- Email: [email protected]
Multi-criteria fuzzy algorithm for energy management of a domestic photovoltaic panel
ARTICLE IN PRESS
Renewable Energy 33 (2008) 993–1001 www.elsevier.com/locate/renene
Multi-criteria fuzzy algorithm for energy management of a domestic photovoltaic panel Chokri Ben Salahb, Maher Chaabenea,b,, Mohsen Ben Ammara,b a
The High Institute of Technological Studies (ISET), Sfax, Tunisia Unite´ de Commande de Machines et Re´seaux de Puissance CMERP-ENIS, Tunisia
b
Received 2 October 2006; accepted 19 May 2007 Available online 3 July 2007
Abstract This paper presents a fuzzy algorithm which makes decision so as to connect domestic apparatus on either the electrical grid or a photovoltaic panel (PVP). The decision is made in real time with respect to multi-energy save criteria and upon the PVP maximum available power and apparatus states. The algorithm is validated on a 1 kW peak (kWp) PVP and domicile apparatus of different powers installed at the Energy and Thermal Research Centre (CRTEn) in the north of Tunisia. Criteria are verified on the system behaviour during days covering the different seasons of the year. The power audit, established using measures, confirms that the energy save during daylight reaches 90% of the PVP available energy. r 2007 Elsevier Ltd. All rights reserved. Keywords: Energy management; Fuzzy decision; Photovoltaic; Energy saves
1. Introduction Household electric apparatus have become increasingly diversified during last years, which has led to an increase in energy need. Yet, the energy crisis does not cease being accentuated. These two constraints yield a heavy additional financial expense to the consumer. Several researches have confirmed that more than 60% of total useful energy represents buildings electric energy consumption [1], much of which could be recovered by integrating renewable energy and by formulating adequate energy management strategies inside buildings. For this reason, the exploitation of photovoltaic electricity has become an important issue of debate. Thus, three operating modes of PVP (photovoltaic panel) are distinguished: stand alone, grid connected and hybrid mode. In stand alone mode, the PVP represents the only source of electric energy for equipment. This mode is adopted Corresponding author. Rte Mahdia Km 2, BP88A, ElBustan, 3099 Sfax, Tunisia. Tel.: +216 74431425; fax: +216 74431386. E-mail addresses: [email protected], maherchaabane@ yahoo.com (M. Chaabene).
0960-1481/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.renene.2007.05.036
when the network is not available or when the equipment function depends only on the sun occurrence (pumping, lighting, air-conditioning, heating, etc.). Research interests are essentially related to the modelling [2–5], the optimization [6] and the adaptation system [7] of the PVP supply according to equipment needs. As for researches carried out on grid connected PVP, they generally deal with system assessment and characterization depending on site climate [8,9]. Finally, the hybrid mode is the combination of PVP with other energy sources. Published studies proposed either new design of PVP hybrid energy systems [10] or PVP hybrid power systems sizing [11]. For all operating modes, other researches developed energy management strategies so as to offer optimum function [12–14]. Nevertheless, the main problem in photovoltaic applications remains the battery cost, and the protection and synchronization systems of grid connected PVP [2] essentially when using large scale photovoltaic power station. In this paper, a new operating mode is proposed where a domestic PVP is considered as a complementary electric source to supply energy to domestic apparatus. There is no need for batteries neither for grid protection system. The installation incorporates a 1 kWp PVP, six apparatus of
ARTICLE IN PRESS C. Ben Salah et al. / Renewable Energy 33 (2008) 993–1001
994
powers varying between 50 and 500 W and a switching unit. A fuzzy decision making algorithm gives orders to the switching unit so as to connect each device either to the PVP output or to the electric grid. The decision of the appropriate connection mode is based on criteria that offer maximum exploitation of the energy delivered by the PVP during daylight depending on load demand without disturbing however apparatus’ function. The energy management system is implemented at the Energy and Thermal Research Centre (CRTEn) in the north of Tunisia since January 2005. The results validation is illustrated over four days representing the seasons of the year. Furthermore an energy audit was established and showed that the proposed system is able to bring an energy save during daylight up to 90% of the PVP generated energy. The various sections of this paper are organized as follows. Section 2 describes the system and fixes the energy management criteria. The fuzzy management algorithm is introduced in Section 3. Section 4 shows the system design and implementation. Validation and results are presented in Section 5. Finally, Section 6 provides perspectives and conclusion. 2. The management criteria The system studied in the present work aims to offer a utility decision tool on the connection way of domestic apparatus either on a domestic PVP output or on the electric grid. The decision is made in real time on the basis of the following criteria:
The connection of an active apparatus to PVP output cannot be decided unless PVP maximum available power is more than 110% of the apparatus operating Respecting low power apparatus priority
power, which guarantees continuous electric supply for active apparatus face to possible climate perturbation. Respecting apparatus priority: apparatuses of lower powers are more requested to be connected to PVP output so that to consume remaining PVP power from connected high power apparatuses. This criterion minimizes the power drawn from the electric grid. Maximizing connection time of a PVP connected apparatus: Since an apparatus is connected to PVP output, it has priority to remain connected so as to avoid relays’ commutations and ensure power supply stability for apparatuses.
The considered system contains many input/output variables. Furthermore, the decision to take must respect numerous and severe criteria. Indeed, the management algorithm has to acquire the domestic apparatus states and the PVP maximum available power, to treat the information according to the above fixed criteria and, at the same time, to ensure the apparatus switching control. Fig. 1 traces the synoptic schema of the proposed approach. The two available sources of electric energy are managed to provide power for apparatus, through fuzzy commands given to apparatus relays with respect of the above decision criteria. 3. The fuzzy management algorithm Fuzzy logic is one of the most powerful control methods. It is known by multi-rules-based resolution and multivariables consideration [15]. Compared to other methods such as neural networks and genetic algorithms, it provides fast results using only the expert knowledge. Hence, fuzzy logic method has been selected as a management tool for
Maximising connection time of a PVP connected apparatus
Reserving a power margin of +10% for PVP connected apparatus
CRITERIA PVP generation Electric grid Apparatus states Connections status
I N P U T S
ENERGY MANAGEMENT ALGORITHM
O U T P U T S
Decision commands for apparatus relays
OBJECTIVES
To minimise the power drawn from the electric grid.
To guarantee continuous electric supply for active apparatus face to possible climate perturbation.
To ensure power supply stability for apparatuses.
Fig. 1. The synoptic schema of the proposed approach.
ARTICLE IN PRESS C. Ben Salah et al. / Renewable Energy 33 (2008) 993–1001
the present system. This selection is judicious considering that it fulfills well the system requirements. Since the energy management approach uses fuzzy logic, its algorithm is based on three steps: the knowledge base of the expert, the fuzzification, the inference diagram and the defuzzification [15].
the symmetric triangular type (Fig. 2). These membership functions are be expressed as 8 < 1 jxj x0i j ex0i mAji ðx0i Þ ¼ : 0
According to apparatus states: The fuzzy partition of apparatus states is composed of N s ¼ 2 fuzzy subsets. Aji ¼ ðOFF; ONÞ is the ith fuzzy subset, i ¼ f1; 2g, of the jth apparatus, j ¼ f1; 2; 3; 4; 5; 6g. These subsets cover the fuzzy P s domain x ¼ ½0; 1 and verify 8 xj ¼ ERj 2 x; N i¼1 mAji ðxj Þ ¼ 1, where ERj is the state of the jth apparatus and mAji the membership function. According to 1 kW p PVP generation: Here the fuzzy partition is composed of N s ¼ 20 fuzzy subsets Bl ¼ ðA; B; . . . ; S; TÞ, l ¼ f1; 2; . . . ; 20g, which cover the fuzzy domain P y ¼ ½0; 1000. These fuzzy subsets verify s 8 yl ¼ Pl 2 Y ; N l¼1 mBl ðyÞ ¼ 1, where Pl is the PVP generation and mBl is the membership function. According to relays control: The relays command requires N s ¼ 2 fuzzy subsets. C jk ¼(grid,PVP) is the kth fuzzy subset, k ¼ f1; 2g, of the jth apparatus relay. These fuzzy subsets coverPthe fuzzy domain z ¼ ½0; 1 s and verify 8 zj ¼ ESj 2 z; N k¼1 mC jk ðzj Þ ¼ 1, where ESj is the command given to the jth apparatus relay and mC jk is the membership function.
3.2. The fuzzification The determined fuzzy partitions lead to the calculation of the membership functions mAji ; mBl and mC jk considering
if jxj x0i jpex0i
for apparatus states,
otherwise;
(1) (
3.1. The knowledge base of the expert The approach handles a multi-criteria resolution for which three fuzzy partitions are judged necessary:
995
mBl ðy0l Þ ¼
0l j 1 jyy ey
if jyj y0l jpey0l
0
otherwise;
0l
for PVP generation,
(2) ( mC jk ðz0k Þ ¼
1
jzj z0k j ez0k
0
if jzj z0k jpez0k otherwise;
for relays’commands,
(3) where x0i , y0l , z0k are, respectively, the real values of the variables xj , y, zj in their membership domains and ex0i , ey0l , ez0k are, respectively, the range values of x0i , y0l , z0k . 3.3. Inference diagram By means of the obtained membership functions and the apparatuses operating powers which are: 50, 100, 200, 300, 400 and 500 W, a rule base is established, according to Mamdani [16], using the general rule format: Rilk : if ðX is Ai and yl is Bl Þ then Z is C k ,
(4)
where X ¼ ½x1 x2 x6 is the apparatus states vector and Ai ¼ ½A1i A2i A6i its linguistic values vector, yl the PVP available generation and Bl its linguistic value, Z ¼ ½z1 z2 z6 the command vector of apparatus relays and C k ¼ ½C 1i C 2i C 6i its linguistic values vector. It can be seen that for a validated condition ðX is Ai and yl is Bl Þ of Eq. (4), many actions C k can be affected to the command vector Z. Consequently, a decision making procedure selects the action C k which verifies the criteria of Section 2.
Fig. 2. Membership functions according to: (a) apparatus state, (b) relay command, and (c) PVP generation.
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That is, consider the available PVP generation is 680 W ðBl ¼ NÞ, all apparatus are active (Ai ¼ [ON ON ON ON ON ON]). Subsequently, according to the rules base (Eq. (4), the following actions are generated: 1. C k ¼ [grid PVP PVP PVP grid grid], 2. C k ¼ [grid grid PVP grid PVP grid], and 3. C k ¼ [grid PVP grid grid grid PVP].
3.5. The management algorithm
By executing the decision making procedure, the maintained action is selected on the basis of the management criteria. Hence, the following cases are examined:
If all apparatuses are already connected to grid then the first decision is taken because it respects the priority of the apparatuses of lower powers (second criteria). If only the apparatus of 400 W operating power is already connected to PVP then the second decision is taken to respect the third management criterion. If only the apparatus of 500 W operating power is already connected to PVP then the third decision is taken to respect the third management criterion.
Since the decision is taken (which case to consider), Eq. (4) is therefore computed for i ¼ 1; 2; l ¼ 1 20 and P k ¼ 1; 2 to generate a rules base composed of 20 6j¼1 C j6 ¼ 1280 rules. The rules’ aggregations are given by computing the minimum norm conjunction implication of each fuzzy subset of the jth apparatus relay: mC 0j1 ¼ minðwj1 ; mcj1 Þ
for the first fuzzy subset,
(5)
mC 0j2 ¼ minðwj2 ; mcj2 Þ
for the second fuzzy subset,
(6)
where wj1 is the minimum norm fuzzy conjunction between the first fuzzy subset of the jth apparatus and the lth fuzzy subset of the PVP generation: wj1 ¼ minðmAj1 ; mBl Þ,
Hence, the relay control of the jth apparatus is determined by ( ESj ¼ grid if z0k o0:5; (11) ESj ¼ PVP if z0k X0:5:
Acquire: Pl ; ER1 ; . . . ; ER6 {Read the available PVP generation and apparatus states} Pl ¼ 90 %Pl {Let a power margin of 10% to respect the first management criterion} Pl l ¼ E 50 {The fuzzy subsets’ number of the PVP generation} Fuzzification: Compute mAji ; mBl ; mC jk {The membership functions} Inference diagram: Compute Rilk : if ðX is Ai and y is Bl Þ then Z is C k : {The rules base} Make the decision {Basing on management criteria} Calculate mC 1 ; . . . ; mC 6 {The membership functions of the operating points} Defuzzification: Compute z0k the centres of mC j {using the centroid method} Compute ES1 ; . . . ; ES6 {The apparatus relays’ commands}. 4. The system implementation The system is implemented at the Energy and Thermal Research Centre (CRTEn) in the north of Tunisia since January 2005. It includes:
(7)
and wj2 is the minimum norm fuzzy conjunction between the second fuzzy subset of the jth apparatus and the ðl þ 1Þth fuzzy subset of the PVP generation: wj2 ¼ minðmAj2 ; mBlþ1 Þ.
(8)
Using the maximum t-conorm rule aggregation, the membership function for an operating point of the jth apparatus relay is given by mC j ¼ maxðmC 0j1 ; mC 0j2 Þ.
(9)
3.4. Defuzzification Since the rules are aggregated, the defuzzification consists of calculating the real value z0k of the relay state of each apparatus using the centroid method (z0k is the centre of mC j ): R1 zj mC j dzj . (10) z0k ¼ R0 1 0 mC j dzj
1 kW p PVP and the electric grid as energy sources. The PVP is equipped with a Maximum Power point Tracker (MPPT) [13] which is an electronic device that monitors PVP generation to operate near its maximum power point along the I–V curve and an inverter that provides the same output voltage as the electric grid (230 V/50 Hz) [7]. Six household apparatus of different power: 50, 100, 200, 300, 400 and 500 W (230 V/50 Hz). Each one is controlled by a two position relay in order to be connected either to the PVP output or to the electric grid.
When sizing the PVP power rating, the main objective consisted to minimize the lost power generated by the PVP during the system function. Yet, the maximum load power of the installation is 1500 W (if all apparatuses are switched on). So, it has been estimated that PVP generation must cover 23 of the total needed power (1000 W). This proportion is judicious since it is rarely encountered that all apparatuses are switched on. Furthermore, as the PVP is used for domestic application, we took into consideration that the system cost would be reduced as much as possible.
ARTICLE IN PRESS C. Ben Salah et al. / Renewable Energy 33 (2008) 993–1001
Apparatus 1
Apparatus 2
997
Apparatus 6
ON/OFF switches
Apparatus states ER j
ES1
ES6
ES2
MPPT & Inverter
Output commands (Defuzzification) Rule base
Decision making
Electric grid
Relays
Criteria base
1kWp PVP
Fuzzification
Ta Data acquisition system
I Fig. 3. System components and implementation.
Fig. 3 shows the connection schema of the system components. The decision centre is composed of a personnel computer equipped with a data acquisition and control card. The PVP maximum available power ðPl Þ is calculated on the basis of a published 1 kW p PVP validated model [17]: I I 3 Pl ¼ 20 3:33 þ 1:210 T a þ 25 1000 40 I þ3:35 1 upv , 1000
ð12Þ
where I and T a are, respectively, the acquired solar radiation and the ambient temperature measured at the surface of the PVP. upv is the PVP output voltage fixed to 12 V by the MMPT device. The algorithm is implemented using the Matlab software as a programming tool. After implementation, the system has been tested during the year 2005. All its input/output ðT a ; I; ERj ; ESj Þ have been daily recorded using a time step of 5 min. A power audit has been also established in order to determine the system performance. Even so, for clearness reason the system behaviour and performance is given only for four days representing the year’s seasons. Fig. 4 shows the fuzzy commands timing of relays during daylight. During function, all apparatus were switched on in order to evaluate the contribution of the PVP generation to the whole installation. By examining the fuzzy decisions, it can be easily deduced that most commutations between grid and PVP output are observed at apparatus of lower power. This is due to the above management constraints (Section 2) which affect the higher priority to apparatus of lower power in order to recuperate the remaining power of the ones of higher power. As well, commutations can be
seen at apparatus of high power when PVP generation is available (June and September). In this case these commutations are limited to the time around midday. Finally, only lower power apparatus are connected to PVP output while PVP generation is weak (December). Since it holds the lower priority, the apparatus of 500 W could not be connected to the PVP output unless other apparatus are switched off and there is enough PVP generation (Fig. 5). In fact, in case 1 all apparatus of 100–400 W are switched off to give the chance to apparatus of 500 W to be connected to PVP output. However, in case 2, the apparatus of 500 W is switched off, and as a consequence any other apparatus will be connected to PVP output, respecting management criteria (Section 2), as soon as it is switched on. 5. Approach valorization The valorization of the designed system consists of daily and monthly assessments. 5.1. Daily assessment The approach assessment is ensured by the establishment of a daily power audit. Fig. 6 plots in real time the curves of the PVP related powers (PVPA : maximum available, consumed: PVPC , lost: PVPL ) and of the power load from grid (GLP) during the four chosen representative days (Section 4). It is noted that the curve of PVPC follows the variations of PVPA in order to minimize PVPL . Similarly, GLP decreases considerably around midday especially during days of sunny seasons. These interpretations confirm the approach contribution in term of energy save and management for the whole installation.
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Fig. 4. Timing of commands given to apparatus relays (all apparatus switched on): X-axis—1 unit ¼ 5 min of the daylight, and Y-axis—0: apparatus connected to grid; and 1: apparatus connected to PVP output.
5.2. Monthly assessment The same study was renewed to form a monthly energy balance (Fig. 7) so as to prove the effectiveness of the management approach. All PVP related powers are integrated over daylight (from sunrise (SR) to sunset (SS)). Obtained energies are cumulated over the month length (ML) to compute PVP monthly energies (maximum
available: PVPAE , consumed: PVPCE , lost: PVPLE Þ as follows: ML Z SSðjÞ X PVPA ðtÞ dt; PVPAE ¼ j¼1
PVPCE ¼
ML Z X j¼1
SRðjÞ SSðjÞ
PVPC ðtÞ dt; SRðjÞ
ARTICLE IN PRESS C. Ben Salah et al. / Renewable Energy 33 (2008) 993–1001
999
Fig. 5. Timing of relays commands (apparatus manipulated): X-axis—time: 1 unit ¼ 5 min of the daylight; and Y-axis—apparatus state: 0: switched off; 1: connected to grid; and 2: connected to PVP output.
PVPLE ¼
ML Z X j¼1
SSðjÞ
PVPL ðtÞ dt.
SRðjÞ
While the electric energy produced by the PVP varies between 80 and 160 kW h/month, the electric energy consumed from the PVP varies between 65 and 145 kW h/ month which involves an unused energy about 15 kW h/ month. This lost energy is generally produced during the sunrise and sunset times where PVP maximum available power is insufficient ðo50 WÞ to supply energy for even the
lower power apparatus. A second valorization consists of the calculation of a monthly effectiveness coefficient defined by Z% ¼
PVPAE PVPLE PVPCE 100 ¼ 100. PVPAE PVPAE
Table 1 gives the ðZ%Þ. This coefficient is almost constant through the months of the year and it varies between 80% and 90% which justifies the continuous energy save contribution of the proposed solution.
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Fig. 6. The daily power audit: X-axis—1 unit ¼ 5 mn of the daylight and Y-axis—the power (W).
Fig. 7. The monthly energy balance.
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Table 1 The monthly effectiveness coefficient
PVPAE PVPCE PVPLE Z%
January
February
March
April
May
June
July
August
September
October
November
December
86.2 69.8 16.4 81.0
98.8 85.7 13.1 86.7
129.1 115.8 13.3 89.7
135.2 120.2 15 88.9
148.3 129.8 18.5 87.5
149.4 133.7 15.7 89.5
156.4 139.2 17.2 89
161.3 145.4 15.9 90.1
136.9 122.2 14.7 89.3
123.3 109.5 13.8 88.8
92.5 79.3 13.2 85.7
78.6 62.8 15.9 79.9
6. Conclusion The efficient management of the energy produced by a conversion system depends on consumption needs on the one hand and on the supplied energy (generated by the conversion system) on the other hand. Herein the energy produced by a PVP of 1 kWp is optimally managed to provide a complementary energy for household apparatus so as to offer a maximum energy saving. The management approach consists of a fuzzy algorithm which decides whether each domestic apparatus should be connected to PVP output or to grid. Decision is made on the basis of optimum management criteria, PVP generation and apparatus states. The system is implemented and tested during 2005 at the Energy and Thermal Research Centre (CRTEn) in the north of Tunisia. A carried out energetic audit confirms that 90% of PVP generated energy is brought to the installation as energy save. References [1] Fanny AH, Dougherty BP, Davis MW. Measured performance of building integrated photovoltaic panels. Solar energy: The power to choose, Forum 2001, Washington, DC. [2] Xu M, Melnik RVN, Borup U. Modelling anti-islanding protection devices for photovoltaic systems. Renew Energy 2004;29:2195–216. [3] Kawamura H, Naka K, Yonekura N. Simulation of I–V characteristics of a PV module with shaded PV cells. Solar Energy Mater Solar Cells 2003;75:613–21. [4] Gergaud O, Multon B, Ben Ahmed H. Analysis and experimental validation of various photovoltaic system models. Seventh international ELECTRIMACS Congress, Montre´al, August 2002. [5] De Soto W, Klein SA, Beckman WA. Improvement and validation of a model for photovoltaic array performance. Solar Energy 2006; 80(1):78–88.
[6] Gong X, Kulkarni M. Design optimization of a large scale rooftop photovoltaic system. Solar Energy 2005;78:362–74. [7] Kang FS, Su Eog Cho, Park SJ. A new control scheme of a cascaded transformer type multilevel inverter for a residential photovoltaic conditioning system. Solar Energy 2005;78: 727–38. [8] Abdullah AH, Ghoneim AA, AlHasen AY. Assessment of grid connected photovoltaic systems in the Kuwaiti climate. Renew Energy 2002;26:189–99. [9] Sheriff F, Turcotte D, Ross M. PV Toolbox: a comprehensive set of PV system components for the MATLAB/SIMULINK Environment. SESCI’2003, Queen’s University Canada. [10] Manolakos D, Papadakis G, Papantonis D, Kyritsis S. A simulationoptimisation programme for designing hybrid energy systems for supplying electricity and fresh water through desalination to remote areas. Appl Energy 2001; July: 679–704. [11] Muselli M, Notton G, Poggi P, Louche A. PV-hybrid power systems sizing incorporating battery storage: an analysis via simulation calculations. Renew Energy 2000;20:1–7. [12] Shouten NJ, Salman MA, Kheir NA. Energy management strategies for parallel hybrid vehicles using fuzzy logic. Control Eng Pract 2003;11(2):171–7. [13] ElShatter TF, Eskandar MN, Elhagry MT. Energy flow and management of hybrid wind/PV/fuel cell generation system. Energy Convers Manage 2006;47(9–10):1264–80. [14] Chaabene M, Annabi M. Dynamic thermal model for predicting solar plant adequate energy management. Energy Convers Manag 1998;39(3–4):349–55. [15] Beccali M, Cellura M, Ardente D. Decision making in energy planning: the ELECTRE multicriteria analysis approach compared to a FUZZY-SETS methodology. Energy Convers Manage 1998;39(16–18):1869–81. [16] Jeong K-S, Lee W-Y, Kim C-S. Energy management strategies of a fuel cell/battery hybrid system using fuzzy logics. J Power Sources 2005;145(2):319–26. [17] Ishengoma FM, Norum LE. Design and implementation of a digitally controlled stand-alone photovoltaic power supply. Nordic workshop on power and industrial electronics, 12–14 August 2002, NORPIE/2002, Stockholm, Sweden.
Renewable Energy 33 (2008) 993–1001 www.elsevier.com/locate/renene
Multi-criteria fuzzy algorithm for energy management of a domestic photovoltaic panel Chokri Ben Salahb, Maher Chaabenea,b,, Mohsen Ben Ammara,b a
The High Institute of Technological Studies (ISET), Sfax, Tunisia Unite´ de Commande de Machines et Re´seaux de Puissance CMERP-ENIS, Tunisia
b
Received 2 October 2006; accepted 19 May 2007 Available online 3 July 2007
Abstract This paper presents a fuzzy algorithm which makes decision so as to connect domestic apparatus on either the electrical grid or a photovoltaic panel (PVP). The decision is made in real time with respect to multi-energy save criteria and upon the PVP maximum available power and apparatus states. The algorithm is validated on a 1 kW peak (kWp) PVP and domicile apparatus of different powers installed at the Energy and Thermal Research Centre (CRTEn) in the north of Tunisia. Criteria are verified on the system behaviour during days covering the different seasons of the year. The power audit, established using measures, confirms that the energy save during daylight reaches 90% of the PVP available energy. r 2007 Elsevier Ltd. All rights reserved. Keywords: Energy management; Fuzzy decision; Photovoltaic; Energy saves
1. Introduction Household electric apparatus have become increasingly diversified during last years, which has led to an increase in energy need. Yet, the energy crisis does not cease being accentuated. These two constraints yield a heavy additional financial expense to the consumer. Several researches have confirmed that more than 60% of total useful energy represents buildings electric energy consumption [1], much of which could be recovered by integrating renewable energy and by formulating adequate energy management strategies inside buildings. For this reason, the exploitation of photovoltaic electricity has become an important issue of debate. Thus, three operating modes of PVP (photovoltaic panel) are distinguished: stand alone, grid connected and hybrid mode. In stand alone mode, the PVP represents the only source of electric energy for equipment. This mode is adopted Corresponding author. Rte Mahdia Km 2, BP88A, ElBustan, 3099 Sfax, Tunisia. Tel.: +216 74431425; fax: +216 74431386. E-mail addresses: [email protected], maherchaabane@ yahoo.com (M. Chaabene).
0960-1481/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.renene.2007.05.036
when the network is not available or when the equipment function depends only on the sun occurrence (pumping, lighting, air-conditioning, heating, etc.). Research interests are essentially related to the modelling [2–5], the optimization [6] and the adaptation system [7] of the PVP supply according to equipment needs. As for researches carried out on grid connected PVP, they generally deal with system assessment and characterization depending on site climate [8,9]. Finally, the hybrid mode is the combination of PVP with other energy sources. Published studies proposed either new design of PVP hybrid energy systems [10] or PVP hybrid power systems sizing [11]. For all operating modes, other researches developed energy management strategies so as to offer optimum function [12–14]. Nevertheless, the main problem in photovoltaic applications remains the battery cost, and the protection and synchronization systems of grid connected PVP [2] essentially when using large scale photovoltaic power station. In this paper, a new operating mode is proposed where a domestic PVP is considered as a complementary electric source to supply energy to domestic apparatus. There is no need for batteries neither for grid protection system. The installation incorporates a 1 kWp PVP, six apparatus of
ARTICLE IN PRESS C. Ben Salah et al. / Renewable Energy 33 (2008) 993–1001
994
powers varying between 50 and 500 W and a switching unit. A fuzzy decision making algorithm gives orders to the switching unit so as to connect each device either to the PVP output or to the electric grid. The decision of the appropriate connection mode is based on criteria that offer maximum exploitation of the energy delivered by the PVP during daylight depending on load demand without disturbing however apparatus’ function. The energy management system is implemented at the Energy and Thermal Research Centre (CRTEn) in the north of Tunisia since January 2005. The results validation is illustrated over four days representing the seasons of the year. Furthermore an energy audit was established and showed that the proposed system is able to bring an energy save during daylight up to 90% of the PVP generated energy. The various sections of this paper are organized as follows. Section 2 describes the system and fixes the energy management criteria. The fuzzy management algorithm is introduced in Section 3. Section 4 shows the system design and implementation. Validation and results are presented in Section 5. Finally, Section 6 provides perspectives and conclusion. 2. The management criteria The system studied in the present work aims to offer a utility decision tool on the connection way of domestic apparatus either on a domestic PVP output or on the electric grid. The decision is made in real time on the basis of the following criteria:
The connection of an active apparatus to PVP output cannot be decided unless PVP maximum available power is more than 110% of the apparatus operating Respecting low power apparatus priority
power, which guarantees continuous electric supply for active apparatus face to possible climate perturbation. Respecting apparatus priority: apparatuses of lower powers are more requested to be connected to PVP output so that to consume remaining PVP power from connected high power apparatuses. This criterion minimizes the power drawn from the electric grid. Maximizing connection time of a PVP connected apparatus: Since an apparatus is connected to PVP output, it has priority to remain connected so as to avoid relays’ commutations and ensure power supply stability for apparatuses.
The considered system contains many input/output variables. Furthermore, the decision to take must respect numerous and severe criteria. Indeed, the management algorithm has to acquire the domestic apparatus states and the PVP maximum available power, to treat the information according to the above fixed criteria and, at the same time, to ensure the apparatus switching control. Fig. 1 traces the synoptic schema of the proposed approach. The two available sources of electric energy are managed to provide power for apparatus, through fuzzy commands given to apparatus relays with respect of the above decision criteria. 3. The fuzzy management algorithm Fuzzy logic is one of the most powerful control methods. It is known by multi-rules-based resolution and multivariables consideration [15]. Compared to other methods such as neural networks and genetic algorithms, it provides fast results using only the expert knowledge. Hence, fuzzy logic method has been selected as a management tool for
Maximising connection time of a PVP connected apparatus
Reserving a power margin of +10% for PVP connected apparatus
CRITERIA PVP generation Electric grid Apparatus states Connections status
I N P U T S
ENERGY MANAGEMENT ALGORITHM
O U T P U T S
Decision commands for apparatus relays
OBJECTIVES
To minimise the power drawn from the electric grid.
To guarantee continuous electric supply for active apparatus face to possible climate perturbation.
To ensure power supply stability for apparatuses.
Fig. 1. The synoptic schema of the proposed approach.
ARTICLE IN PRESS C. Ben Salah et al. / Renewable Energy 33 (2008) 993–1001
the present system. This selection is judicious considering that it fulfills well the system requirements. Since the energy management approach uses fuzzy logic, its algorithm is based on three steps: the knowledge base of the expert, the fuzzification, the inference diagram and the defuzzification [15].
the symmetric triangular type (Fig. 2). These membership functions are be expressed as 8 < 1 jxj x0i j ex0i mAji ðx0i Þ ¼ : 0
According to apparatus states: The fuzzy partition of apparatus states is composed of N s ¼ 2 fuzzy subsets. Aji ¼ ðOFF; ONÞ is the ith fuzzy subset, i ¼ f1; 2g, of the jth apparatus, j ¼ f1; 2; 3; 4; 5; 6g. These subsets cover the fuzzy P s domain x ¼ ½0; 1 and verify 8 xj ¼ ERj 2 x; N i¼1 mAji ðxj Þ ¼ 1, where ERj is the state of the jth apparatus and mAji the membership function. According to 1 kW p PVP generation: Here the fuzzy partition is composed of N s ¼ 20 fuzzy subsets Bl ¼ ðA; B; . . . ; S; TÞ, l ¼ f1; 2; . . . ; 20g, which cover the fuzzy domain P y ¼ ½0; 1000. These fuzzy subsets verify s 8 yl ¼ Pl 2 Y ; N l¼1 mBl ðyÞ ¼ 1, where Pl is the PVP generation and mBl is the membership function. According to relays control: The relays command requires N s ¼ 2 fuzzy subsets. C jk ¼(grid,PVP) is the kth fuzzy subset, k ¼ f1; 2g, of the jth apparatus relay. These fuzzy subsets coverPthe fuzzy domain z ¼ ½0; 1 s and verify 8 zj ¼ ESj 2 z; N k¼1 mC jk ðzj Þ ¼ 1, where ESj is the command given to the jth apparatus relay and mC jk is the membership function.
3.2. The fuzzification The determined fuzzy partitions lead to the calculation of the membership functions mAji ; mBl and mC jk considering
if jxj x0i jpex0i
for apparatus states,
otherwise;
(1) (
3.1. The knowledge base of the expert The approach handles a multi-criteria resolution for which three fuzzy partitions are judged necessary:
995
mBl ðy0l Þ ¼
0l j 1 jyy ey
if jyj y0l jpey0l
0
otherwise;
0l
for PVP generation,
(2) ( mC jk ðz0k Þ ¼
1
jzj z0k j ez0k
0
if jzj z0k jpez0k otherwise;
for relays’commands,
(3) where x0i , y0l , z0k are, respectively, the real values of the variables xj , y, zj in their membership domains and ex0i , ey0l , ez0k are, respectively, the range values of x0i , y0l , z0k . 3.3. Inference diagram By means of the obtained membership functions and the apparatuses operating powers which are: 50, 100, 200, 300, 400 and 500 W, a rule base is established, according to Mamdani [16], using the general rule format: Rilk : if ðX is Ai and yl is Bl Þ then Z is C k ,
(4)
where X ¼ ½x1 x2 x6 is the apparatus states vector and Ai ¼ ½A1i A2i A6i its linguistic values vector, yl the PVP available generation and Bl its linguistic value, Z ¼ ½z1 z2 z6 the command vector of apparatus relays and C k ¼ ½C 1i C 2i C 6i its linguistic values vector. It can be seen that for a validated condition ðX is Ai and yl is Bl Þ of Eq. (4), many actions C k can be affected to the command vector Z. Consequently, a decision making procedure selects the action C k which verifies the criteria of Section 2.
Fig. 2. Membership functions according to: (a) apparatus state, (b) relay command, and (c) PVP generation.
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That is, consider the available PVP generation is 680 W ðBl ¼ NÞ, all apparatus are active (Ai ¼ [ON ON ON ON ON ON]). Subsequently, according to the rules base (Eq. (4), the following actions are generated: 1. C k ¼ [grid PVP PVP PVP grid grid], 2. C k ¼ [grid grid PVP grid PVP grid], and 3. C k ¼ [grid PVP grid grid grid PVP].
3.5. The management algorithm
By executing the decision making procedure, the maintained action is selected on the basis of the management criteria. Hence, the following cases are examined:
If all apparatuses are already connected to grid then the first decision is taken because it respects the priority of the apparatuses of lower powers (second criteria). If only the apparatus of 400 W operating power is already connected to PVP then the second decision is taken to respect the third management criterion. If only the apparatus of 500 W operating power is already connected to PVP then the third decision is taken to respect the third management criterion.
Since the decision is taken (which case to consider), Eq. (4) is therefore computed for i ¼ 1; 2; l ¼ 1 20 and P k ¼ 1; 2 to generate a rules base composed of 20 6j¼1 C j6 ¼ 1280 rules. The rules’ aggregations are given by computing the minimum norm conjunction implication of each fuzzy subset of the jth apparatus relay: mC 0j1 ¼ minðwj1 ; mcj1 Þ
for the first fuzzy subset,
(5)
mC 0j2 ¼ minðwj2 ; mcj2 Þ
for the second fuzzy subset,
(6)
where wj1 is the minimum norm fuzzy conjunction between the first fuzzy subset of the jth apparatus and the lth fuzzy subset of the PVP generation: wj1 ¼ minðmAj1 ; mBl Þ,
Hence, the relay control of the jth apparatus is determined by ( ESj ¼ grid if z0k o0:5; (11) ESj ¼ PVP if z0k X0:5:
Acquire: Pl ; ER1 ; . . . ; ER6 {Read the available PVP generation and apparatus states} Pl ¼ 90 %Pl {Let a power margin of 10% to respect the first management criterion} Pl l ¼ E 50 {The fuzzy subsets’ number of the PVP generation} Fuzzification: Compute mAji ; mBl ; mC jk {The membership functions} Inference diagram: Compute Rilk : if ðX is Ai and y is Bl Þ then Z is C k : {The rules base} Make the decision {Basing on management criteria} Calculate mC 1 ; . . . ; mC 6 {The membership functions of the operating points} Defuzzification: Compute z0k the centres of mC j {using the centroid method} Compute ES1 ; . . . ; ES6 {The apparatus relays’ commands}. 4. The system implementation The system is implemented at the Energy and Thermal Research Centre (CRTEn) in the north of Tunisia since January 2005. It includes:
(7)
and wj2 is the minimum norm fuzzy conjunction between the second fuzzy subset of the jth apparatus and the ðl þ 1Þth fuzzy subset of the PVP generation: wj2 ¼ minðmAj2 ; mBlþ1 Þ.
(8)
Using the maximum t-conorm rule aggregation, the membership function for an operating point of the jth apparatus relay is given by mC j ¼ maxðmC 0j1 ; mC 0j2 Þ.
(9)
3.4. Defuzzification Since the rules are aggregated, the defuzzification consists of calculating the real value z0k of the relay state of each apparatus using the centroid method (z0k is the centre of mC j ): R1 zj mC j dzj . (10) z0k ¼ R0 1 0 mC j dzj
1 kW p PVP and the electric grid as energy sources. The PVP is equipped with a Maximum Power point Tracker (MPPT) [13] which is an electronic device that monitors PVP generation to operate near its maximum power point along the I–V curve and an inverter that provides the same output voltage as the electric grid (230 V/50 Hz) [7]. Six household apparatus of different power: 50, 100, 200, 300, 400 and 500 W (230 V/50 Hz). Each one is controlled by a two position relay in order to be connected either to the PVP output or to the electric grid.
When sizing the PVP power rating, the main objective consisted to minimize the lost power generated by the PVP during the system function. Yet, the maximum load power of the installation is 1500 W (if all apparatuses are switched on). So, it has been estimated that PVP generation must cover 23 of the total needed power (1000 W). This proportion is judicious since it is rarely encountered that all apparatuses are switched on. Furthermore, as the PVP is used for domestic application, we took into consideration that the system cost would be reduced as much as possible.
ARTICLE IN PRESS C. Ben Salah et al. / Renewable Energy 33 (2008) 993–1001
Apparatus 1
Apparatus 2
997
Apparatus 6
ON/OFF switches
Apparatus states ER j
ES1
ES6
ES2
MPPT & Inverter
Output commands (Defuzzification) Rule base
Decision making
Electric grid
Relays
Criteria base
1kWp PVP
Fuzzification
Ta Data acquisition system
I Fig. 3. System components and implementation.
Fig. 3 shows the connection schema of the system components. The decision centre is composed of a personnel computer equipped with a data acquisition and control card. The PVP maximum available power ðPl Þ is calculated on the basis of a published 1 kW p PVP validated model [17]: I I 3 Pl ¼ 20 3:33 þ 1:210 T a þ 25 1000 40 I þ3:35 1 upv , 1000
ð12Þ
where I and T a are, respectively, the acquired solar radiation and the ambient temperature measured at the surface of the PVP. upv is the PVP output voltage fixed to 12 V by the MMPT device. The algorithm is implemented using the Matlab software as a programming tool. After implementation, the system has been tested during the year 2005. All its input/output ðT a ; I; ERj ; ESj Þ have been daily recorded using a time step of 5 min. A power audit has been also established in order to determine the system performance. Even so, for clearness reason the system behaviour and performance is given only for four days representing the year’s seasons. Fig. 4 shows the fuzzy commands timing of relays during daylight. During function, all apparatus were switched on in order to evaluate the contribution of the PVP generation to the whole installation. By examining the fuzzy decisions, it can be easily deduced that most commutations between grid and PVP output are observed at apparatus of lower power. This is due to the above management constraints (Section 2) which affect the higher priority to apparatus of lower power in order to recuperate the remaining power of the ones of higher power. As well, commutations can be
seen at apparatus of high power when PVP generation is available (June and September). In this case these commutations are limited to the time around midday. Finally, only lower power apparatus are connected to PVP output while PVP generation is weak (December). Since it holds the lower priority, the apparatus of 500 W could not be connected to the PVP output unless other apparatus are switched off and there is enough PVP generation (Fig. 5). In fact, in case 1 all apparatus of 100–400 W are switched off to give the chance to apparatus of 500 W to be connected to PVP output. However, in case 2, the apparatus of 500 W is switched off, and as a consequence any other apparatus will be connected to PVP output, respecting management criteria (Section 2), as soon as it is switched on. 5. Approach valorization The valorization of the designed system consists of daily and monthly assessments. 5.1. Daily assessment The approach assessment is ensured by the establishment of a daily power audit. Fig. 6 plots in real time the curves of the PVP related powers (PVPA : maximum available, consumed: PVPC , lost: PVPL ) and of the power load from grid (GLP) during the four chosen representative days (Section 4). It is noted that the curve of PVPC follows the variations of PVPA in order to minimize PVPL . Similarly, GLP decreases considerably around midday especially during days of sunny seasons. These interpretations confirm the approach contribution in term of energy save and management for the whole installation.
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Fig. 4. Timing of commands given to apparatus relays (all apparatus switched on): X-axis—1 unit ¼ 5 min of the daylight, and Y-axis—0: apparatus connected to grid; and 1: apparatus connected to PVP output.
5.2. Monthly assessment The same study was renewed to form a monthly energy balance (Fig. 7) so as to prove the effectiveness of the management approach. All PVP related powers are integrated over daylight (from sunrise (SR) to sunset (SS)). Obtained energies are cumulated over the month length (ML) to compute PVP monthly energies (maximum
available: PVPAE , consumed: PVPCE , lost: PVPLE Þ as follows: ML Z SSðjÞ X PVPA ðtÞ dt; PVPAE ¼ j¼1
PVPCE ¼
ML Z X j¼1
SRðjÞ SSðjÞ
PVPC ðtÞ dt; SRðjÞ
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Fig. 5. Timing of relays commands (apparatus manipulated): X-axis—time: 1 unit ¼ 5 min of the daylight; and Y-axis—apparatus state: 0: switched off; 1: connected to grid; and 2: connected to PVP output.
PVPLE ¼
ML Z X j¼1
SSðjÞ
PVPL ðtÞ dt.
SRðjÞ
While the electric energy produced by the PVP varies between 80 and 160 kW h/month, the electric energy consumed from the PVP varies between 65 and 145 kW h/ month which involves an unused energy about 15 kW h/ month. This lost energy is generally produced during the sunrise and sunset times where PVP maximum available power is insufficient ðo50 WÞ to supply energy for even the
lower power apparatus. A second valorization consists of the calculation of a monthly effectiveness coefficient defined by Z% ¼
PVPAE PVPLE PVPCE 100 ¼ 100. PVPAE PVPAE
Table 1 gives the ðZ%Þ. This coefficient is almost constant through the months of the year and it varies between 80% and 90% which justifies the continuous energy save contribution of the proposed solution.
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Fig. 6. The daily power audit: X-axis—1 unit ¼ 5 mn of the daylight and Y-axis—the power (W).
Fig. 7. The monthly energy balance.
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Table 1 The monthly effectiveness coefficient
PVPAE PVPCE PVPLE Z%
January
February
March
April
May
June
July
August
September
October
November
December
86.2 69.8 16.4 81.0
98.8 85.7 13.1 86.7
129.1 115.8 13.3 89.7
135.2 120.2 15 88.9
148.3 129.8 18.5 87.5
149.4 133.7 15.7 89.5
156.4 139.2 17.2 89
161.3 145.4 15.9 90.1
136.9 122.2 14.7 89.3
123.3 109.5 13.8 88.8
92.5 79.3 13.2 85.7
78.6 62.8 15.9 79.9
6. Conclusion The efficient management of the energy produced by a conversion system depends on consumption needs on the one hand and on the supplied energy (generated by the conversion system) on the other hand. Herein the energy produced by a PVP of 1 kWp is optimally managed to provide a complementary energy for household apparatus so as to offer a maximum energy saving. The management approach consists of a fuzzy algorithm which decides whether each domestic apparatus should be connected to PVP output or to grid. Decision is made on the basis of optimum management criteria, PVP generation and apparatus states. The system is implemented and tested during 2005 at the Energy and Thermal Research Centre (CRTEn) in the north of Tunisia. A carried out energetic audit confirms that 90% of PVP generated energy is brought to the installation as energy save. References [1] Fanny AH, Dougherty BP, Davis MW. Measured performance of building integrated photovoltaic panels. Solar energy: The power to choose, Forum 2001, Washington, DC. [2] Xu M, Melnik RVN, Borup U. Modelling anti-islanding protection devices for photovoltaic systems. Renew Energy 2004;29:2195–216. [3] Kawamura H, Naka K, Yonekura N. Simulation of I–V characteristics of a PV module with shaded PV cells. Solar Energy Mater Solar Cells 2003;75:613–21. [4] Gergaud O, Multon B, Ben Ahmed H. Analysis and experimental validation of various photovoltaic system models. Seventh international ELECTRIMACS Congress, Montre´al, August 2002. [5] De Soto W, Klein SA, Beckman WA. Improvement and validation of a model for photovoltaic array performance. Solar Energy 2006; 80(1):78–88.
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