27th European Photovoltaic Solar Energy Conference and Exhibition
DEVELOPMENT OF A RELIABILITY MODEL FOR THE ESTIMATION OF THE LOSS OF LOAD PROBABILITY AND O&M COST FOR AN OFF-GRID PV SYSTEM Marios Theristis1,3,*, Georgios C. Bakos1, Ioannis A. Papazoglou2 Department of Electrical & Computer Engineering, Democritus University of Thrace, Xanthi, 67 100, Greece 2 Institute of Nuclear Technology & Radiation Protection, N.C.S.R. “Demokritos”, Athens, 15 310, Greece 3 Presently at the School of Engineering & Physical Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, U.K. *Corresponding author email:
[email protected] 1
ABSTRACT: A residential standalone photovoltaic system is evaluated in terms of its optimum configuration taking into consideration cost and reliability aspects. Given a specific electricity demand, the optimum combination of PV arrays and batteries is assessed using the Loss of Load Probability (LOLP) as a criterion. Both the sizing of the system and the reliability of its components are also taken into consideration for assessing the LOLP. The supply performance of the system is simulated based on hourly demand and meteorological data while the stochastic behaviour of the system, with regards to its reliability, is simulated by a Markov model. Literature based failure data are used to quantify the reliability model and, thus, estimate the mean operation and maintenance cost of the system. Keywords: Standalone Photovoltaic system, Reliability, Markovian Models, Optimum Sizing, O&M Cost
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INTRODUCTION
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This paper examines the reliability of a standalone PV system in order to estimate the mean operation and maintenance (O&M) cost throughout the system’s lifetime. The system is sized using the Loss of Load Probability (LOLP or LLP). Many studies have investigated or applied this parameter for various standalone PV systems [1-4]. The LOLP is given in two different definitions in literature; the first defines LOLP as a measure of the system’s performance which is the ratio between the energy deficit to the energy demand, over the total operation time of the application [1]: ∫
The term reliability represents the ability of a system to perform its required functions under stated conditions, identified during its design, for a specified period of time [5]. The mean time to failure of a system (MTTF), is the expected time until the first system’s failure takes place. Given a system reliability R(t), the MTTF can be calculated as [6]: ∫
(1)
while the second, which is used in the present work, defines the LOLP as the percentage of time were the system doesn’t satisfy the energy load demand: ⋃(
) (2)
where N is the total number of hours which are considered, EA is the available energy, ED is the energy demand and ⋃(EA-ED) is the unit-step function which is defined as: (
)
{
( )
(4) In order to solve and use the reliability models, it is necessary to study a number of fundamental parameters; failure rates (λ), repair rates (μ), error coverage probability (c) and reward rate (r). Nevertheless, the ones that concern us in this present work are the first two. Failure rate (λ) is defined as how often a mechanical system, component or sub-system fails. It is usually expressed in failures per hours and is equal to 1/MTTF. The repair rate should be considered in accurate models of systems reliability however, it is very difficult to represent the repair activity in an analytical way. There are many factors that affect the rate at which repair occurs involving human skill, required transport time, diagnostic capability and the components’ or parts availability. Despite the lack of in-depth theoretical knowledge, the probabilistic models make assumptions about the repair rate in a similar way to that of the failure rate. In order to solve a reliability model, which contains both failure and repair rates, the use of a Reliability Block Diagram (RBD) and Fault Tree Analysis (FTA) or Markovian model are required. These models usually assume that the repair of a failed system restores the system in a way that the system’s failure rate remains the same as if nothing had happened. In order to analyse a system using the FTA, it is necessary to build a RBD. The FTA represents the effect of a component’s failure to the systems overall performance. A Markov process is a stochastic process that the dynamics are in such a way that the probability distribution for its future development depends only on the current state rather than how the process has reached this state [7].
∫
∑
RELIABILITY THEORY
(3)
Any combination of the number of PV panels (A) versus the number of batteries (B) for any desired LOLP are not a realistic reliability approach as none mechanical system works without failure during its lifetime. This paper investigates a more realistic approach taking into consideration the probability of each component or sub-system to fail during the system’s operation using reliability models. Thus, to predict the cost over 30 years of operation.
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Moreover, in order to estimate the mean O&M cost of the system, the Poisson distribution can be used. This distribution describes the number of events/failures that will take place between a time interval (0, t). The number of these events follows the Poisson distribution as: ( ) ( ) (5) where k=0, 1, 2,..., μ=λΤΝ and λ is the parameter that indicates the average number of events/failures (failure rate), which is always independent from the last event.
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Figure 1: Standalone PV system configuration.
METHODOLOGY
The reliability assessment was based on methodology where the application was regarded as a complex system composed of components logically and operationally linked. Each component may fail in one or more ways (failure modes) which determine the impact of the failure on the general operation of the system. The failure rate of each component in most cases is known from other applications (systems with statistical data) therefore, by using the data from literature and the reliability models, the stochastic behaviour of the model (e.g. mean time between failures) under the System Reliability Theory has been predicted. A logical model was then developed which simulated the operation of the system using hourly meteorological data for a remote household for a period of one year. For the estimation of the model’s parameters, specifications from random PV and battery manufacturers were selected as well as a hypothetical hourly electrical load profile for a residential house. The methodology applied for the stochastic sizing and O&M cost estimation was divided in the following steps: 1) Solar radiation data from the investigated site. 2) Load demand where all the household appliances are summed in an hourly basis profile. 3) PV and battery specification data. 4) First simulation where the system is simulated for the period of a year in order to calculate the number of panels (A) and batteries (B) which are needed for a corresponding LOLP. 5) Integration of FTA, Markov modelling using failure data from [8-10]. 6) Second simulation which quantifies the realistic LOLP for the A and B which were found in step 4. 7) O&M cost estimation using Poisson distribution.
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Figure 2: Load curve of the remote area household near Athens, Greece. The system was then analysed by the reliability models to see which one is more appropriate for this case.
Figure 3: Reliability Block Diagram of standalone PV system.
CASE OF STUDY
A residential standalone photovoltaic system which is situated in a remote area near Athens is evaluated in the present work. A random electricity load demand was chosen based on the average households energy consumption in Greece. Figure 1 shows the system’s configuration while in figure 2 the selected hourly profile of the residence is illustrated over four different days of the year. From figure 2, it is apparent that the spring and autumn load curves are very similar. The household energy load demand for the whole year was found to be 3700kWh with a maximum peak power of 3.1kW per hour.
Figure 4: Fault Tree Analysis of standalone PV system. From the FTA in figure 4 it can be seen that the components must fail in different combinations in order to cause failure to the system. A battery bank (No. 4) “OR” a charge controller (No. 3) failure “AND” simultaneously, a PV generator (No.1) “OR” a control unit (No.2) failure, will cause the system to go OFF. These four components are connected to the logic gates as shown in figure 4. Moreover, a failure of the inverter (No.5) “OR” the combination with the above mentioned
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types of failure, will also cause the system to go OFF/DOWN. These two failure modes are united with the top gate "OR" as shown in the figure. However, either the RBD (Figure 3) method or the FTA are applicable to systems that are characterised by two states and are consisted by components which also have only two states (UP or DOWN). A PV system is characterised by many states. For this reason and for the present case of study, the Markov models were preferred. 5
3 and for the charge controller 3.75. Therefore the mean O&M cost in this case is, as shown in table II. Thus, the total mean O&M cost for the duration of 30 years of operation was estimated to be €42,520. However, it should be noted that the cost estimation is approximate and does not include labour costs over the 30 years. The currency fluctuations should be considered as well, in order to achieve a more accurate estimation of the O&M cost.
RESULTS AND DISCUSSION 6
The desired LOLP was assumed to be 2%. The first simulation showed that the combination of 26 PV panels and 16 batteries can satisfy the desired LOLP with the most economic, in terms of cost and unsatisfied load demand, way. However, after running the simulation integrated with the Markovian models, the LOLP was increased as expected to 2.5%. This increment was due of course to the components’ failure and repair rates that were included in the model. The failure rates for each component were found in literature [8-10] to be λm=0.04year-1 for the PV panel, λCC=0.125year-1 for the charge controller, λbat=0.1year-1 for the battery, λinv=0.1year-1 for the inverter and λcontr=0.1year-1 for the control unit. Also, the repair rate (μ) was assumed to be 0.137day-1 which is equal to approximately one week. As mentioned in section 2, in order to calculate the number of failures of a component which the failure rate is already known, the Poisson distribution can be used. The mean O&M cost of the standalone PV system depends on the number of failures of each component separately throughout the system’s lifetime. In each case of any component’s failure, it was assumed that the faulty component was replaced with a new one while the system’s lifetime was considered to be for 30 years. According to the PV market prices of August 2011 (when the work was done), the price per PV panel from a random Greek PV company was €339, for each battery €228, for the inverter €1190 and the charge controller €260. The full installation cost can be seen in table I. Table I: PV system installation cost. Component 26xPV Panels 185Wp (Solar Energy Power Plus) 16xBatteries (Effekta) Inverter (Cotek) Charge Controller (Phocos) Wiring Support Labour TOTAL
CONCLUSIONS AND FUTURE WORK
The simulation of the stochastic behaviour of the PV system’s components with respect to the advent of failures and their repair, allows a more realistic assessment of the potential loss of load probability (LOLP) and the load that is finally satisfied. Therefore, the Markov method, allows a more realistic total O&M cost estimation and sizing of the system. Other reliability models such as Reliability Block Diagrams (RBDs) and Fault Tree Analysis (FTAs) were investigated. It is concluded that these models cannot be applied in a PV system because the components that consist such a system have more than two states. These results may lead in future to an accurate quantification through the data collection by observing the behaviour of many systems in real operating conditions or by conducting accelerated tests (HALT) in indoor laboratory facilities. The models presented can be easily applied to other types of PV systems, grid-connected or hybrid.
ACKNOWLEDGEMENTS The authors acknowledge the “Solar and Other Energy Systems Laboratory” of N.C.S.R. “Demokritos” and especially Dr. Vasilis Belesiotis for providing the meteorological data used in this study. Also, the authors wish to thank Dr. Olga Aneziris for her valuable comments.
Price (€) 8814
REFERENCES [1] E. Lorenzo and L. Narvarte, On the usefulness of stand-alone PV sizing methods. Progress in Photovoltaics, 2000. 8(4): p. 391-409. [2] P. Tsalides and A. Thanailakis, Loss-of-Load Probability and Related Parameters in Optimum Computer-Aided-Design of Stand-Alone Photovoltaic Systems. Solar Cells, 1986. 18(2): p. 115-127. [3] M. Egido and E. Lorenzo, The Sizing of Stand Alone Pv-Systems - a Review and a Proposed New Method. Solar Energy Materials and Solar Cells, 1992. 26(12): p. 51-69. [4] C. Soras and V. Makios, A Novel Method for Determining the Optimum Size of Stand-Alone Photovoltaic Systems. Solar Cells, 1988. 25(2): p. 127-142. [5] A. Garro and F. Barrara. Reliability Analysis of Residential Photovoltaic Systems. In International Conference on Renewable Energies and Power Quality (ICREPQ'11). 2011. Las Palmas de Gran Canaria (Spain).
3648 1190 260 160 1482 900 16,454
Table II: Mean O&M cost over 30 years of operation. Component Price (€) PV Panels 10,577 Batteries 10,944 Inverter 3570 Charge Controller 975 TOTAL 26,066 By applying the Poisson distribution, it was found that the mean number of PV failures during 30 years of operation would be 31.2, for the batteries 48, the inverter
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[6] M. Modarres, M. Kaminskiy and V. Krivtsov, Reliability Engineering and Risk Analysis: A Practical Guide. Second Edition ed2010: CRC Press. [7] K.S. Trivedi, Probability and Statistics with Reliability, Queuing and Computer Science Applications2002: John Wiley and Sons Ltd. [8] W.M. Rohouma, I.M. Molokhia and A.H. Esuri, Comparative study of different PV modules configuration reliability. Desalination, 2007. 209(13): p. 122-128. [9] M.A. Eltawil and Z.M. Zhao, Grid-connected photovoltaic power systems: Technical and potential problems-A review. Renewable & Sustainable Energy Reviews, 2010. 14(1): p. 112-129. [10] R.H. Bonn, Developing a "next generation" PV inverter. Conference Record of the Twenty-Ninth IEEE Photovoltaic Specialists Conference 2002, 2002: p. 1352-1355.
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