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Optimal Sampling and Maintenance Plans for the Lighting Retrofit Projects Towards Sustainable Energy Savings
Available online at www.sciencedirect.com
ScienceDirect Energy Procedia 61 (2014) 648 – 651
The 6th International Conference on Applied Energy – ICAE2014
Optimal Sampling and Maintenance Plans for the Lighting Retrofit Projects towards Sustainable Energy Savings Xianming Ye*, Xiaohua Xia Department of Electrical, Electronic and Computer Engineering, University of Pretoria, Pretoria 0002, South Africa
Abstract In this article, the optimal sampling and maintenance plans are both designed for the EE lighting retrofit projects. By adopting the optimal solutions, the project sponsors receive additional and sustainable energy savings over a 10years’ crediting period. The reported project performance is accurate enough to satisfy the project sampling accuracy requirements. In addition, the PDs’ profit is maximised with a proper reinvestment for the lighting project maintenance. A case study of designing the optimal sampling and maintenance plans for an EE lighting retrofit project is presented for illustrative purpose. © 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
© 2014 The Authors. Published by Elsevier Ltd. (http://creativecommons.org/licenses/by-nc-nd/3.0/). peer-review of under responsibility of ICAE Selection Peer-reviewand/or under responsibility the Organizing Committee of ICAE2014
Keywords: Lighting; Energy Efficiency; Sample size determination; Optimal control.
1. Introduction A great potential of energy savings can be generated with the implementation of energy efficiency (EE) lighting retrofit projects ([1]). The lighting retrofit solution is to replace inefficient lamps with efficient ones. In the literature, a large number of lighting retrofit projects has been implemented by adopting the compact fluorescent lamp (CFL) and light emitting diode (LED) technologies ([2]). Practically, the following barriers hold the lighting project developers (PDs) back from obtaining their maximum benefits. Firstly, the energy saving performance for the implemented lighting project is not sustainable and vanishes rapidly due to poor maintenance for the installed lighting systems as the lighting population will decay as time goes by. The scope of the maintenance refers to the replacement of the nonrepairable lamp burnouts. Secondly, to accurately evaluate the lighting project performance is very costly when continuously monitoring and sampling efforts are required to the large decentralised lighting population. In order to maximise the PDs profits and encourage the future implementation of EE lighting projects, previous study [3] has proposed a control system approach to design an optimal maintenance plan at a fixed schedule, by which both the PDs’ benefits and the project energy savings performance are maximised. In addition, studies ([5-6]) have developed both spatial and longitudinal metering cost minimisation models to design the optimal monitoring and sampling plans as to evaluate lighting project * Corresponding author. Tel.: +27 (0)12 420 4353; fax: +27 (0)12 362 5000; E-mail address: [email protected].
1876-6102 © 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/). Peer-review under responsibility of the Organizing Committee of ICAE2014 doi:10.1016/j.egypro.2014.11.934
649
Xianming Ye and Xiaohua Xia / Energy Procedia 61 (2014) 648 – 651
performance accurately and cost-effectively. To further improve the PDs’ benefits in implementing EE lighting retrofit projects, this study aims to incorporate the advantages of both the optimal maintenance and sampling plan for typical lighting EE retrofit projects. 2. Problem formulation In this study, the optimal maintenance plan (OMP) decides the optimal replacement quantities for each maintenance interval instead of simply replacing all the failed EE devices to the original full population. Once the optimally controlled lighting population is decided, the metering cost minimisation model in [56] is adopted to design the longitudinal optimal sampling plan for the project performance evaluation. The two separate problems for the EE lighting projects are then combined and formulated as one cost optimisation problem, of which the objective is to maximise the PDs’ benefits with the satisfaction of the projects’ practical constraints. 2.1. Lamp population decay dynamics and optimal maintenance plan modelling Given an EE lighting retrofit project with homogeneous lamp population involved, let t0 and tf denote the beginning and end of the project crediting period, respectively. T denotes the fixed maintenance interval, tk=t0+kT, k=0, 1,..., K−1 is used to denote the time schedules for the maintenance. When time sequence {tk} and T are both determined, tk can be simply denoted by k and the time period [tk, tk+1) is simplified as [k, k+1). x(0) denotes the initial lighting project population. Generally, the OMP problem is to find an optimal control sequence u(k) within the time period [0, K). Here u(k) is the control system input, which is the replacement quantity for the interval [k, k+1). The OMP problem under the control system framework is formulated in the following general form: ° x k 1 f x k u k , ® °¯ y k g x k ,
(1)
where x(k) denotes the state variable that corresponds to the number of survived the lamps for the time interval [k, k+1), the system output y(k) is a function of x(k). f(x(k)) denotes the function to model the lamp population decay dynamics. As discussed in [3-4], the discrete and dynamic form of the lamp population decay is given as follows: 2 (2) f x k bcx k / x 0 bx k x k , for different lighting devices, the coefficients b and c are different and can be obtained by the system identification approach proposed in [4]. 2.2. Sample size determination and optimal longitudinal sampling plan As discussed in [5-6], the sample size n can be determined by the population N, the coefficient of variance (CV) of the sampling records, the required confidence and precision levels. CV 2 z 2 N , (3) n= f N , z, p, CV CV 2 z 2 Np 2 where CV is defined as the standard deviation of the sampling records divided by the mean. If CV is unknown, 0.5 is historically recommended by [7] as an initial CV. z denotes the abscissas of the normal distribution curve that cut off an area at the tails to give desired confidence level, also known as the zscore and p is the relative precision. As given in (3), the required sample size varies when the targeted sampling population changes. In this study, the lamp population is optimally controlled during the project maintenance. Thus the annual required sample sizes can also be optimally decided to achieve the required sampling accuracy. More details of the optimal longitudinal sampling plan are presented in [6].
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Xianming Ye and Xiaohua Xia / Energy Procedia 61 (2014) 648 – 651
2.3. Lighting retrofit project profit modelling and optimisation 4.5
x 10
5
x(k)
x(0)
No control
Adopted meters
u(k)
Backup meters
35
4
30
3.5 Number of meters
Number of lamps
25
3 2.5 2 1.5
20
15
10
1 5
0.5 0
0
0
2
4
6
8
10
Year
0
2
4
6
8
10
Year
(a) (b) Fig. 1. (a) Optimal lighting population control strategy; (b) annual adopted meters and backup meters
Let 41 be the initial investment of a lighting retrofit project, 42 and 3 2 denote the total project investment and the total project profits over the K crediting years. n(k)is the required number of meters to measure the daily energy consumption per lamp while nˆ k is the number of samples required to check the lamp survive rate. α denotes the cost related to individual lighting EE device, including the procurement price, delivery, removal of an old lamp and installation of a new lamp; β denotes the project transaction cost, occupies 5% of 41 ; and γ is the sampling cost per lamp. τ1, τ2 and τ3 are the individual meter procurement price, installation fee and annual data service cost, respectively. B(k) denotes the backup meters in the kth year, B(0)=0 and S(k) is the mathematic sign of B(k). The problem is to find the optimal lamp control sequence u(k) and the optimal annual sample size n(k) that maximise PDs’ profits by implementing an EE lighting retrofit project. As given in (3), the sample size n(k) can be denoted by the survived lamp population x(k), CV(k), z(k) and p(k) in the kth crediting year. 41 = D x 0 W1 W 2 n 0 E , 42
K-1
41 +¦ ¬ªD u k W 3n k B k S k W 1 W 2 J nˆ k ¼º ,
(4) (5)
k=0
where B k 1 max B k ,0 +n k n(k + 1) and S k 0.5sgn B k 0.5 , sgn(.) is the sign function. 32
K-1
¦ rx k 4
2
,
(6)
k=0
The objective function is defined as 3 J 2, 2
42
(7)
subject to the constraints (8) and (1). x(k ) d x 0 , ° ° x k t 0.5 x 0 , ° k 1 ° ® ¦ ª¬D u j W 3n j B j S j W 1 W 2 J nˆ j º¼ rx j d 0, °j 0 ° Z G t 1.645, ° °¯ P G d 0.1,
(8)
where Z(δ) and P(δ) are the the cumulative z-score and precision from the first up to the δth crediting year. Detailed formulas to calculate Z(δ) and P(δ) are given in [6]. 3. Case Study A lighting retrofit project in the residential households is going to be implemented. There are 404 876 units of EE 12 W CFLs to be installed to replace existing 60 W incandescent lamps (ICLs). These lamps are burning 6 hours per day on average. The PDs of this project will receive a rebate rate at R 0.42 per
Xianming Ye and Xiaohua Xia / Energy Procedia 61 (2014) 648 – 651
kWh savings realised annually from the project sponsors. R is short for the South Africa Currency Rand. The coefficients in (2) are bc=0.8268, b=0.8863, respectively. The meter device prices τ1, τ2 and τ3 are R 4032 per unit, R 520 per unit and R 1464 per year, respectively. The performance reporting years δ=2, 4, 6, 8 and 10 and in each reporting year, the performance evaluation accuracy must satisfy the 90/10 criterion [5-6]. The computations to solve the model formulated in Section 2.3 are carried out by the ‘fmincon’ code of the Matlab Optimisation Toolbox. The results are presented in Fig.1 and Table 1. In Table 1, The key performance indicators (KPI), such as the total investments (TotalInv) , total profits (TotalPro), the inputoutput ratio (ioRatio), and the total energy savings (EngSav) for the EE lighting project under the scenarios with/without optimisations (without optimisation, u(k)=0, z(k)=1.645 and p(k)=0.1) are summarised and compared. The ioRatio increase 6% and the total project energy savings with the optimisation model increase 108%. Table 1. Project KPI analysis KPI
No optimisation
Optimisation
Increase (%)
TotalInv (MR)
16.520
32.688
98%
TotalPro (MR)
58.769
123.75
111%
ioRatio
3.5575
3.7859
6%
EngSav (MWh)
179 260
372 480
108%
4. Conclusion In this study, the optimal sampling and maintenance plans are both designed for the lighting EE retrofit project. With the adoption of the optimal sampling and maintenance plans, the project sponsors receive additional energy savings. The reported project performance is accurate enough to satisfy the project sampling accuracy requirements. In addition, the PDs’ profits is maximised with proper reinvestment for the lighting project maintenance. References [1] Mills E. Global lighting energy savings potential. Light & Engineering 2002;10(4):5–10. [2] Mahlia T, Said M, Masjuki H, Tamjis M. Cost-benefit analysis and emission reduction of lighting retrofits in residential sector. Energy and Buildings 2005;37(6):573 –8. [3] Ye X, Xia X. Optimal lighting project maintenance planning by a control system approach. Submitted to IFAC 2014 (under review). [4] Carstens H, Xia X, Zhang J, Ye X. Characterising compact fluorescent lamp population decay. Mauritius: IEEE AFRICON 2013; 2013. [5] Ye X, Xia X, Zhang J. Optimal sampling plan for clean development mechanism energy efficiency lighting projects. Applied Energy 2013;112:1006–15. [6] Ye X, Xia X, Zhang J. Optimal sampling plan for clean development mechanism lighting projects with lamp population decay. Submitted to Applied Energy 2013 (under review). [7] EVO. International performance measurement and verification protocol: concepts and options for determining energy and water savings, Volume 1. Technical Report; 2012.
Biography Mr. Xianming Ye obtained both B.Eng and M.Eng at Wuhan University, Wuhan, China in 2008 and 2010, respectively. He is a PhD candidate in Electrical Engineering at University of Pretoria since September 2010. His research interests are energy efficiency and demand side management, energy modelling and optimisation. Prof. Xiaohua Xia obtained his PhD degree at Beijing University of Aeronautics and Astronautics, Beijing, China, in 1989. He is the director of both the Centre of New Energy Systems at the University of Pretoria and the National Hub for the Postgraduate Programme in Energy Efficiency and Demand Side Management.
651
ScienceDirect Energy Procedia 61 (2014) 648 – 651
The 6th International Conference on Applied Energy – ICAE2014
Optimal Sampling and Maintenance Plans for the Lighting Retrofit Projects towards Sustainable Energy Savings Xianming Ye*, Xiaohua Xia Department of Electrical, Electronic and Computer Engineering, University of Pretoria, Pretoria 0002, South Africa
Abstract In this article, the optimal sampling and maintenance plans are both designed for the EE lighting retrofit projects. By adopting the optimal solutions, the project sponsors receive additional and sustainable energy savings over a 10years’ crediting period. The reported project performance is accurate enough to satisfy the project sampling accuracy requirements. In addition, the PDs’ profit is maximised with a proper reinvestment for the lighting project maintenance. A case study of designing the optimal sampling and maintenance plans for an EE lighting retrofit project is presented for illustrative purpose. © 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
© 2014 The Authors. Published by Elsevier Ltd. (http://creativecommons.org/licenses/by-nc-nd/3.0/). peer-review of under responsibility of ICAE Selection Peer-reviewand/or under responsibility the Organizing Committee of ICAE2014
Keywords: Lighting; Energy Efficiency; Sample size determination; Optimal control.
1. Introduction A great potential of energy savings can be generated with the implementation of energy efficiency (EE) lighting retrofit projects ([1]). The lighting retrofit solution is to replace inefficient lamps with efficient ones. In the literature, a large number of lighting retrofit projects has been implemented by adopting the compact fluorescent lamp (CFL) and light emitting diode (LED) technologies ([2]). Practically, the following barriers hold the lighting project developers (PDs) back from obtaining their maximum benefits. Firstly, the energy saving performance for the implemented lighting project is not sustainable and vanishes rapidly due to poor maintenance for the installed lighting systems as the lighting population will decay as time goes by. The scope of the maintenance refers to the replacement of the nonrepairable lamp burnouts. Secondly, to accurately evaluate the lighting project performance is very costly when continuously monitoring and sampling efforts are required to the large decentralised lighting population. In order to maximise the PDs profits and encourage the future implementation of EE lighting projects, previous study [3] has proposed a control system approach to design an optimal maintenance plan at a fixed schedule, by which both the PDs’ benefits and the project energy savings performance are maximised. In addition, studies ([5-6]) have developed both spatial and longitudinal metering cost minimisation models to design the optimal monitoring and sampling plans as to evaluate lighting project * Corresponding author. Tel.: +27 (0)12 420 4353; fax: +27 (0)12 362 5000; E-mail address: [email protected].
1876-6102 © 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/). Peer-review under responsibility of the Organizing Committee of ICAE2014 doi:10.1016/j.egypro.2014.11.934
649
Xianming Ye and Xiaohua Xia / Energy Procedia 61 (2014) 648 – 651
performance accurately and cost-effectively. To further improve the PDs’ benefits in implementing EE lighting retrofit projects, this study aims to incorporate the advantages of both the optimal maintenance and sampling plan for typical lighting EE retrofit projects. 2. Problem formulation In this study, the optimal maintenance plan (OMP) decides the optimal replacement quantities for each maintenance interval instead of simply replacing all the failed EE devices to the original full population. Once the optimally controlled lighting population is decided, the metering cost minimisation model in [56] is adopted to design the longitudinal optimal sampling plan for the project performance evaluation. The two separate problems for the EE lighting projects are then combined and formulated as one cost optimisation problem, of which the objective is to maximise the PDs’ benefits with the satisfaction of the projects’ practical constraints. 2.1. Lamp population decay dynamics and optimal maintenance plan modelling Given an EE lighting retrofit project with homogeneous lamp population involved, let t0 and tf denote the beginning and end of the project crediting period, respectively. T denotes the fixed maintenance interval, tk=t0+kT, k=0, 1,..., K−1 is used to denote the time schedules for the maintenance. When time sequence {tk} and T are both determined, tk can be simply denoted by k and the time period [tk, tk+1) is simplified as [k, k+1). x(0) denotes the initial lighting project population. Generally, the OMP problem is to find an optimal control sequence u(k) within the time period [0, K). Here u(k) is the control system input, which is the replacement quantity for the interval [k, k+1). The OMP problem under the control system framework is formulated in the following general form: ° x k 1 f x k u k , ® °¯ y k g x k ,
(1)
where x(k) denotes the state variable that corresponds to the number of survived the lamps for the time interval [k, k+1), the system output y(k) is a function of x(k). f(x(k)) denotes the function to model the lamp population decay dynamics. As discussed in [3-4], the discrete and dynamic form of the lamp population decay is given as follows: 2 (2) f x k bcx k / x 0 bx k x k , for different lighting devices, the coefficients b and c are different and can be obtained by the system identification approach proposed in [4]. 2.2. Sample size determination and optimal longitudinal sampling plan As discussed in [5-6], the sample size n can be determined by the population N, the coefficient of variance (CV) of the sampling records, the required confidence and precision levels. CV 2 z 2 N , (3) n= f N , z, p, CV CV 2 z 2 Np 2 where CV is defined as the standard deviation of the sampling records divided by the mean. If CV is unknown, 0.5 is historically recommended by [7] as an initial CV. z denotes the abscissas of the normal distribution curve that cut off an area at the tails to give desired confidence level, also known as the zscore and p is the relative precision. As given in (3), the required sample size varies when the targeted sampling population changes. In this study, the lamp population is optimally controlled during the project maintenance. Thus the annual required sample sizes can also be optimally decided to achieve the required sampling accuracy. More details of the optimal longitudinal sampling plan are presented in [6].
650
Xianming Ye and Xiaohua Xia / Energy Procedia 61 (2014) 648 – 651
2.3. Lighting retrofit project profit modelling and optimisation 4.5
x 10
5
x(k)
x(0)
No control
Adopted meters
u(k)
Backup meters
35
4
30
3.5 Number of meters
Number of lamps
25
3 2.5 2 1.5
20
15
10
1 5
0.5 0
0
0
2
4
6
8
10
Year
0
2
4
6
8
10
Year
(a) (b) Fig. 1. (a) Optimal lighting population control strategy; (b) annual adopted meters and backup meters
Let 41 be the initial investment of a lighting retrofit project, 42 and 3 2 denote the total project investment and the total project profits over the K crediting years. n(k)is the required number of meters to measure the daily energy consumption per lamp while nˆ k is the number of samples required to check the lamp survive rate. α denotes the cost related to individual lighting EE device, including the procurement price, delivery, removal of an old lamp and installation of a new lamp; β denotes the project transaction cost, occupies 5% of 41 ; and γ is the sampling cost per lamp. τ1, τ2 and τ3 are the individual meter procurement price, installation fee and annual data service cost, respectively. B(k) denotes the backup meters in the kth year, B(0)=0 and S(k) is the mathematic sign of B(k). The problem is to find the optimal lamp control sequence u(k) and the optimal annual sample size n(k) that maximise PDs’ profits by implementing an EE lighting retrofit project. As given in (3), the sample size n(k) can be denoted by the survived lamp population x(k), CV(k), z(k) and p(k) in the kth crediting year. 41 = D x 0 W1 W 2 n 0 E , 42
K-1
41 +¦ ¬ªD u k W 3n k B k S k W 1 W 2 J nˆ k ¼º ,
(4) (5)
k=0
where B k 1 max B k ,0 +n k n(k + 1) and S k 0.5sgn B k 0.5 , sgn(.) is the sign function. 32
K-1
¦ rx k 4
2
,
(6)
k=0
The objective function is defined as 3 J 2, 2
42
(7)
subject to the constraints (8) and (1). x(k ) d x 0 , ° ° x k t 0.5 x 0 , ° k 1 ° ® ¦ ª¬D u j W 3n j B j S j W 1 W 2 J nˆ j º¼ rx j d 0, °j 0 ° Z G t 1.645, ° °¯ P G d 0.1,
(8)
where Z(δ) and P(δ) are the the cumulative z-score and precision from the first up to the δth crediting year. Detailed formulas to calculate Z(δ) and P(δ) are given in [6]. 3. Case Study A lighting retrofit project in the residential households is going to be implemented. There are 404 876 units of EE 12 W CFLs to be installed to replace existing 60 W incandescent lamps (ICLs). These lamps are burning 6 hours per day on average. The PDs of this project will receive a rebate rate at R 0.42 per
Xianming Ye and Xiaohua Xia / Energy Procedia 61 (2014) 648 – 651
kWh savings realised annually from the project sponsors. R is short for the South Africa Currency Rand. The coefficients in (2) are bc=0.8268, b=0.8863, respectively. The meter device prices τ1, τ2 and τ3 are R 4032 per unit, R 520 per unit and R 1464 per year, respectively. The performance reporting years δ=2, 4, 6, 8 and 10 and in each reporting year, the performance evaluation accuracy must satisfy the 90/10 criterion [5-6]. The computations to solve the model formulated in Section 2.3 are carried out by the ‘fmincon’ code of the Matlab Optimisation Toolbox. The results are presented in Fig.1 and Table 1. In Table 1, The key performance indicators (KPI), such as the total investments (TotalInv) , total profits (TotalPro), the inputoutput ratio (ioRatio), and the total energy savings (EngSav) for the EE lighting project under the scenarios with/without optimisations (without optimisation, u(k)=0, z(k)=1.645 and p(k)=0.1) are summarised and compared. The ioRatio increase 6% and the total project energy savings with the optimisation model increase 108%. Table 1. Project KPI analysis KPI
No optimisation
Optimisation
Increase (%)
TotalInv (MR)
16.520
32.688
98%
TotalPro (MR)
58.769
123.75
111%
ioRatio
3.5575
3.7859
6%
EngSav (MWh)
179 260
372 480
108%
4. Conclusion In this study, the optimal sampling and maintenance plans are both designed for the lighting EE retrofit project. With the adoption of the optimal sampling and maintenance plans, the project sponsors receive additional energy savings. The reported project performance is accurate enough to satisfy the project sampling accuracy requirements. In addition, the PDs’ profits is maximised with proper reinvestment for the lighting project maintenance. References [1] Mills E. Global lighting energy savings potential. Light & Engineering 2002;10(4):5–10. [2] Mahlia T, Said M, Masjuki H, Tamjis M. Cost-benefit analysis and emission reduction of lighting retrofits in residential sector. Energy and Buildings 2005;37(6):573 –8. [3] Ye X, Xia X. Optimal lighting project maintenance planning by a control system approach. Submitted to IFAC 2014 (under review). [4] Carstens H, Xia X, Zhang J, Ye X. Characterising compact fluorescent lamp population decay. Mauritius: IEEE AFRICON 2013; 2013. [5] Ye X, Xia X, Zhang J. Optimal sampling plan for clean development mechanism energy efficiency lighting projects. Applied Energy 2013;112:1006–15. [6] Ye X, Xia X, Zhang J. Optimal sampling plan for clean development mechanism lighting projects with lamp population decay. Submitted to Applied Energy 2013 (under review). [7] EVO. International performance measurement and verification protocol: concepts and options for determining energy and water savings, Volume 1. Technical Report; 2012.
Biography Mr. Xianming Ye obtained both B.Eng and M.Eng at Wuhan University, Wuhan, China in 2008 and 2010, respectively. He is a PhD candidate in Electrical Engineering at University of Pretoria since September 2010. His research interests are energy efficiency and demand side management, energy modelling and optimisation. Prof. Xiaohua Xia obtained his PhD degree at Beijing University of Aeronautics and Astronautics, Beijing, China, in 1989. He is the director of both the Centre of New Energy Systems at the University of Pretoria and the National Hub for the Postgraduate Programme in Energy Efficiency and Demand Side Management.
651