A simple model for sizing stand alone photovoltaic systems

We consider a general model for sizing a stand-alone photovoltaic system, using as energy input data the information available in any radiation atlas. The parameters of the model are estimated by multivariate linear regression. The results obtained from a numerical sizing method were used as initial input data to fit the model. The expression proposed allows us to determine the photovoltaic array size, with a coefficient of determination ranging from 0.94 to 0.98. System parameters and mean monthly values for daily global radiation on the solar modules surface are taken as independent variables in the model. It is also shown that the proposed model can be used with the same accuracy for other locations not considered in the estimation of the model.     

A general multivariate qualitative model for sizing stand-alone photovoltaic systems

We considered a general model for sizing a stand-alone photovoltatic system, using as energy input data the information available in any irradiation atlas. The parameters of the model are estimated by multivariate linear regression. The results obtained from the numerical loss of load probability size method (LOLP) were used as initial input data to fit the mode. For this fit we have used daily global irradiation data taken from 222 US meteorological stations for the period 1961–1990. The expression proposed allows us to determine the photovoltatic array size, with a coefficient of determination to 0.96. This coefficient is independent of the used LOLP value. System parameters and mean monthly values for daily global irradiation on the modules surface are taken as independent variables in the model. It also shows that the proposed model can be used with the same accuracy for other locations not considered in the estimation of the model. We also propose a model which would allow us to calculate optimum tilts for the array surface taking the latitude into account as well as the variability of the incident irradiation.     

Systematic procedures for sizing photovoltaic pumping system,using water tank storage

In this work, the performances of the photovoltaic pumping destined to supply drinking water in remote and scattered small villages have been studied. The methodology adopted proposes various procedures based on the water consumption profiles, total head, tank capacity and photovoltaic array peak power. A method of the load losses probability (LLP) has been used to optimize sizing of the photovoltaic pumping systems with a similarity between the storage energy in batteries and water in tanks. The results were carried out using measured meteorological data for four localities in Algeria: Algiers and Oran in the north, Bechar and Tamanrasset in the south. The results show that the performance of the photovoltaic pumping system depends deeply on the pumping total head and the peak power of the photovoltaic array. Also, for the southern localities, the LLP method shows that the size of the photovoltaic array varies versus LLP on a small scale. On the other hand, for the northern localities, the sizing of the photovoltaic array is situated on a large scale power. Because of the current high crud-oil price, the photovoltaic pumping still to be the best adopted energy resource to supply drinking water in remote and scattered villages.     

Loss-of-load probability of photovoltaic water pumping systems

This paper presents a method for estimating the loss-of-load probability (LLP) of a photovoltaic water pumping system. The study has been carried out for a constant profile, using a tank with a two day autonomy capacity and two pumping heads applied to a centrifugal pump. The method developed in this paper gives a simple tool for LLP calculation. The procedure can also be used to draw LLP maps with normalised parameters using long term observed or generated sequences of meteorological data. This technique gives a generalised and practical graphical tool for systems sizing. Some examples from Algeria are used. But the method can be applied to any geographical area.     

Optimal sizing of photovoltaic pumping system with water tank storage using LPSP concept

This paper recommends an optimal sizing model, to optimize the capacity sizes of different components of photovoltaic water pumping system (PWPS) using water tank storage. The recommended model takes into account the submodels of the pumping system and uses two optimization criteria, the loss of power supply probability (LPSP) concept for the reliability and the life cycle cost (LCC) for the economic evaluation.With this presented model, the sizing optimization of photovoltaic pumping system can be achieved technically and economically according to the system reliability requirements. The methodology adopted proposes various procedures based on the water consumption profiles, total head, tank capacity and photovoltaic array peak power. A case study is conducted to analyze one photovoltaic pumping project, which is designed to supply drinking water in remote and scattered small villages situated in Ghardaia, Algeria (32°29′N, 3°40′E, 450 m).     

Economic viability of photovoltaic water pumping systems

A comparison of the economic viability of photovoltaic and diesel water pumping systems is presented for system sizes in the range 2.8 kW_p to 15 kW_p. Actual performance data from installed systems are employed for the base case. Sensitivity analysis is carried out to generalize results for other locations and conditions. The effect of system oversizing due to mismatch of water supply and demand patterns on the economic viability of PV water pumping system is illustrated based on real data and three-year operational experience of eight installations. Investment prospects in PV water pumping applications for different selling price scenarios of water have been investigated.     

A new approach for sizing stand alone photovoltaic systems based in neural networks

Several methods for sizing stand alone photovoltaic (pv) systems has been developed. The more simplistic are called intuitive methods. They are a useful tool for a first approach in sizing stand alone photovoltaic systems. Nevertheless they are very inaccurate. Analytical methods use equations to describe the pv system size as a function of reliability. These ones are more accurate than the previous ones but they are also not accurate enough for sizing of high reliability. In a third group there are methods which use system simulations. These ones are called numerical methods.Many of the analytical methods employ the concept of reliability of the system or the complementary term: loss of load probability (LOLP). In this paper an improvement for obtaining LOLP curves based on the neural network called Multilayer Perceptron (MLP) is presented. A unique MLP for many locations of Spain has been trained and after the training, the MLP is able to generate LOLP curves for any value and location.     

Optimal sizing of array and inverter for grid-connected photovoltaic systems

Optimum PV/inverter sizing ratios for grid-connected PV systems in selected European locations were determined in terms of total system output, system output per specific cost of a system, system output per annualised specific cost of a system, PV surface orientation, inclination, tracking system, inverter characteristics, insolation and PV/inverter cost ratio. Maximum total system output was determined for horizontal, vertical and 45° inclined surfaces for a low efficiency inverter for sizing ratios of 1.5, 1.8 and 1.3, respectively; and for a medium efficiency inverter with sizing ratios of 1.4, 1.5 and 1.2. PV surface orientation and inclination have little impact on the performance of a high efficiency inverter. For different PV tracking systems and for different inverter characteristics, the optimum sizing ratio varied from 1.1 to 1.3. The PV/inverter cost ratio and the PV and inverter lifetimes have significant impact on the optimum PV/inverter sizing ratio. A correlation relating optimum sizing ratio and PV/inverter cost ratio has been developed; the correlation coefficients were found to be functions of insolation and inverter type. The impact of PV/inverter sizing ratio on PV array performance was less when PV array has a much higher cost than the inverter. The optimum sizing ratio for PV/inverter cost ratio of 6 and low efficiency inverter system varied from 1.4 to 1.2 for low to high insolation sites. For a high efficiency inverter system, the corresponding variation was from 1.3 to 1.1.     

Inverter sizing of grid-connected photovoltaic systems in the light of local solar resource distribution characteristics and temperature

Inverter sizing strategies for grid-connected photovoltaic (PV) systems often do not take into account site-dependent peculiarities of ambient temperature, inverter operating temperature and solar irradiation distribution characteristics. The operating temperature affects PV modules and inverters in different ways and PV systems will hardly ever have a DC output equal to or above their STC-rated nominal power. Inverters are usually sized with a nominal AC output power some 30% (sometimes even more) below the PV array nominal power. In this paper, we show that this practice might lead to considerable energy losses, especially in the case of PV technologies with high temperature coefficients of power operating at sites with cold climates and of PV technologies with low temperature coefficients of power operating at sites with warm climates and an energy distribution of sunlight shifted to higher irradiation levels. In energy markets where PV kW h’s are paid premium tariffs, like in Germany, energy yield optimization might result in a favorable payback of the extra capital invested in a larger inverter.This paper discusses how the time resolution of solar radiation data influences the correct sizing of PV plants.We demonstrate that using instant (10 s) irradiation values instead of average hourly irradiation values leads to considerable differences in optimum inverter sizing. When calculating inverter yearly efficiency values using both, hourly averages and 1-min averages, we can show that with increased time resolution of solar irradiation data there are higher calculated losses due to inverter undersizing. This reveals that hourly averages hide important irradiation peaks that need to be considered.We performed these calculations for data sets from pyranometer readings from Freiburg (48°N, Germany) and Florianopolis (27°S, Brazil) to further show the peculiarities of the site-dependent distribution of irradiation levels and its effects on inverter sizing.     

A fuzzy global efficiency optimization of a photovoltaic water pumping system

This paper presents an on-line fuzzy optimization of the global efficiency of a photovoltaic water pumping system driven by a separately excited DC motor (DCM), a permanent magnet synchronous motor (PMSM), or an induction motor (IM), coupled to a centrifugal pump.The fuzzy optimization procedure stated above, which aims to the maximization of the global efficiency, will lead consequently to maximize the drive speed and the water discharge rate of the coupled centrifugal pump. The proposed solution is based on a judicious fuzzy adjustment of a chopper ratio which adapts on-line the load impedance to the photovoltaic generator (PVG). Simulation results show the effectiveness of the drive system for both transient and steady state operations. Hence it is suitable to use this fuzzy logic procedure as a standard optimization algorithm for such photovoltaic water pumping drives.     

Methodology for optimal sizing of stand-alone photovoltaic/wind-generator systems using genetic algorithms

A methodology for optimal sizing of stand-alone PV/WG systems is presented. The purpose of the proposed methodology is to suggest, among a list of commercially available system devices, the optimal number and type of units ensuring that the 20-year round total system cost is minimized subject to the constraint that the load energy requirements are completely covered, resulting in zero load rejection. The 20-year round total system cost is equal to the sum of the respective components capital and maintenance costs. The cost (objective) function minimization is implemented using genetic algorithms, which, compared to conventional optimization methods such as dynamic programming and gradient techniques, have the ability to attain the global optimum with relative computational simplicity. The proposed method has been applied for the design of a power generation system which supplies a residential household. The simulation results verify that hybrid PV/WG systems feature lower system cost compared to the cases where either exclusively WG or exclusively PV sources are used.     

Optimization of a photovoltaic pumping system based on the optimal control theory

This paper suggests how an optimal operation of a photovoltaic pumping system based on an induction motor driving a centrifugal pump can be realized. The optimization problem consists in maximizing the daily pumped water quantity via the optimization of the motor efficiency for every operation point. The proposed structure allows at the same time the minimization the machine losses, the field oriented control and the maximum power tracking of the photovoltaic array. This will be attained based on multi-input and multi-output optimal regulator theory. The effectiveness of the proposed algorithm is described by simulation and the obtained results are compared to those of a system working with a constant air gap flux.     

Comparative study of artificial intelligence techniques for sizing of a hydrogen-based stand-alone photovoltaic/wind hybrid system

As non-polluting reliable energy sources, stand-alone photovoltaic/wind/fuel cell (PV/wind/FC) hybrid systems are being studied from various aspects in recent years. In such systems, optimum sizing is the main issue for having a cost-effective system. This paper evaluates the performance of different artificial intelligence (AI) techniques for optimum sizing of a PV/wind/FC hybrid system to continuously satisfy the load demand with the minimal total annual cost. For this aim, the sizing problem is formulated and four well-known heuristic algorithms, namely, particle swarm optimization (PSO), tabu search (TS), simulated annealing (SA), and harmony search (HS), are applied to the system and the results are compared in terms of the total annual cost. It can be seen that not only average results produced by PSO are more promising than those of the other algorithms but also PSO has the most robustness. As another investigation, the sizing is also performed for a PV/wind/battery hybrid system and the results are compared with those of the PV/wind/FC system.     

Renewable energy technologies for irrigation water pumping in India: A preliminary attempt towards potential estimation

Simple frameworks have been developed for estimating the utilization potential of: (a) solar photovoltaic (SPV) pumps; (b) windmill pumps; (c) producer gas based dual fuel engine pumps; and (d) biogas based dual fuel engine pumps for irrigation water pumping in India. The approach takes into account factors such as: solar radiation intensity, wind speed, availability of bovine dung and agri-residues, and their alternative uses, ground water requirements for irrigation and its availability, affordability, and propensity of the users to invest in renewable energy devices, etc. SPV pumps are estimated to have the maximum utilization potential in India, followed by windmill pumps.     

A model for optimal sizing of solar thermal hydroelectric power plant

This paper presents the model for optimal sizing of a Solar Thermal (ST) power plant with parabolic collectors, which operates with Pump Storage Hydroelectric (PSH), all for the purpose of providing full energy independence of an isolated consumer. The sustainability of such system is based exclusively on solar energy input (without hybridization with any fossil fuel), as a renewable and pure energy resource, and the use of hydro energy, due to the possibility of its continuous production of energy. The feasibility and characteristics of the ST-PSH power plant were tested on power supply of the Island of Vis in Croatia, and the results show that the proposed model describes the operation of the power plant very well. For average solar irradiation of about 1500 kW h/m²/a, precipitation 644 mm/a, evaporation 1444 mm/a, volume of PSH upper reservoir of 20 h m³, electric energy consumption of 18 GV A h/a and reserve in the system for 3-4 months, the obtained power of the ST power plant is 22 MW, which can produce unit value of the annual thermal energy of 459 kW h/m²/a and electric energy of 160 kW h/m²/a, while the total collector aperture in the observed case is about 16 ha. These results show that ST-PSH plants can be successfully applied on locations with relatively low irradiation, wherein the key element that ensures continuous production of energy is precisely the PSH technology that can in the best way, in economic-technical, and especially in ecological sense, balance the relatively large summer surpluses and winter energy shortages.     

Financial evaluation of renewable energy technologies for irrigation water pumping in India

An attempt to develop a simple framework for financial evaluation of renewable energy technologies (RETs) such as photovoltaic (PV) pump, windmill pump, biogas and producer gas-driven dual fuel engine pumps for irrigation water pumping has been made. The unit cost of water and unit cost of useful energy delivered by the RETs have been estimated. The monetary benefits that accrued to the end-user have been quantified in terms of the amount of diesel or electricity saved. Financial figures of merit for the investments made in the RETs have been estimated. The effect of fuel price escalation on these measures of financial performance has also been evaluated along with the estimation of the break-even prices of fuels likely to be substituted by RETs. Results of some exemplifying calculations are presented and briefly discussed.     

Approaches for developing a sizing method for stand-alone PV systems with variable demand

Accurate sizing is one of the most important aspects to take into consideration when designing a stand-alone photovoltaic system (SAPV). Various methods, which differ in terms of their simplicity or reliability, have been developed for this purpose. Analytical methods, which seek functional relationships between variables of interest to the sizing problem, are one of these approaches.A series of rational considerations are presented in this paper with the aim of shedding light upon the basic principles and results of various sizing methods proposed by different authors. These considerations set the basis for a new analytical method that has been designed for systems with variable monthly energy demands.Following previous approaches, the method proposed is based on the concept of loss of load probability (LLP)—a parameter that is used to characterize system design. The method includes information on the standard deviation of loss of load probability (σ_LLP) and on two new parameters: annual number of system failures (f) and standard deviation of annual number of failures (σ_f).The method proves useful for sizing a PV system in a reliable manner and serves to explain the discrepancies found in the research on systems with LLP<10⁻². We demonstrate that reliability depends not only on the sizing variables and on the distribution function of solar radiation, but on the minimum value as well, which in a given location and with a monthly average clearness index, achieves total solar radiation on the receiver surface.     

Improvement of photovoltaic pumping systems based on standard frequency converters by means of programmable logic controllers

Photovoltaic pumping systems (PVPS) based on standard frequency converters (SFCs) are currently experiencing a growing interest in pumping programmes implemented in remote areas because of their high performance in terms of component reliability, low cost, high power range and good availability of components virtually anywhere in the world. However, in practical applications there have appeared a number of problems related to the adaptation of the SFCs to the requirements of the photovoltaic pumping systems (PVPS). Another disadvantage of dedicated PVPS is the difficulty in implementing maximum power point tracking (MPPT). This paper shows that these problems can be solved through the addition of a basic industrial programmable logic controller (PLC) to the system. This PLC does not increase the cost and complexity of the system, but improves the adaptation of the SFC to the photovoltaic pumping system, and increases the overall performance of the system.     

A novel optimization method for designing stand alone photovoltaic system

This paper presents a novel optimization method for sizing and design of stand alone photovoltaic systems. Loss of power supply probability analysis is set as a benchmark to determine all possible PV array and battery capacity. Then, the optimum design is proposed based on the lowest levelized cost of energy. The case study, with reference to Malaysia's meteorological data and typical load profile of rural area, has been simulated and compared to selected three past researches.     

A stochastic method for stand-alone photovoltaic system sizing

Photovoltaic systems utilize solar energy to generate electrical energy to meet load demands. Optimal sizing of these systems includes the characterization of solar radiation. Solar radiation at the Earth’s surface has random characteristics and has been the focus of various academic studies. The objective of this study was to stochastically analyze parameters involved in the sizing of photovoltaic generators and develop a methodology for sizing of stand-alone photovoltaic systems. Energy storage for isolated systems and solar radiation were analyzed stochastically due to their random behavior. For the development of the methodology proposed stochastic analysis were studied including the Markov chain and beta probability density function. The obtained results were compared with those for sizing of stand-alone using from the Sandia method (deterministic), in which the stochastic model presented more reliable values. Both models present advantages and disadvantages, however, the stochastic one is more complex and provides more reliable and realistic results.