, showing also the maximum value of α that evoid glare on the working plane), the reference is increased of 10%. The performance of Kalman filter is shown in Figure 10
where: x ˆ is the estimated state; yˆ is the estimated output, equal to the first state; u(t) is the input vector formed by Ph and Tout ; Ae and Be are the corresponding parameter matrices, obtained from (1); Ke is the Kalman gain, computed solving the Riccati equation as follows Ae Pe + Pe ATe − Pe CeT Re−1 Ce Pe + Qe = (13a) 0 Ke = Pe CeT R−1
(13b)
with Ce the output matrix and Qe and Re weighting factors to be set. Once computed the estimated state, it has been substituted in (11c).
Finally, in order to show the capability of the proposed control strategy to reduce the energy consumption, a simple test is reported aimed at comparing the performance of our controller with a similar control strategy. This acts on airconditioning system via an LQ controller but commands the window blind opening at the glare controller value. Figure 11 shows a comparison of Ph in the first plot and the working plane illuminance in the second plot. It is evident an energy saving due to a better control strategy on the blind opening.
P int
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Room Model
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Fig. 6. Energy Optimization controller scheme
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It is important to note that the control strategy is the same in both cases of user presence or absence. What it is changing are the reference signals and the bounds on the window blind opening.
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4. SIMULATION
time [h]
Fig. 7. Inner temperature T1 , reference (dot-dashed) and measurement (solid), and air-conditioning power Ph .
The strategy has been tested by means of our simulator, developed in Java language, and Matlab/Simulink environment. Several tests have been conducted, simulating different weather conditions both in summer and winter period. Here we choose to discuss the results simulated during a summer day since in this period we can obtain a more significant energy saving due to action of blind to reject the solar gain.
5. CONCLUSION In this paper we have proposed an innovative optimization strategy tested with a purposely designed simulator for home/building systems. In particular, it is proposed an integrated automatic
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Fig. 11. Energy saving: air-conditioning power and working plane illuminance. The solid line refers to the proposed strategy.
Fig. 8. Working plane illuminance Ep , reference (dotdashed) and measurement (solid), and power of lighting system Pal . The vertical line (dashed) marks the activation time of the Artificial Illuminance controller.
REFERENCES A.R. Al-Ali and M. Al-Rousan. Java-based home automation system. IEEE Transactions on Consumer Electronics, 50(May), 2004. A. Guillemin. Using Genetic Algorithms to take into accoumt user whishes in an advanced building control system. PhD thesis, Institut des infrastructures, des ressources de l’environnement section Architecture, 2003. A. Guillemin and N. Morel. An innovative lighting controller integrated in a self-adaptive building control system. Energy and Buildings, (33):477– 487, 2001. F.J. Olmo, J. Vida, I. Foyo, Y. Castro-Diez, and L. Alados-Arboledas. Prediction of global irradiance on inclined surfaces from horizontal global irradiance. Energy, (24):689704, 1999. C. Priolo, S. Sciuto, and F. Sperduto. Efficient design incorporating fundamentals improvements for control and integrated optimisation. Technical report, Conphoebus SpA, 2002. D. Snoonian. Smart buildings. IEEE Spectrum, pages 18–23, August 2003. K. Spasokukotskiy, D. Jelondz, and H.R. Traenkler. Technical base for separated rooms climate automatic control. Workshop on Intelligent Data Acquisition and Advanced Computing Systems, 1-4 July 2001. P.R. Tregenza. Mean daylight illuminance in rooms facing sunlit street. Buildings and Enviroment, 30(1):83–89, 1995. M. Wilson, E.H. Magill, and M. Kolberg. An online approach for the service interaction problem in home automation. Consumer Communications and Networking Conference, pages 251 – 256, 2005. M.P. Wilson and L. Brotas. Daylight and domestic buildings. XI national conference on lighting, pages 27–32, 13 15 June 2001, Bulgaria. K. Yonezawa. Comfort air-conditioning control for building energy-saving. IEEE Conference on Industrial Electronics, pages 1737–1742, 2000. L. Zuojun, X. Wenlong, and H. Yalou. The energy saving control of air condition system in intelligent building. IEEE World Congress on Intelligent Control and Automation, 3:2240 – 2243, 10-14 June 2002.
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Fig. 9. External illuminance Evglob , and window blind
opening α, actuated (solid) and upper bound αmax (dot-dashed). The vertical line (dashed) marks the activation time of the Artificial Illuminance controller.
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controller that improves the user comfort and optimizes the energy consumption. The simulation results confirm the effectiveness of the strategy.
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